L. Engelhardt, M. Burger, G. Bitsch

Real-time simulation of multibody- systems for on-board applications

Berichte des Fraunhofer ITWM, Nr. 193 (2010)

© Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM 2010

ISSN 1434-9973

Bericht 193 (2010)

Alle Rechte vorbehalten. Ohne ausdrückliche schriftliche Genehmigung des Herausgebers ist es nicht gestattet, das Buch oder Teile daraus in irgendeiner Form durch Fotokopie, Mikrofilm oder andere Verfahren zu reproduzieren oder in eine für Maschinen, insbesondere Datenverarbei tungsanlagen, ver-wendbare Sprache zu übertragen. Dasselbe gilt für das Recht der öffentlichen Wiedergabe.

Warennamen werden ohne Gewährleistung der freien Verwendbarkeit benutzt.

Die Veröffentlichungen in der Berichtsreihe des Fraunhofer ITWM können bezogen werden über:

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM Fraunhofer-Platz 1

67663 Kaiserslautern Germany

Telefon: +49 (0) 6 31/3 16 00-0 Telefax: +49 (0) 6 31/3 16 00-10 99 E-Mail: info@itwm.fraunhofer.de Internet: www.itwm.fraunhofer.de

Vorwort

Das Tätigkeitsfeld des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik ITWM umfasst anwendungsnahe Grundlagenforschung, angewandte Forschung sowie Beratung und kundenspezifische Lösungen auf allen Gebieten, die für Tech-no- und Wirtschaftsmathematik bedeutsam sind.

In der Reihe »Berichte des Fraunhofer ITWM« soll die Arbeit des Instituts kontinu-ierlich einer interessierten Öffentlichkeit in Industrie, Wirtschaft und Wissenschaft vorgestellt werden. Durch die enge Verzahnung mit dem Fachbereich Mathema-tik der Universität Kaiserslautern sowie durch zahlreiche Kooperationen mit inter-nationalen Institutionen und Hochschulen in den Bereichen Ausbildung und For-schung ist ein großes Potenzial für Forschungsberichte vorhanden. In die Bericht-reihe werden sowohl hervorragende Diplom- und Projektarbeiten und Disserta-tionen als auch Forschungsberichte der Institutsmitarbeiter und Institutsgäste zu aktuellen Fragen der Techno- und Wirtschaftsmathematik aufgenommen.

Darüber hinaus bietet die Reihe ein Forum für die Berichterstattung über die zahl-reichen Kooperationsprojekte des Instituts mit Partnern aus Industrie und Wirt-schaft.

Berichterstattung heißt hier Dokumentation des Transfers aktueller Ergebnisse aus mathematischer Forschungs- und Entwicklungsarbeit in industrielle Anwendungen und Softwareprodukte – und umgekehrt, denn Probleme der Praxis generieren neue interessante mathematische Fragestellungen.

Prof. Dr. Dieter Prätzel-Wolters Institutsleiter

Kaiserslautern, im Juni 2001

The 1st Joint International Conference on Multibody System DynamicsMay 25–27, 2010, Lappeenranta, Finland

Real-Time Simulation of Multibody-Systems for On-Board Applications

Lilli Engelhardt∗, Michael Burger∗, Gerd Bitsch∗

∗Department Mathematical Methods for Dynamics and DurabilityFraunhofer ITWM

Fraunhofer-Platz 1, 67663 Kaiserslautern, Germanye-mail: Lilli.Engelhardt@itwm.fraunhofer.de, Michael.Burger@itwm.fraunhofer.de,

Gerd.Bitsch@itwm.fraunhofer.de

ABSTRACT

Simulation of multibody systems (mbs) is an inherent part indeveloping and design of complex mechanicalsystems. Moreover, simulation during operation gained in importance in the recent years, e.g. for HIL-,MIL- or monitoring applications. In this paper we discuss the numerical simulation of multibody systemson different platforms. The main section of this paper dealswith the simulation of an established truckmodel [9] on different platforms, one microcontroller and two real-time processor boards. Additional tonumerical C-code the latter platforms provide the possibility to build the model with a commercial mbstool, which is also investigated. A survey of different waysof generating code and equations of mbs modelsis given and discussed concerning handling, possible limitations as well as performance.

The presented benchmarks are processed under terms of on-board real time applications. A further im-portant restriction, caused by the real-time requirement,is a fixed integration step size. Whence, carefullychosen numerical integration algorithms are necessary, especially in the case of closed loops in the model.We investigate linearly-implicit time integration methods with fixed step size, so-called Rosenbrock meth-ods, and compare them with respect to their accuracy and performance on the tested processors.

The paper gives an overview of significant characteristics to regard, like model type (DAE, ODE), choiceof solver and attended time for simulation, when pursuing the intention of a mbs simulation on an on-boardplatform.

Keywords: multibody system simulation, real-time simulation, on-board simulation, Rosenbrock meth-ods

1 INTRODUCTION

The real-time simulation demand implicates limitations regarding step size, simulation time and thereforemodel complexity, choice of integration method and simulation platform. For most applications these de-pendencies are neither linear nor straightforward.

The result of one integration step is required in ana priori defined time interval to guarantee real-time,which claims for fixed integration step sizes [8, 13]. A further limitation regarding the choice of solveris given by the fact, that on-board platforms generally havea comparable weak performance and lowermemory capacity than standard pcs.

For many practical applications the system is too stiff for efficient integration methods like the explicitEuler method, which often is favored for real-time applications. Then it is more suitable to consider them asconstraint systems, which are described with so-called differential algebraic equations (DAE), and integratethem with adequate solver techniques. In this paper both approaches are pursued, integrating DAEs andODEs (ordinary differential equations) with stable solvertechniques with fixed step size (sect.3).

Due to the fact that modelling as C-code is impractical for many industrial projects and to guarantee theapplication to more complex system like 3D models e.g., we additionally pursue the way of modelling mbsmodels with commercial software tools, exemplarily with SIMPACK [3] and SimMechanics [4] (4.2.2and4.2.3), and simulate them on on-board platforms.

(a) ODE (b) DAE

Figure 1. Truck model [9]

2 BENCHMARK TRUCK MODEL

A mbs model of a planar truck with9 degrees of freedom, [9], is implemented for benchmarking purposes.The truck is excited by a vertical road profile. Between wheels and chassis are pneumatic springs, i.e., themodel includes non-linear spring-characteristics.

The truck model was built in two versions: an unconstrained and a constrained one. In the former, the traileris mounted to the chassis by three springs, two of them are replaced by a constraint for the second version,cf. Fig. 1.

The equations of motion of the unconstrained truck model aregiven as a nonlinear system of ordinarydifferential equations (ODE)

q̇ = v

Mv̇ = f(t, q, v, u),(1)

whereq, v ∈ R9 denote the positions and velocities respectively, andu ∈ R denotes the excitation vector,the vertical road profile in this case. The dot above a symbol denotes the derivative with respect to timet.f represents the vector of applied forces and the mass and inertia matrixM of the truck model is constantand diagonal.

The considered constrained truck model (in redundant coordinates) leads to a system of differential algebraicequations:

q̇ = v

Mv̇ = f(t, q, v, u) − G(q)T λ

0 = g(q),

(2)

where the last algebraic equation describes the constrainton position level. The additional constraint-forces,G(p)T λ with G(p) := ∂g

∂p, ensure, that the constraint is satisfied. In the present model g is a function

g : R9 → R2 and consequentlyG(p) ∈ R2×9 andλ ∈ R2. In [9] eqns. (1) and (2) are given more detailed.

3 INTEGRATION METHODS

In this section the integration schemes, which are used for the presented benchmarking analysis, are brieflysketched.

3.1 ODE Time Integration

An essential real-time requirement is, that the equations of motion are solved fast enough and in an a prioridefined fixed time. This may lead to explicit integration schemes with a fixed step size. Indeed, in many

application the simple one-step explicit Euler-scheme is used. However, many elements of a typical mbs,such as springs, bushings can lead to very stiff ODEs. But forthose types of equation explicit integrationschemes are not suitable, since they would require too smallstep sizes or completely fail. On the otherhand, implicit methods that do not need such small step sizesare based on nonlinear equations and theirnumerical solution in an a priori defined time cannot be guaranteed. Therefore, they do not fit the real-timerequirement either. A compromise, which avoids both the small step sizes and the nonlinear equations, areso-called Rosenbrock methods. They can be interpreted as anapplication of one Newton-iteration to thenonlinear equations that arise in an implicit Runge-Kutta scheme, see [11] for a detailed derivation of thesemethods. Adapted to the special structure of the equations of motion of a mbs, a generals-stage Rosenbrockmethod with fixed step sizeh applied to the ODE (1) is given by the formulas:

( (1 00 M

)

− h · γ · Jn

) [

(kq)i(kv)i

]

=

[

Vif(Ti, Qi, Vi, u(Ti))

]

+ h · Jn

i−1∑

j=1

γij

[

(kq)i(kv)i

]

+ h2 ·

i−1∑

j=1

γij

[

0∂f∂u

∂u∂t

+ ∂f∂t

]

, i = 1, .., s

Qi = qn + h ·

i−1∑

j=1

αij(kq)j , Vi = vn + h ·

i−1∑

j=1

αij(kv)j , Ti = tn + h ·

i−1∑

j=1

αij ,

qn+1 = qn + h ·

s∑

i=1

bi · (kq)i,

vn+1 = vn + h ·

s∑

i=1

bi · (kv)i.

(3)The Jacobian matrixJn has the structure

Jn :=

(

0 1∂f∂q

∂f∂v

)∣

∣

∣

∣

(qn,vn,u(tn))

(4)

The method is uniquely determined by the coefficients((αij), (γij), (bi), γ). The crucial feature of thesemethods is, that for each stage only a linear equation has to be solved and this can be achieved within an apriori known time. Nevertheless, with suitable chosen coefficients, the methods provide stability propertiesas they are typical from fully implicit schemes, cf. [11, 5].

For our benchmarking purposes we apply two methods of this class to the ODE (1): the first one is thelinearly-implicit Euler-method. This is a 1-stage method and its coefficients are given by:

γ = 1, b1 = 1. (5)

The method is of orderp = 1 andA − stable.

The second method, we consider, is based on the4− stage GRK4T -algorithm by Kaps and Rentrop [12],which has proven to be a good choice for stiff MBS. It is of order p = 4 and isA(89.3◦) − stable.

3.2 DAE Time Integration

For the DAE-case, eq. (2), we restrict ourselves to the linearly-implicit Euler-method.

The DAE as it is given in eq. (2) with the constraint equation on position level is a DAE of index 3, whosenumerical solution under real-time conditions is merely not to realize. Therefore, it is a commonly usedapproach to reduce the index at most by one by replacing the constraint equation by its first time-derivative,

0 =d

dtg(q) =

∂g

∂q(q)q̇ = G(q)v, (6)

the constraint on velocity level, yielding an index-2-DAE.However, this procedure brings up the well-known drift-off effect in the constraint, i.e., a violationof the constraint equation, [11]. This effect is of

course more severe when using a low-order integration method such as the linearly-implicit Euler-method.To overcome this drawback two stabilization techniques areapplied and compared.

We make one modification in the integration formulas: calculating the position coordinates explicitly bysetting

kq = vn ⇒ qn+1 = qn + hvn. (7)

Taking into account, that the constraint on velocity level has to be fulfilled in the new integration step, i.e.,

0 = G(qn+1)vn+1, (8)

the linearly-implicit Euler-scheme for the DAE-case is given by

qn+1 = qn + hvn,(

M − h∂f∂q

− h2 ∂f∂v

G(qn)T

G(qn+1) 0

) [

kvλ

]

=

[

f(qn, vn, u(tn)) + h∂f∂q

vn−(1/h)G(qn+1)vn

]

,

vn+1 = vn + hkv.

(9)

The first stabilization technique to avoid the drift-off effect is based on the Baumgarte-approach [6]: replac-ing the constraint on velocity level by a linear combinationof the constraints on velocity and position level,i.e.,

0 = G(qn+1)vn+1 + αg(qn+1), (10)

with α ≈ 1/h. The right-hand-side of eq. (9) has to be modified correspondingly.

The second stabilization technique can be interpreted as anapplication of the Gear-Gupta-Leimkuhler-formulation (GGL) [10]. In that approach the new position coordinate,qn+1, is obtained by the solution ofthe equation

Mqn+1 − qn

h= Mvn − G

T (qn)η

0 = g(qn+1),(11)

with additional multipliersη. The numerical solution has to be calculated by an iterativealgorithm. Toguarantee real-time capability, the number of iterations must be fixed. For most calculations, one iterationstep is sufficient. With the solutionqn+1 the new velocities,vn+1, are obtained by the solution of the linearsystem in (9) as before.

For a more detailed analysis of higher order integration methods and non-iterative stabilization-techniquesfor real-time purposes we refer to [5], see [7] for considerations concerning matters of stability.

3.3 Implementation

All tested integration methods have been handcoded in C. These solver routines have been incorporated intothe platform dependent, generated code for the equations ofmotion of the truck model, which has requiredsome involved modifications both on the solver side as well ason the MBS side, see sect.4 for details.

For the Jacobian matrixJn we have used a partitioned approximation:∂f∂q

(q0, v0, u(t0)) has been computed

once before integration in a preprocessing step, whereas∂f∂v

as well as∂f∂u

and ∂f∂q

kq are calculated at eachintegration step by forward differences and the last one as directional derivative to reduce computation time.

To solve eq. (11) for the GGL-stabilization we have applied only one iteration step of a simple Newton-algorithm.

4 SIMULATION RESULTS

For all simulations the planar truck model has been exited bya bump excitation. The results are analyzedfor a simulation time of100s, in which the truck is excited by three bumps of the height of0.2m. To make

0 5 10 15 20 25 301.95

2

2.05

2.1

2.15

2.2

2.25

seconds

met

erVertical movement of chassis (P2)

referencenonlin liE, h=0.03lin liE, h=0.002nonlin GRK4Tlin GRK4T

(a) Vertical movement chassis

0 5 10 15 20 25 30−1.52

−1.5

−1.48

−1.46

−1.44

−1.42

−1.4

−1.38

−1.36

seconds

met

er

Tilt angle of trailer (P7)

referencenonlin liElin liEnonlin GRK4Tlin GRK4T

(b) Tilt angle trailer

Figure 2. Simulation results on microcontroller

a conclusion on the accuracy of a simulation result, the residuals

erri = refi − qi, i = 1, . . . , 9 (12)

are compared. Therebyrefi is the reference solution for the nine degrees of freedom of the truck model.

For comparing performance the actual time for one integration steptstep is listed, although in section4.2all simulations are made with step sizeh = 0.001s.

4.1 Real-time Simulation on Microcontroller

With its 150MHz CPU the TriBoard TC1796 (TriCore) is the platform with the lowest performance but alsothe cheapest one, which is used for the presented benchmark tests. Because of its 32-bit architecture thesimulation was made only with single precision numbers to optimize the performance.

Results are presented for the integration of ODEs (1) of the unconstrained model (Fig.1 (a)) and comparedto a reference solutionrefi, i = 1, . . . 9, which is integrated with a variable step size solver (RADAU5) ona standard pc.

Because of the comparable small performance of microcontroller, the integration of a linearization of thetruck model is examined in addition.

As expected, the integration time of the linearized formulation is much smaller than for the nonlinear case,one integration step of the nonlinear model takes about10 times longer than one step of the linearizedmodel. This leads to more accurate simulation results than for the nonlinear model compared to a referencesolution. The maximalL2-norm of the residuals is about ten times smaller for the integration result withthe linearly-implicit Euler method, e.g. Attention shouldbe paid to the fact, that these simulations had beenmade with an incrementh > tstep to achieve real-time. This leads to the result, that for thistest scenariothe linearized model integrated with the 1-stage linearly-implicit Euler method andh = 0.002s is moreaccurate than integrated with the 4-stage GRK4T method andh = 0.008s. And both approaches are betterthan integrating the nonlinear model whith adequate increments (cf. Tab.1).

Model liE grk4t

non-lineartstep [s] 2.39 · 10−2 3.14 · 10−2

i

max ‖erri‖L2 [m] 1.04 · 10−2 7.99 · 10−3

linearizedtstep [s] 1.76 · 10−3 6.66 · 10−3

i

max ‖erri‖L2 [m] 3.62 · 10−3 5.64 · 10−3

Table 1. Simulation results for unconstrained truck model on MCU

The simulation results for the first30 seconds are shown exemplary for the vertical displacement of thechassis and the tilt angle of the trailer in Fig.2.

4.2 Real-Time Simulation on Rapid Prototyping Boards

The real-time platform with the most performance used for the presented benchmarking is the DS1006processor board of the company DSPACE, which is based on a3.0 GHz processor with256 MB RAM. Thesecond real-time processor board is the MicroAutoBox of DSPACE, which has a800 MHz CPU and a mainmemory of 8 MB RAM. [1]

These platforms allow including element libraries of commercial mbs software tools. In sections4.2.2and4.2.3the simulation of mbs models built with SIMPACK and SimMechanics on the DS1006 is discussed.All simulation results presented in the following are made with the step sizeh = 0.001s.

4.2.1 Numerical C-Code

The constrained and unconstrained MBS model is implementedas numerical C-code for this approach. Torun them on rapid prototyping boards one has to recompile them with the dSpace X-compiler. For manyapplications additional simulation elements are required, e.g. data preparation for measured data or furthercontrol elements. In this case, it is suitable to include theC-code for the model and solver as a C-Mex S-function into a MATLAB Simulink model. Afterwards, the executable code is generated by the Real-TimeWorkshop [2].

The main results for simulating the constrained and unconstrained truck model are presented in Tab.2.Every application was real-time capable withh = 0.001s. The effective integration time needed for onelinear-implicit Euler step does not differ that much fromtstep of GRK4T (for the ODE case). But themaximalL2-norm of the residuals is about four times higher for the linearly-implicit Euler integration thanfor the GRK4T results.

Model ODE DAE

Solver li Euler GRK4Tli Euler

unstab BG GGL

tstep [s]MABX 5.24 · 10−4 6.40 · 10−4 4.45 · 10−4 4.45 · 10−4 4.47 · 10−4

DS1006 0.90 · 10−4 1.08 · 10−4 0.75 · 10−4 0.75 · 10−4 0.76 · 10−4

i

max ‖erri‖L2 [m] 4.22 · 10−5 1.80 · 10−5 1.65 · 10−3 1.65 · 10−3 1.65 · 10−3

i

max |g1i| [m] 6.95 · 10−5 1.80 · 10−8 1.50 · 10−15

i

max |g2i| [m] 3.68 · 10−5 1.21 · 10−8 1.31 · 10−15

Table 2. Simulation results for truck model and solver techniques given as handcoded numerical C-code

In Tab. 2 also the maximal violations of the constraint termsg(q) of (2) are compared. The unstabilizedintegration let the violation grow linearly with time (drift-off effect), cf. Fig.3 (a). The maximal constraintviolation for the Gear-Gupta-Leimkuhler stabilized integration is about factor107 smaller than the Baum-garte stabilized simulation. Thus, for systems of this complexity the GGL stabilization is recommended.For more complex systems solving equations (11) might be to time consuming and the Baumgarte-approachis favorable.

4.2.2 SIMPACK Models

The commercial mbs program package SIMPACK generates equations of motion for dynamic systems forthe ODE case as well as DAE case. Both forms of equations and adequate numerical integration methodsare exportable for simulation outside of SIMPACK.

For including the SIMPACK model in MATLAB, the bi-directional interface S-function is used, which callsthe right-hand-side of SIMPACK’s equation of motion in the MATLAB Simulink environment [14]. For theODE case one of MATLAB’s integration methods can be used as well as the exported SIMPACK solver.After including the mbs model into Simulink, board specific real-time code is generated by the Real-TimeWorkshop, whereby SIMPACK’s element library is linked and loaded onto the processor board.

0 10 20 30 40 50 60 70 80 90 100−7

−6

−5

−4

−3

−2

−1

0

1x 10−5 g1

seconds

me

ter

unstabilizedGGL−stabilizedBaumgarte−stabilized

(a)

0 5 10 15 20 25 30−18

−16

−14

−12

−10

−8

−6

−4

−2

0x 10

−9 g1

seconds

me

ter

unstabilizedGGL−stabilizedBaumgarte−stabilized

(b) first 30 seconds, zoom

Figure 3. Horizontal constraint violation, g1

0 5 10 15 20 25 30−6

−4

−2

0

2

4

6x 10−4

seconds

me

ter

Residua for P2

Simpack liEGRK4T

(a) Vertical movement chassis

0 5 10 15 20 25 30−3

−2

−1

0

1

2

3

4x 10−4

seconds

me

ter

Residua for P7

Simpack liEGRK4T

(b) Tilt angle trailer

Figure 4. Residuals of simulating SIMPACK’s ODE truck model with SIMPACK’s linearly-implicitEuler method and handcoded GRK4T solver

Additional to using a SIMPACK or MATLAB solver for integrating the mbs model one can solve theequations of motion with an own integration technique. Therefore, the generated C-files of SIMPACK haveto be extended and modified with the additional integration routine and recompiled. In table3 the resultsof simulating the ODE truck model with SIMPACKs linearly-implicit Euler method and with a handcoded4-stage GRK4T integration method are compared. As one can see, the required integration step timetstepfor the simulation on the DS1006 processor board does not differ for these two applications, but again theresult for the GRK4T integration is more accurate (cf Fig.4). The reference solution for these applicationsis an ODE truck model simulated with SODASRT in SIMPACK.

(spck) li Euler GRK4Ttstep [s] 2.63 · 10−4 2.99 · 10−4

i

max ‖erri‖L2 [m] 4.30 · 10−5 0.41 · 10−5

Table 3. Simulation of SIMPACK’s ODE truck model on DS1006

Real-Time Simulation of SIMPACK DAE-Equations Since implicit DAE integration schemes, whichare implemented in SIMPACK, are numerically very costly andtime consuming and integrate with variablestep sizes, they are not suitable for real-time applications. Therefore, the SIMPACK generated C-code hasbeen extended with the handcoded routines for the linearly-implicit Euler method with Baumgarte and GGLstabilization techniques (see3.2).

As it is shown in Tab.4 this procedure is real-time capable when proposing to simulate withh = 0.001s.Again, the best constraint satisfaction is gained with the GGL stabilization technique (cf. also Fig.6).

liEunstab bg ggl

tstep [s] 7.14 · 10−4 7.97 · 10−4 8.00 · 10−4

i

max |g1i| 1.5253 · 10−4 8.2610 · 10−8 3.8855 · 10−12

i

max |g2i| 8.6976 · 10−5 3.1297 · 10−8 1.6564 · 10−11

Table 4. Simulation of SIMPACK’s DAE model with handcoded linearly-implicit Euler method onDS1006

0 10 20 30 40 50 60 70 80 90 100−16

−14

−12

−10

−8

−6

−4

−2

0

2x 10−5 g1

seconds

met

er

unstabBaumgarteGGL

(a)

0 5 10 15 20 25 30

−8

−6

−4

−2

0

x 10−8 g1

seconds

met

er

unstabBaumgarteGGL

(b) first 30 seconds, zoom

Figure 5. Horizontal constraint violation, cf. Tab.4

4.2.3 SimMechanics Models

SimMechanics is given as a MATLAB Toolbox and thus is simple to connect to other control or physicalmodeling elements of MATLAB. Furthermore, C-code can be generated as usual for all MATLAB modelswith the Real-Time Workshop. However, the mechanical element library is not as elaborate as in other MBStools like SIMPACK, but can be extended with given MATLAB Simulink functionalities.

DAEs are simulated with the usual Simulink solver methods, which are extended by constraint-solvingtechniques, thus simulation with fixed step size is possible. The simulation on the DS1006 processor boardsof the unconstraint truck model needs2.13 · 10−4s for one integrationstep and the constraint model3.11 ·10−4s when using the 2-stage Heun integration method.

0 10 20 30 40 50 60 70 80 90 1001.95

2

2.05

2.1

2.15

2.2

2.25

2.3

2.35

seconds

met

er

P2

ODEDAE

(a) Vertical movement chassis

0 10 20 30 40 50 60 70 80 90 100−1.65

−1.6

−1.55

−1.5

−1.45

−1.4

−1.35

−1.3

−1.25

−1.2

seconds

met

er

P7

ODEDAE

(b) Tilt angle trailer

Figure 6. Simulation of ODE and DAE truck model, modelled with SimMechanics, on DS1006

5 CONCLUSION

We have analyzed the possibilities and features of simulating a mbs benchmark model under real-time con-ditions with respect to three main criteria: modelling approach, onboard platform and integration method.

The considered truck model has been implemented by hand as C-code, in the commercial mbs tools SIM-PACK and SimMechanics. The handcoded variant is naturally most flexible, among others concerninglicense issues. It is also the most elaborate one, but realistic only for systems of moderate size and complex-ity. Large and complex mbs models can only be handled effectively with an appropriate software package,which offers a navigation, element libraries, etc. A drawback of that approach in turn is, that one needsspecial (platform dependent) licenses to export and to solve the mbs.

Concerning the used simulation-platforms, the microcontroller is the cheapest and most mobile solution,but it requires a lot of work to implement and simulate the mbson it and the specific configurations dependstrongly on the used board, the programming language etc. Infact, only the C-code version of the mbs couldbe exported and simulated in a reasonable way on the microcontroller. Additionally, the microcontrollerprovides the lowest performance properties. Due to these limitations, the microcontroller is a suitable andcheap platform only for small systems, which can be implement by hand. If the system is of moderate orlarge size and complexity (including the nonlinear truck model) and has to be modelled in a mbs softwaretool, rapid prototyping boards are more favorable, they provide a much higher performance.

The usage of the integration scheme is a question of the required results. Of course, it is relatively easy tocombine handwritten mbs systems with handwritten solver routines. We have seen, that besides the oftenused linearly-implicit Euler method higher order methods can be applied successfully. In the DAE case,which is very important regarding ’real-life’ mbs models, one has to add a stabilization technique. TheGGL-method brings up the best result, but can be costly for larger systems, since additional equations haveto be solved. This is avoided by the Baumgarte-approach, which leads to simulation results, which are stillvery good. As a last important aspect, we emphasize the demonstrated possibility to use own, specific,problem-oriented solver routines in combination with commercial mbs tools and rapid prototyping boards.

To summarize, this paper shows, that with each configurationat most one real-time solution is possible. Tochoose a specific configuration, one has to strike the balancebetween model complexity and size, simulationrequirements and available hardware.

REFERENCES

[1] dSPACE GmbH. http://www.dspace.com, Paderborn.

[2] The MathWork, Inc. Real-Time Workshop 7 User’s Guide, 2008.

[3] SIMPACK AG. SIMDOC v8.901, Gilching, 2008.

[4] The MathWork, Inc. SimMechanicsTM 3 User’s Guide, 2009.

[5] A RNOLD, M., BURGERMEISTER, B., AND EICHBERGER, A. Linearly implicit time integrationmethods in real-time applications: Daes and stiff odes.Multibody Syst Dyn 17 (2007), 99–117.

[6] BAUMGARTE, J. Stabilization of constraints and integrals of motion indynamical systems.Comput.Methods Appl. Mech. Eng. 1 (1972), 1–16.

[7] BURGERMEISTER, B., ARNOLD, M., AND ESTERL, B. Dae time integration for real-time applica-tions in multibody dynamics.Z. Angew. Math. Mech. 86 (2006), 759–771.

[8] DE JALON , J. G.,AND BAYO , E. Kinematic and Dynamic Simulation of Multibody Systems. Springer-Verlag, New York Berlin Heidelberg, 1994.

[9] EICH-SOELLNER, E., AND FÜHRER, C. Numerical Methods in Multibody Dynamics. B. G. Teubner,Stuttgart, 1998.

[10] GEAR, C., LEIMKUHLER , B., AND GUPTA, G. Automatic integration of euler-lagrange equationswith constraints.J. Comp. Appl. Math. 12 u. 13 (1985), 77–90.

[11] HAIRER, E., AND WANNER, G. Solving Ordinary Differential Equations II. Springer-Verlag, BerlinHeidelberg New York, 2002.

[12] KAPS, P.,AND RENTROP, P. Generalized runge-kutta methods of order four with stepsize control forstiff ordinary differential equations.Numer. Math. 38 (1979), 55–68.

[13] KOPETZ, H. Real-Time Systems. KluwerAcademic Publishers, 2004.

[14] KRÜGER, W., VACULIN , O., AND KORTÜM, W. Multi-disciplinary simulation of vehicle system dy-namics. InRTO/AVT Symposium on Reduction of Military Vehicle Acquisition Time and Cost throughAdvanced Modelling and Virtual Simulation (Paris, 2002).

Published reports of the Fraunhofer ITWM

The PDF-files of the following reports are available under: www.itwm.fraunhofer.de/de/zentral__berichte/berichte

1. D. Hietel, K. Steiner, J. StruckmeierA Finite - Volume Particle Method for Compressible Flows(19 pages, 1998)

2. M. Feldmann, S. SeiboldDamage Diagnosis of Rotors: Application of Hilbert Transform and Multi-Hypothe-sis TestingKeywords: Hilbert transform, damage diagnosis, Kalman filtering, non-linear dynamics(23 pages, 1998)

3. Y. Ben-Haim, S. SeiboldRobust Reliability of Diagnostic Multi- Hypothesis Algorithms: Application to Rotating MachineryKeywords: Robust reliability, convex models, Kalman fil-tering, multi-hypothesis diagnosis, rotating machinery, crack diagnosis(24 pages, 1998)

4. F.-Th. Lentes, N. SiedowThree-dimensional Radiative Heat Transfer in Glass Cooling Processes(23 pages, 1998)

5. A. Klar, R. WegenerA hierarchy of models for multilane vehicu-lar traffic Part I: Modeling(23 pages, 1998)

Part II: Numerical and stochastic investigations(17 pages, 1998)

6. A. Klar, N. SiedowBoundary Layers and Domain Decomposi-tion for Radiative Heat Transfer and Diffu-sion Equations: Applications to Glass Manu-facturing Processes(24 pages, 1998)

7. I. ChoquetHeterogeneous catalysis modelling and numerical simulation in rarified gas flows Part I: Coverage locally at equilibrium (24 pages, 1998)

8. J. Ohser, B. Steinbach, C. LangEfficient Texture Analysis of Binary Images(17 pages, 1998)

9. J. OrlikHomogenization for viscoelasticity of the integral type with aging and shrinkage(20 pages, 1998)

10. J. MohringHelmholtz Resonators with Large Aperture(21 pages, 1998)

11. H. W. Hamacher, A. SchöbelOn Center Cycles in Grid Graphs(15 pages, 1998)

12. H. W. Hamacher, K.-H. KüferInverse radiation therapy planning - a multiple objective optimisation approach(14 pages, 1999)

13. C. Lang, J. Ohser, R. HilferOn the Analysis of Spatial Binary Images(20 pages, 1999)

14. M. JunkOn the Construction of Discrete Equilibrium Distributions for Kinetic Schemes(24 pages, 1999)

15. M. Junk, S. V. Raghurame RaoA new discrete velocity method for Navier-Stokes equations(20 pages, 1999)

16. H. NeunzertMathematics as a Key to Key Technologies(39 pages (4 PDF-Files), 1999)

17. J. Ohser, K. SandauConsiderations about the Estimation of the Size Distribution in Wicksell’s Corpuscle Problem(18 pages, 1999)

18. E. Carrizosa, H. W. Hamacher, R. Klein, S. Nickel

Solving nonconvex planar location prob-lems by finite dominating setsKeywords: Continuous Location, Polyhedral Gauges, Finite Dominating Sets, Approximation, Sandwich Algo-rithm, Greedy Algorithm(19 pages, 2000)

19. A. BeckerA Review on Image Distortion MeasuresKeywords: Distortion measure, human visual system(26 pages, 2000)

20. H. W. Hamacher, M. Labbé, S. Nickel, T. Sonneborn

Polyhedral Properties of the Uncapacitated Multiple Allocation Hub Location Problem Keywords: integer programming, hub location, facility location, valid inequalities, facets, branch and cut(21 pages, 2000)

21. H. W. Hamacher, A. SchöbelDesign of Zone Tariff Systems in Public Transportation(30 pages, 2001)

22. D. Hietel, M. Junk, R. Keck, D. TeleagaThe Finite-Volume-Particle Method for Conservation Laws(16 pages, 2001)

23. T. Bender, H. Hennes, J. Kalcsics, M. T. Melo, S. Nickel

Location Software and Interface with GIS and Supply Chain ManagementKeywords: facility location, software development, geographical information systems, supply chain man-agement(48 pages, 2001)

24. H. W. Hamacher, S. A. TjandraMathematical Modelling of Evacuation Problems: A State of Art(44 pages, 2001)

25. J. Kuhnert, S. TiwariGrid free method for solving the Poisson equationKeywords: Poisson equation, Least squares method, Grid free method(19 pages, 2001)

26. T. Götz, H. Rave, D. Reinel-Bitzer, K. Steiner, H. Tiemeier

Simulation of the fiber spinning processKeywords: Melt spinning, fiber model, Lattice Boltz-mann, CFD(19 pages, 2001)

27. A. Zemitis On interaction of a liquid film with an obstacleKeywords: impinging jets, liquid film, models, numeri-cal solution, shape(22 pages, 2001)

28. I. Ginzburg, K. SteinerFree surface lattice-Boltzmann method to model the filling of expanding cavities by Bingham FluidsKeywords: Generalized LBE, free-surface phenomena, interface boundary conditions, filling processes, Bing-ham viscoplastic model, regularized models(22 pages, 2001)

29. H. Neunzert»Denn nichts ist für den Menschen als Men-schen etwas wert, was er nicht mit Leiden-schaft tun kann« Vortrag anlässlich der Verleihung des Akademie preises des Landes Rheinland-Pfalz am 21.11.2001Keywords: Lehre, Forschung, angewandte Mathematik, Mehrskalenanalyse, Strömungsmechanik(18 pages, 2001)

30. J. Kuhnert, S. TiwariFinite pointset method based on the projec-tion method for simulations of the incom-pressible Navier-Stokes equationsKeywords: Incompressible Navier-Stokes equations, Meshfree method, Projection method, Particle scheme, Least squares approximation AMS subject classification: 76D05, 76M28(25 pages, 2001)

31. R. Korn, M. KrekelOptimal Portfolios with Fixed Consumption or Income StreamsKeywords: Portfolio optimisation, stochastic control, HJB equation, discretisation of control problems(23 pages, 2002)

32. M. KrekelOptimal portfolios with a loan dependent credit spreadKeywords: Portfolio optimisation, stochastic control, HJB equation, credit spread, log utility, power utility, non-linear wealth dynamics(25 pages, 2002)

33. J. Ohser, W. Nagel, K. SchladitzThe Euler number of discretized sets – on the choice of adjacency in homogeneous lattices Keywords: image analysis, Euler number, neighborhod relationships, cuboidal lattice(32 pages, 2002)

34. I. Ginzburg, K. Steiner Lattice Boltzmann Model for Free-Surface flow and Its Application to Filling Process in Casting Keywords: Lattice Boltzmann models; free-surface phe-nomena; interface boundary conditions; filling pro-cesses; injection molding; volume of fluid method; in-terface boundary conditions; advection-schemes; up-wind-schemes(54 pages, 2002)

35. M. Günther, A. Klar, T. Materne, R. Wegener

Multivalued fundamental diagrams and stop and go waves for continuum traffic equationsKeywords: traffic flow, macroscopic equations, kinetic derivation, multivalued fundamental diagram, stop and go waves, phase transitions(25 pages, 2002)

36. S. Feldmann, P. Lang, D. Prätzel-WoltersParameter influence on the zeros of net-work determinantsKeywords: Networks, Equicofactor matrix polynomials, Realization theory, Matrix perturbation theory(30 pages, 2002)

37. K. Koch, J. Ohser, K. Schladitz Spectral theory for random closed sets and es timating the covariance via frequency spaceKeywords: Random set, Bartlett spectrum, fast Fourier transform, power spectrum(28 pages, 2002)

38. D. d’Humières, I. GinzburgMulti-reflection boundary conditions for lattice Boltzmann modelsKeywords: lattice Boltzmann equation, boudary condis-tions, bounce-back rule, Navier-Stokes equation(72 pages, 2002)

39. R. KornElementare FinanzmathematikKeywords: Finanzmathematik, Aktien, Optionen, Port-folio-Optimierung, Börse, Lehrerweiterbildung, Mathe-matikunterricht(98 pages, 2002)

40. J. Kallrath, M. C. Müller, S. NickelBatch Presorting Problems: Models and Complexity ResultsKeywords: Complexity theory, Integer programming, Assigment, Logistics(19 pages, 2002)

41. J. LinnOn the frame-invariant description of the phase space of the Folgar-Tucker equation Key words: fiber orientation, Folgar-Tucker equation, in-jection molding(5 pages, 2003)

42. T. Hanne, S. Nickel A Multi-Objective Evolutionary Algorithm for Scheduling and Inspection Planning in Software Development Projects Key words: multiple objective programming, project management and scheduling, software development, evolutionary algorithms, efficient set(29 pages, 2003)

43. T. Bortfeld , K.-H. Küfer, M. Monz, A. Scherrer, C. Thieke, H. Trinkaus

Intensity-Modulated Radiotherapy - A Large Scale Multi-Criteria Programming Problem

Keywords: multiple criteria optimization, representa-tive systems of Pareto solutions, adaptive triangulation, clustering and disaggregation techniques, visualization of Pareto solutions, medical physics, external beam ra-diotherapy planning, intensity modulated radiotherapy(31 pages, 2003)

44. T. Halfmann, T. WichmannOverview of Symbolic Methods in Industrial Analog Circuit Design Keywords: CAD, automated analog circuit design, sym-bolic analysis, computer algebra, behavioral modeling, system simulation, circuit sizing, macro modeling, dif-ferential-algebraic equations, index(17 pages, 2003)

45. S. E. Mikhailov, J. OrlikAsymptotic Homogenisation in Strength and Fatigue Durability Analysis of Compos-itesKeywords: multiscale structures, asymptotic homoge-nization, strength, fatigue, singularity, non-local con-ditions(14 pages, 2003)

46. P. Domínguez-Marín, P. Hansen, N. Mladenovi ́c , S. Nickel

Heuristic Procedures for Solving the Discrete Ordered Median ProblemKeywords: genetic algorithms, variable neighborhood search, discrete facility location(31 pages, 2003)

47. N. Boland, P. Domínguez-Marín, S. Nickel, J. Puerto

Exact Procedures for Solving the Discrete Ordered Median ProblemKeywords: discrete location, Integer programming(41 pages, 2003)

48. S. Feldmann, P. LangPadé-like reduction of stable discrete linear systems preserving their stability Keywords: Discrete linear systems, model reduction, stability, Hankel matrix, Stein equation(16 pages, 2003)

49. J. Kallrath, S. NickelA Polynomial Case of the Batch Presorting Problem Keywords: batch presorting problem, online optimization, competetive analysis, polynomial algorithms, logistics(17 pages, 2003)

50. T. Hanne, H. L. TrinkausknowCube for MCDM – Visual and Interactive Support for Multicriteria Decision MakingKey words: Multicriteria decision making, knowledge management, decision support systems, visual interfac-es, interactive navigation, real-life applications.(26 pages, 2003)

51. O. Iliev, V. LaptevOn Numerical Simulation of Flow Through Oil FiltersKeywords: oil filters, coupled flow in plain and porous media, Navier-Stokes, Brinkman, numerical simulation(8 pages, 2003)

52. W. Dörfler, O. Iliev, D. Stoyanov, D. VassilevaOn a Multigrid Adaptive Refinement Solver for Saturated Non-Newtonian Flow in Porous MediaKeywords: Nonlinear multigrid, adaptive refinement, non-Newtonian flow in porous media(17 pages, 2003)

53. S. KruseOn the Pricing of Forward Starting Options under Stochastic VolatilityKeywords: Option pricing, forward starting options, Heston model, stochastic volatility, cliquet options(11 pages, 2003)

54. O. Iliev, D. StoyanovMultigrid – adaptive local refinement solver for incompressible flowsKeywords: Navier-Stokes equations, incompressible flow, projection-type splitting, SIMPLE, multigrid methods, adaptive local refinement, lid-driven flow in a cavity (37 pages, 2003)

55. V. Starikovicius The multiphase flow and heat transfer in porous media Keywords: Two-phase flow in porous media, various formulations, global pressure, multiphase mixture mod-el, numerical simulation(30 pages, 2003)

56. P. Lang, A. Sarishvili, A. WirsenBlocked neural networks for knowledge ex-traction in the software development processKeywords: Blocked Neural Networks, Nonlinear Regres-sion, Knowledge Extraction, Code Inspection(21 pages, 2003)

57. H. Knaf, P. Lang, S. Zeiser Diagnosis aiding in Regulation Thermography using Fuzzy Logic Keywords: fuzzy logic,knowledge representation, expert system(22 pages, 2003)

58. M. T. Melo, S. Nickel, F. Saldanha da GamaLarge scale models for dynamic multi-commodity capacitated facility location Keywords: supply chain management, strategic planning, dynamic location, modeling(40 pages, 2003)

59. J. Orlik Homogenization for contact problems with periodically rough surfacesKeywords: asymptotic homogenization, contact problems(28 pages, 2004)

60. A. Scherrer, K.-H. Küfer, M. Monz, F. Alonso, T. Bortfeld

IMRT planning on adaptive volume struc-tures – a significant advance of computa-tional complexityKeywords: Intensity-modulated radiation therapy (IMRT), inverse treatment planning, adaptive volume structures, hierarchical clustering, local refinement, adaptive clustering, convex programming, mesh gener-ation, multi-grid methods(24 pages, 2004)

61. D. KehrwaldParallel lattice Boltzmann simulation of complex flowsKeywords: Lattice Boltzmann methods, parallel com-puting, microstructure simulation, virtual material de-sign, pseudo-plastic fluids, liquid composite moulding(12 pages, 2004)

62. O. Iliev, J. Linn, M. Moog, D. Niedziela, V. Starikovicius

On the Performance of Certain Iterative Solvers for Coupled Systems Arising in Dis-cretization of Non-Newtonian Flow Equa-tions

Keywords: Performance of iterative solvers, Precondi-tioners, Non-Newtonian flow(17 pages, 2004)

63. R. Ciegis, O. Iliev, S. Rief, K. Steiner On Modelling and Simulation of Different Regimes for Liquid Polymer Moulding Keywords: Liquid Polymer Moulding, Modelling, Simu-lation, Infiltration, Front Propagation, non-Newtonian flow in porous media (43 pages, 2004)

64. T. Hanne, H. NeuSimulating Human Resources in Software Development ProcessesKeywords: Human resource modeling, software process, productivity, human factors, learning curve(14 pages, 2004)

65. O. Iliev, A. Mikelic, P. PopovFluid structure interaction problems in de-formable porous media: Toward permeabil-ity of deformable porous mediaKeywords: fluid-structure interaction, deformable po-rous media, upscaling, linear elasticity, stokes, finite el-ements(28 pages, 2004)

66. F. Gaspar, O. Iliev, F. Lisbona, A. Naumovich, P. Vabishchevich

On numerical solution of 1-D poroelasticity equations in a multilayered domainKeywords: poroelasticity, multilayered material, finite volume discretization, MAC type grid(41 pages, 2004)

67. J. Ohser, K. Schladitz, K. Koch, M. NötheDiffraction by image processing and its ap-plication in materials scienceKeywords: porous microstructure, image analysis, ran-dom set, fast Fourier transform, power spectrum, Bar-tlett spectrum(13 pages, 2004)

68. H. NeunzertMathematics as a Technology: Challenges for the next 10 YearsKeywords: applied mathematics, technology, modelling, simulation, visualization, optimization, glass processing, spinning processes, fiber-fluid interaction, trubulence effects, topological optimization, multicriteria optimiza-tion, Uncertainty and Risk, financial mathematics, Mal-liavin calculus, Monte-Carlo methods, virtual material design, filtration, bio-informatics, system biology(29 pages, 2004)

69. R. Ewing, O. Iliev, R. Lazarov, A. NaumovichOn convergence of certain finite difference discretizations for 1 D poroelasticity inter-face problems Keywords: poroelasticity, multilayered material, finite volume discretizations, MAC type grid, error estimates (26 pages,2004)

70. W. Dörfler, O. Iliev, D. Stoyanov, D. Vassileva On Efficient Simulation of Non-Newto-nian Flow in Saturated Porous Media with a Multigrid Adaptive Refinement Solver Keywords: Nonlinear multigrid, adaptive renement, non-Newtonian in porous media(25 pages, 2004)

71. J. Kalcsics, S. Nickel, M. Schröder Towards a Unified Territory Design Approach – Applications, Algorithms and GIS IntegrationKeywords: territory desgin, political districting, sales territory alignment, optimization algorithms, Geo-graphical Information Systems(40 pages, 2005)

72. K. Schladitz, S. Peters, D. Reinel-Bitzer, A. Wiegmann, J. Ohser

Design of acoustic trim based on geometric modeling and flow simulation for non-woven Keywords: random system of fibers, Poisson line process, flow resistivity, acoustic absorption, Lattice-Boltzmann method, non-woven(21 pages, 2005)

73. V. Rutka, A. WiegmannExplicit Jump Immersed Interface Method for virtual material design of the effective elastic moduli of composite materials Keywords: virtual material design, explicit jump im-mersed interface method, effective elastic moduli, composite materials(22 pages, 2005)

74. T. HanneEine Übersicht zum Scheduling von BaustellenKeywords: Projektplanung, Scheduling, Bauplanung, Bauindustrie(32 pages, 2005)

75. J. LinnThe Folgar-Tucker Model as a Differetial Algebraic System for Fiber Orientation Calculation Keywords: fiber orientation, Folgar–Tucker model, in-variants, algebraic constraints, phase space, trace sta-bility(15 pages, 2005)

76. M. Speckert, K. Dreßler, H. Mauch, A. Lion, G. J. Wierda

Simulation eines neuartigen Prüf systems für Achserprobungen durch MKS-Model-lierung einschließlich RegelungKeywords: virtual test rig, suspension testing, multibody simulation, modeling hexapod test rig, opti-mization of test rig configuration(20 pages, 2005)

77. K.-H. Küfer, M. Monz, A. Scherrer, P. Süss, F. Alonso, A. S. A. Sultan, Th. Bortfeld, D. Craft, Chr. Thieke

Multicriteria optimization in intensity modulated radiotherapy planning Keywords: multicriteria optimization, extreme solu-tions, real-time decision making, adaptive approxima-tion schemes, clustering methods, IMRT planning, re-verse engineering (51 pages, 2005)

78. S. Amstutz, H. Andrä A new algorithm for topology optimization using a level-set methodKeywords: shape optimization, topology optimization, topological sensitivity, level-set(22 pages, 2005)

79. N. EttrichGeneration of surface elevation models for urban drainage simulationKeywords: Flooding, simulation, urban elevation models, laser scanning(22 pages, 2005)

80. H. Andrä, J. Linn, I. Matei, I. Shklyar, K. Steiner, E. Teichmann

OPTCAST – Entwicklung adäquater Struk-turoptimierungsverfahren für Gießereien Technischer Bericht (KURZFASSUNG)Keywords: Topologieoptimierung, Level-Set-Methode, Gießprozesssimulation, Gießtechnische Restriktionen, CAE-Kette zur Strukturoptimierung(77 pages, 2005)

81. N. Marheineke, R. WegenerFiber Dynamics in Turbulent Flows Part I: General Modeling Framework Keywords: fiber-fluid interaction; Cosserat rod; turbu-lence modeling; Kolmogorov’s energy spectrum; dou-ble-velocity correlations; differentiable Gaussian fields(20 pages, 2005)

Part II: Specific Taylor Drag Keywords: flexible fibers; k-e turbulence model; fi-ber-turbulence interaction scales; air drag; random Gaussian aerodynamic force; white noise; stochastic differential equations; ARMA process (18 pages, 2005)

82. C. H. Lampert, O. Wirjadi An Optimal Non-Orthogonal Separation of the Anisotropic Gaussian Convolution FilterKeywords: Anisotropic Gaussian filter, linear filtering, ori-entation space, nD image processing, separable filters(25 pages, 2005)

83. H. Andrä, D. StoyanovError indicators in the parallel finite ele-ment solver for linear elasticity DDFEM Keywords: linear elasticity, finite element method, hier-archical shape functions, domain decom-position, par-allel implementation, a posteriori error estimates(21 pages, 2006)

84. M. Schröder, I. SolchenbachOptimization of Transfer Quality in Regional Public TransitKeywords: public transit, transfer quality, quadratic assignment problem(16 pages, 2006)

85. A. Naumovich, F. J. Gaspar On a multigrid solver for the three-dimen-sional Biot poroelasticity system in multi-layered domains Keywords: poroelasticity, interface problem, multigrid, operator-dependent prolongation(11 pages, 2006)

86. S. Panda, R. Wegener, N. MarheinekeSlender Body Theory for the Dynamics of Curved Viscous Fibers Keywords: curved viscous fibers; fluid dynamics; Navier-Stokes equations; free boundary value problem; asymp-totic expansions; slender body theory(14 pages, 2006)

87. E. Ivanov, H. Andrä, A. KudryavtsevDomain Decomposition Approach for Auto-matic Parallel Generation of Tetrahedral GridsKey words: Grid Generation, Unstructured Grid, Delau-nay Triangulation, Parallel Programming, Domain De-composition, Load Balancing(18 pages, 2006)

88. S. Tiwari, S. Antonov, D. Hietel, J. Kuhnert, R. Wegener

A Meshfree Method for Simulations of In-teractions between Fluids and Flexible StructuresKey words: Meshfree Method, FPM, Fluid Structure Interaction, Sheet of Paper, Dynamical Coupling(16 pages, 2006)

89. R. Ciegis , O. Iliev, V. Starikovicius, K. SteinerNumerical Algorithms for Solving Problems of Multiphase Flows in Porous MediaKeywords: nonlinear algorithms, finite-volume method, software tools, porous media, flows(16 pages, 2006)

90. D. Niedziela, O. Iliev, A. LatzOn 3D Numerical Simulations of Viscoelastic FluidsKeywords: non-Newtonian fluids, anisotropic viscosity, integral constitutive equation (18 pages, 2006)

91. A. WinterfeldApplication of general semi-infinite Pro-gramming to Lapidary Cutting ProblemsKeywords: large scale optimization, nonlinear program-ming, general semi-infinite optimization, design center-ing, clustering(26 pages, 2006)

92. J. Orlik, A. OstrovskaSpace-Time Finite Element Approximation and Numerical Solution of Hereditary Linear Viscoelasticity ProblemsKeywords: hereditary viscoelasticity; kern approxima-tion by interpolation; space-time finite element approxi-mation, stability and a priori estimate(24 pages, 2006)

93. V. Rutka, A. Wiegmann, H. AndräEJIIM for Calculation of effective Elastic Moduli in 3D Linear ElasticityKeywords: Elliptic PDE, linear elasticity, irregular do-main, finite differences, fast solvers, effective elas-tic moduli(24 pages, 2006)

94. A. Wiegmann, A. ZemitisEJ-HEAT: A Fast Explicit Jump Harmonic Averaging Solver for the Effective Heat Conductivity of Composite MaterialsKeywords: Stationary heat equation, effective ther-mal conductivity, explicit jump, discontinuous coeffi-cients, virtual material design, microstructure simula-tion, EJ-HEAT(21 pages, 2006)

95. A. NaumovichOn a finite volume discretization of the three-dimensional Biot poroelasticity sys-tem in multilayered domainsKeywords: Biot poroelasticity system, interface problems, finite volume discretization, finite difference method(21 pages, 2006)

96. M. Krekel, J. WenzelA unified approach to Credit Default Swap-tion and Constant Maturity Credit Default Swap valuationKeywords: LIBOR market model, credit risk, Credit De-fault Swaption, Constant Maturity Credit Default Swap-method(43 pages, 2006)

97. A. DreyerInterval Methods for Analog CirciutsKeywords: interval arithmetic, analog circuits, tolerance analysis, parametric linear systems, frequency response, symbolic analysis, CAD, computer algebra(36 pages, 2006)

98. N. Weigel, S. Weihe, G. Bitsch, K. DreßlerUsage of Simulation for Design and Optimi-zation of TestingKeywords: Vehicle test rigs, MBS, control, hydraulics, testing philosophy(14 pages, 2006)

99. H. Lang, G. Bitsch, K. Dreßler, M. SpeckertComparison of the solutions of the elastic and elastoplastic boundary value problems

Keywords: Elastic BVP, elastoplastic BVP, variational inequalities, rate-independency, hysteresis, linear kine-matic hardening, stop- and play-operator(21 pages, 2006)

100. M. Speckert, K. Dreßler, H. MauchMBS Simulation of a hexapod based sus-pension test rigKeywords: Test rig, MBS simulation, suspension, hydraulics, controlling, design optimization(12 pages, 2006)

101. S. Azizi Sultan, K.-H. KüferA dynamic algorithm for beam orientations in multicriteria IMRT planningKeywords: radiotherapy planning, beam orientation optimization, dynamic approach, evolutionary algo-rithm, global optimization(14 pages, 2006)

102. T. Götz, A. Klar, N. Marheineke, R. WegenerA Stochastic Model for the Fiber Lay-down Process in the Nonwoven ProductionKeywords: fiber dynamics, stochastic Hamiltonian sys-tem, stochastic averaging(17 pages, 2006)

103. Ph. Süss, K.-H. KüferBalancing control and simplicity: a variable aggregation method in intensity modulated radiation therapy planningKeywords: IMRT planning, variable aggregation, clus-tering methods (22 pages, 2006)

104. A. Beaudry, G. Laporte, T. Melo, S. NickelDynamic transportation of patients in hos-pitalsKeywords: in-house hospital transportation, dial-a-ride, dynamic mode, tabu search (37 pages, 2006)

105. Th. HanneApplying multiobjective evolutionary algo-rithms in industrial projectsKeywords: multiobjective evolutionary algorithms, dis-crete optimization, continuous optimization, electronic circuit design, semi-infinite programming, scheduling(18 pages, 2006)

106. J. Franke, S. HalimWild bootstrap tests for comparing signals and imagesKeywords: wild bootstrap test, texture classification, textile quality control, defect detection, kernel estimate, nonparametric regression(13 pages, 2007)

107. Z. Drezner, S. NickelSolving the ordered one-median problem in the planeKeywords: planar location, global optimization, ordered median, big triangle small triangle method, bounds, numerical experiments(21 pages, 2007)

108. Th. Götz, A. Klar, A. Unterreiter, R. Wegener

Numerical evidance for the non- existing of solutions of the equations desribing rota-tional fiber spinningKeywords: rotational fiber spinning, viscous fibers, boundary value problem, existence of solutions(11 pages, 2007)

109. Ph. Süss, K.-H. KüferSmooth intensity maps and the Bortfeld-Boyer sequencerKeywords: probabilistic analysis, intensity modulated radiotherapy treatment (IMRT), IMRT plan application, step-and-shoot sequencing(8 pages, 2007)

110. E. Ivanov, O. Gluchshenko, H. Andrä, A. Kudryavtsev

Parallel software tool for decomposing and meshing of 3d structuresKeywords: a-priori domain decomposition, unstruc-tured grid, Delaunay mesh generation(14 pages, 2007)

111. O. Iliev, R. Lazarov, J. WillemsNumerical study of two-grid precondition-ers for 1d elliptic problems with highly oscillating discontinuous coefficientsKeywords: two-grid algorithm, oscillating coefficients, preconditioner (20 pages, 2007)

112. L. Bonilla, T. Götz, A. Klar, N. Marheineke, R. Wegener

Hydrodynamic limit of the Fokker-Planck-equation describing fiber lay-down pro-cessesKeywords: stochastic dierential equations, Fokker-Planck equation, asymptotic expansion, Ornstein-Uhlenbeck process(17 pages, 2007)

113. S. RiefModeling and simulation of the pressing section of a paper machineKeywords: paper machine, computational fluid dynam-ics, porous media(41 pages, 2007)

114. R. Ciegis, O. Iliev, Z. LakdawalaOn parallel numerical algorithms for simu-lating industrial filtration problemsKeywords: Navier-Stokes-Brinkmann equations, finite volume discretization method, SIMPLE, parallel comput-ing, data decomposition method (24 pages, 2007)

115. N. Marheineke, R. WegenerDynamics of curved viscous fibers with sur-face tensionKeywords: Slender body theory, curved viscous bers with surface tension, free boundary value problem(25 pages, 2007)

116. S. Feth, J. Franke, M. SpeckertResampling-Methoden zur mse-Korrektur und Anwendungen in der BetriebsfestigkeitKeywords: Weibull, Bootstrap, Maximum-Likelihood, Betriebsfestigkeit(16 pages, 2007)

117. H. KnafKernel Fisher discriminant functions – a con-cise and rigorous introductionKeywords: wild bootstrap test, texture classification, textile quality control, defect detection, kernel estimate, nonparametric regression(30 pages, 2007)

118. O. Iliev, I. RybakOn numerical upscaling for flows in hetero-geneous porous media

Keywords: numerical upscaling, heterogeneous porous media, single phase flow, Darcy‘s law, multiscale prob-lem, effective permeability, multipoint flux approxima-tion, anisotropy(17 pages, 2007)

119. O. Iliev, I. RybakOn approximation property of multipoint flux approximation methodKeywords: Multipoint flux approximation, finite volume method, elliptic equation, discontinuous tensor coeffi-cients, anisotropy(15 pages, 2007)

120. O. Iliev, I. Rybak, J. WillemsOn upscaling heat conductivity for a class of industrial problemsKeywords: Multiscale problems, effective heat conduc-tivity, numerical upscaling, domain decomposition(21 pages, 2007)

121. R. Ewing, O. Iliev, R. Lazarov, I. RybakOn two-level preconditioners for flow in porous mediaKeywords: Multiscale problem, Darcy‘s law, single phase flow, anisotropic heterogeneous porous media, numerical upscaling, multigrid, domain decomposition, efficient preconditioner(18 pages, 2007)

122. M. Brickenstein, A. DreyerPOLYBORI: A Gröbner basis framework for Boolean polynomialsKeywords: Gröbner basis, formal verification, Boolean polynomials, algebraic cryptoanalysis, satisfiability(23 pages, 2007)

123. O. WirjadiSurvey of 3d image segmentation methodsKeywords: image processing, 3d, image segmentation, binarization(20 pages, 2007)

124. S. Zeytun, A. GuptaA Comparative Study of the Vasicek and the CIR Model of the Short RateKeywords: interest rates, Vasicek model, CIR-model, calibration, parameter estimation(17 pages, 2007)

125. G. Hanselmann, A. Sarishvili Heterogeneous redundancy in software quality prediction using a hybrid Bayesian approachKeywords: reliability prediction, fault prediction, non-homogeneous poisson process, Bayesian model aver-aging(17 pages, 2007)

126. V. Maag, M. Berger, A. Winterfeld, K.-H. Küfer

A novel non-linear approach to minimal area rectangular packingKeywords: rectangular packing, non-overlapping con-straints, non-linear optimization, regularization, relax-ation (18 pages, 2007)

127. M. Monz, K.-H. Küfer, T. Bortfeld, C. Thieke Pareto navigation – systematic multi-crite-ria-based IMRT treatment plan determina-tionKeywords: convex, interactive multi-objective optimiza-tion, intensity modulated radiotherapy planning(15 pages, 2007)

128. M. Krause, A. ScherrerOn the role of modeling parameters in IMRT plan optimizationKeywords: intensity-modulated radiotherapy (IMRT), inverse IMRT planning, convex optimization, sensitiv-ity analysis, elasticity, modeling parameters, equivalent uniform dose (EUD)(18 pages, 2007)

129. A. WiegmannComputation of the permeability of porous materials from their microstructure by FFF-StokesKeywords: permeability, numerical homogenization, fast Stokes solver(24 pages, 2007)

130. T. Melo, S. Nickel, F. Saldanha da GamaFacility Location and Supply Chain Manage-ment – A comprehensive reviewKeywords: facility location, supply chain management, network design(54 pages, 2007)

131. T. Hanne, T. Melo, S. NickelBringing robustness to patient flow manage ment through optimized patient transports in hospitalsKeywords: Dial-a-Ride problem, online problem, case study, tabu search, hospital logistics (23 pages, 2007)

132. R. Ewing, O. Iliev, R. Lazarov, I. Rybak, J. Willems

An efficient approach for upscaling proper-ties of composite materials with high con-trast of coefficientsKeywords: effective heat conductivity, permeability of fractured porous media, numerical upscaling, fibrous insulation materials, metal foams(16 pages, 2008)

133. S. Gelareh, S. NickelNew approaches to hub location problems in public transport planningKeywords: integer programming, hub location, trans-portation, decomposition, heuristic(25 pages, 2008)

134. G. Thömmes, J. Becker, M. Junk, A. K. Vai-kuntam, D. Kehrwald, A. Klar, K. Steiner, A. Wiegmann

A Lattice Boltzmann Method for immiscible multiphase flow simulations using the Level Set MethodKeywords: Lattice Boltzmann method, Level Set method, free surface, multiphase flow(28 pages, 2008)

135. J. OrlikHomogenization in elasto-plasticityKeywords: multiscale structures, asymptotic homogeni-zation, nonlinear energy (40 pages, 2008)

136. J. Almquist, H. Schmidt, P. Lang, J. Deitmer, M. Jirstrand, D. Prätzel-Wolters, H. Becker

Determination of interaction between MCT1 and CAII via a mathematical and physiological approachKeywords: mathematical modeling; model reduction; electrophysiology; pH-sensitive microelectrodes; pro-ton antenna (20 pages, 2008)

137. E. Savenkov, H. Andrä, O. Iliev∗An analysis of one regularization approach for solution of pure Neumann problemKeywords: pure Neumann problem, elasticity, regular-ization, finite element method, condition number(27 pages, 2008)

138. O. Berman, J. Kalcsics, D. Krass, S. NickelThe ordered gradual covering location problem on a networkKeywords: gradual covering, ordered median function, network location(32 pages, 2008)

139. S. Gelareh, S. NickelMulti-period public transport design: A novel model and solution approachesKeywords: Integer programming, hub location, public transport, multi-period planning, heuristics(31 pages, 2008)

140. T. Melo, S. Nickel, F. Saldanha-da-GamaNetwork design decisions in supply chainplanningKeywords: supply chain design, integer programming models, location models, heuristics(20 pages, 2008)

141. C. Lautensack, A. Särkkä, J. Freitag, K. Schladitz

Anisotropy analysis of pressed point pro-cessesKeywords: estimation of compression, isotropy test, nearest neighbour distance, orientation analysis, polar ice, Ripley’s K function(35 pages, 2008)

142. O. Iliev, R. Lazarov, J. WillemsA Graph-Laplacian approach for calculating the effective thermal conductivity of com-plicated fiber geometriesKeywords: graph laplacian, effective heat conductivity, numerical upscaling, fibrous materials(14 pages, 2008)

143. J. Linn, T. Stephan, J. Carlsson, R. BohlinFast simulation of quasistatic rod deforma-tions for VR applicationsKeywords: quasistatic deformations, geometrically exact rod models, variational formulation, energy min-imization, finite differences, nonlinear conjugate gra-dients(7 pages, 2008)

144. J. Linn, T. StephanSimulation of quasistatic deformations us-ing discrete rod modelsKeywords: quasistatic deformations, geometrically exact rod models, variational formulation, energy min-imization, finite differences, nonlinear conjugate gra-dients(9 pages, 2008)

145. J. Marburger, N. Marheineke, R. PinnauAdjoint based optimal control using mesh-less discretizationsKeywords: Mesh-less methods, particle methods, Eul-erian-Lagrangian formulation, optimization strategies, adjoint method, hyperbolic equations(14 pages, 2008

146. S. Desmettre, J. Gould, A. SzimayerOwn-company stockholding and work effort preferences of an unconstrained executiveKeywords: optimal portfolio choice, executive compen-sation(33 pages, 2008)

147. M. Berger, M. Schröder, K.-H. KüferA constraint programming approach for the two-dimensional rectangular packing prob-lem with orthogonal orientationsKeywords: rectangular packing, orthogonal orienta-tions non-overlapping constraints, constraint propa-gation(13 pages, 2008)

148. K. Schladitz, C. Redenbach, T. Sych, M. Godehardt

Microstructural characterisation of open foams using 3d imagesKeywords: virtual material design, image analysis, open foams(30 pages, 2008)

149. E. Fernández, J. Kalcsics, S. Nickel, R. Ríos-Mercado

A novel territory design model arising in the implementation of the WEEE-DirectiveKeywords: heuristics, optimization, logistics, recycling(28 pages, 2008)

150. H. Lang, J. LinnLagrangian field theory in space-time for geometrically exact Cosserat rodsKeywords: Cosserat rods, geometrically exact rods, small strain, large deformation, deformable bodies, Lagrangian field theory, variational calculus(19 pages, 2009)

151. K. Dreßler, M. Speckert, R. Müller, Ch. Weber

Customer loads correlation in truck engi-neeringKeywords: Customer distribution, safety critical compo-nents, quantile estimation, Monte-Carlo methods(11 pages, 2009)

152. H. Lang, K. DreßlerAn improved multiaxial stress-strain correc-tion model for elastic FE postprocessingKeywords: Jiang’s model of elastoplasticity, stress-strain correction, parameter identification, automatic differ-entiation, least-squares optimization, Coleman-Li algo-rithm(6 pages, 2009)

153. J. Kalcsics, S. Nickel, M. SchröderA generic geometric approach to territory design and districtingKeywords: Territory design, districting, combinatorial optimization, heuristics, computational geometry(32 pages, 2009)

154. Th. Fütterer, A. Klar, R. WegenerAn energy conserving numerical scheme for the dynamics of hyper elastic rodsKeywords: Cosserat rod, hyperealstic, energy conserva-tion, finite differences(16 pages, 2009)

155. A. Wiegmann, L. Cheng, E. Glatt, O. Iliev, S. Rief

Design of pleated filters by computer sim-ulationsKeywords: Solid-gas separation, solid-liquid separation, pleated filter, design, simulation(21 pages, 2009)

156. A. Klar, N. Marheineke, R. WegenerHierarchy of mathematical models for pro-duction processes of technical textiles

166. J. I. Serna, M. Monz, K.-H. Küfer, C. ThiekeTrade-off bounds and their effect in multi-criteria IMRT planningKeywords: trade-off bounds, multi-criteria optimization, IMRT, Pareto surface(15 pages, 2009)

167. W. Arne, N. Marheineke, A. Meister, R. We-gener

Numerical analysis of Cosserat rod and string models for viscous jets in rotational spinning processesKeywords: Rotational spinning process, curved viscous fibers, asymptotic Cosserat models, boundary value problem, existence of numerical solutions(18 pages, 2009)

168. T. Melo, S. Nickel, F. Saldanha-da-GamaAn LP-rounding heuristic to solve a multi-period facility relocation problemKeywords: supply chain design, heuristic, linear pro-gramming, rounding(37 pages, 2009)

169. I. Correia, S. Nickel, F. Saldanha-da-GamaSingle-allocation hub location problems with capacity choicesKeywords: hub location, capacity decisions, MILP for-mulations(27 pages, 2009)

170. S. Acar, K. Natcheva-AcarA guide on the implementation of the Heath-Jarrow-Morton Two-Factor Gaussian Short Rate Model (HJM-G2++)Keywords: short rate model, two factor Gaussian, G2++, option pricing, calibration(30 pages, 2009)

171. A. Szimayer, G. Dimitroff, S. LorenzA parsimonious multi-asset Heston model: calibration and derivative pricingKeywords: Heston model, multi-asset, option pricing, calibration, correlation(28 pages, 2009)

172. N. Marheineke, R. WegenerModeling and validation of a stochastic drag for fibers in turbulent flowsKeywords: fiber-fluid interactions, long slender fibers, turbulence modelling, aerodynamic drag, dimensional analysis, data interpolation, stochastic partial differen-tial algebraic equation, numerical simulations, experi-mental validations(19 pages, 2009)

173. S. Nickel, M. Schröder, J. SteegPlanning for home health care servicesKeywords: home health care, route planning, meta-heuristics, constraint programming(23 pages, 2009)

174. G. Dimitroff, A. Szimayer, A. WagnerQuanto option pricing in the parsimonious Heston modelKeywords: Heston model, multi asset, quanto options, option pricing(14 pages, 2009) 174. G. Dimitroff, A. Szimayer, A. Wagner

175. S. Herkt, K. Dreßler, R. PinnauModel reduction of nonlinear problems in structural mechanicsKeywords: flexible bodies, FEM, nonlinear model reduc-tion, POD(13 pages, 2009)

Keywords: Fiber-fluid interaction, slender-body theory, turbulence modeling, model reduction, stochastic dif-ferential equations, Fokker-Planck equation, asymptotic expansions, parameter identification(21 pages, 2009)

157. E. Glatt, S. Rief, A. Wiegmann, M. Knefel, E. Wegenke

Structure and pressure drop of real and vir-tual metal wire meshesKeywords: metal wire mesh, structure simulation, model calibration, CFD simulation, pressure loss(7 pages, 2009)

158. S. Kruse, M. MüllerPricing American call options under the as-sumption of stochastic dividends – An ap-plication of the Korn-Rogers modelKeywords: option pricing, American options, dividends, dividend discount model, Black-Scholes model(22 pages, 2009)

159. H. Lang, J. Linn, M. ArnoldMultibody dynamics simulation of geomet-rically exact Cosserat rodsKeywords: flexible multibody dynamics, large deforma-tions, finite rotations, constrained mechanical systems, structural dynamics(20 pages, 2009)

160. P. Jung, S. Leyendecker, J. Linn, M. OrtizDiscrete Lagrangian mechanics and geo-metrically exact Cosserat rodsKeywords: special Cosserat rods, Lagrangian mechanics, Noether’s theorem, discrete mechanics, frame-indiffer-ence, holonomic constraints(14 pages, 2009)

161. M. Burger, K. Dreßler, A. Marquardt, M. Speckert

Calculating invariant loads for system simu-lation in vehicle engineeringKeywords: iterative learning control, optimal control theory, differential algebraic equations(DAEs)(18 pages, 2009)

162. M. Speckert, N. Ruf, K. DreßlerUndesired drift of multibody models excit-ed by measured accelerations or forcesKeywords: multibody simulation, full vehicle model, force-based simulation, drift due to noise(19 pages, 2009)

163. A. Streit, K. Dreßler, M. Speckert, J. Lichter, T. Zenner, P. Bach

Anwendung statistischer Methoden zur Erstellung von Nutzungsprofilen für die Auslegung von MobilbaggernKeywords: Nutzungsvielfalt, Kundenbeanspruchung,Bemessungsgrundlagen(13 pages, 2009)

164. I. Correia, S. Nickel, F. Saldanha-da-GamaAnwendung statistischer Methoden zur Er-stellung von Nutzungsprofilen für die Auslegung von MobilbaggernKeywords: Capacitated Hub Location, MIP formulations(10 pages, 2009)

165. F. Yaneva, T. Grebe, A. ScherrerAn alternative view on global radiotherapy optimization problemsKeywords: radiotherapy planning, path-connected sub-levelsets, modified gradient projection method, improv-ing and feasible directions(14 pages, 2009)

176. M. K. Ahmad, S. Didas, J. IqbalUsing the Sharp Operator for edge detec-tion and nonlinear diffusionKeywords: maximal function, sharp function,image pro-cessing, edge detection, nonlinear diffusion(17 pages, 2009)

177. M. Speckert, N. Ruf, K. Dreßler, R. Müller, C. Weber, S. Weihe

Ein neuer Ansatz zur Ermittlung von Er-probungslasten für sicherheitsrelevante BauteileKeywords: sicherheitsrelevante Bauteile, Kundenbean-spruchung, Festigkeitsverteilung, Ausfallwahrschein-lichkeit, Konfidenz, statistische Unsicherheit, Sicher-heitsfaktoren(16 pages, 2009)

178. J. JegorovsWave based method: new applicability areasKeywords: Elliptic boundary value problems, inho-mogeneous Helmholtz type differential equations in bounded domains, numerical methods, wave based method, uniform B-splines(10 pages, 2009)

179. H. Lang, M. ArnoldNumerical aspects in the dynamic simula-tion of geometrically exact rodsKeywords: Kirchhoff and Cosserat rods, geometri-cally exact rods, deformable bodies, multibody dynamics,artial differential algebraic equations, method of lines, time integration(21 pages, 2009)

180. H. LangComparison of quaternionic and rotation-free null space formalisms for multibody dynamicsKeywords: Parametrisation of rotations, differential-algebraic equations, multibody dynamics, con strained mechanical systems, Lagrangian mechanics (40 pages, 2010)

181. S. Nickel, F. Saldanha-da-Gama, H.-P. ZieglerStochastic programming approaches for risk aware supply chain network design problemsKeywords: Supply Chain Management, multi-stage sto-chastic programming, financial decisions, risk (37 pages, 2010)

182. P. Ruckdeschel, N. HorbenkoRobustness properties of estimators in gen-eralized Pareto ModelsKeywords: global robustness, local robustness, finite sample breakdown point, generalized Pareto distribution (58 pages, 2010)

183. P. Jung, S. Leyendecker, J. Linn, M. OrtizA discrete mechanics approach to Cosserat rod theory – Part 1: static equilibriaKeywords: Special Cosserat rods; Lagrangian mechan-ics; Noether’s theorem; discrete mechanics; frame-indifference; holonomic constraints; variational formu-lation(35 pages, 2010)

184. R. Eymard, G. PrintsyparA proof of convergence of a finite volume scheme for modified steady Richards’ equa-tion describing transport processes in the pressing section of a paper machineKeywords: flow in porous media, steady Richards’ equation, finite volume methods, convergence of approximate solution(14 pages, 2010)

185. P. RuckdeschelOptimally Robust Kalman FilteringKeywords: robustness, Kalman Filter, innovation outlier, additive outlier(42 pages, 2010)

186. S. Repke, N. Marheineke, R. PinnauOn adjoint-based optimization of a free surface Stokes flowKeywords: film casting process, thin films, free surface Stokes flow, optimal control, Lagrange formalism(13 pages, 2010)

187. O. Iliev, R. Lazarov, J. WillemsVariational multiscale Finite Element Method for flows in highly porous mediaKeywords: numerical upscaling, flow in heterogeneous porous media, Brinkman equations, Darcy’s law, subgrid approximation, discontinuous Galerkin mixed FEM(21 pages, 2010)

188. S. Desmettre, A. SzimayerWork effort, consumption, and portfolioselection: When the occupational choicemattersKeywords: portfolio choice, work effort, consumption, occupational choice(34 pages, 2010)

189. O. Iliev, Z. Lakdawala, V. StarikoviciusOn a numerical subgrid upscaling algorithm for Stokes-Brinkman equationsKeywords: Stokes-Brinkman equations, subgrid approach, multiscale problems, numerical upscaling(27 pages, 2010)

190. A. Latz, J. Zausch, O. IlievModeling of species and charge transport in Li-Ion Batteries based on non-equilibrium thermodynamicsKeywords: lithium-ion battery, battery modeling, elec-trochemical simulation, concentrated electrolyte, ion transport(8 pages, 2010)

191. P. Popov, Y. Vutov, S. Margenov, O. IlievFinite volume discretization of equationsdescribing nonlinear diffusion in Li-Ion bat-teriesKeywords: nonlinear diffusion, finite volume discretiza-tion, Newton method, Li-Ion batteries(9 pages, 2010)

192. W. Arne, N. Marheineke, R. WegenerAsymptotic transition from Cosserat rod to string models for curved viscous iner-tial jetsKeywords: rotational spinning processes; inertial and viscous-inertial fiber regimes; asymptotic limits; slender-body theory; boundary value problems(23 pages, 2010)

193. L. Engelhardt, M. Burger, G. BitschReal-time simulation of multibody-systems for on-board applicationsKeywords: multibody system simulation, real-time simu-lation, on-board simulation, Rosenbrock methods(10 pages, 2010)

Status quo: July 2010

EngelhardtBurgerBitsch_paper.pdfINTRODUCTIONBENCHMARK TRUCK MODELINTEGRATION METHODSODE Time Integration DAE Time IntegrationImplementation

SIMULATION RESULTSReal-time Simulation on MicrocontrollerReal-Time Simulation on Rapid Prototyping BoardsNumerical C-CodeSIMPACK ModelsSimMechanics Models

CONCLUSION