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G. Dimitroff, J. de Kock
Calibrating and completing the volatility cube in the SABR Model
Berichte des Fraunhofer ITWM, Nr. 202 (2011)
© Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM 2011
ISSN 1434-9973
Bericht 202 (2011)
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Prof. Dr. Dieter Prätzel-Wolters Institutsleiter
Kaiserslautern, im Juni 2001
Calibrating and Completing the Volatility Cube
in the SABR Model
Georgi DimitroffJohan de Kock
This report describes the calibration and completion of the volatility cubein the SABR model. The description is based on a project done for AssenagonGmbH in Munich. However, we use fictitious market data which resemblesrealistic market data. The problem posed by our client is formulated in section 1.Here we also motivate why this is a relevant problem. The SABR model is brieflyreviewed in section 2. Section 3 discusses the calibration and completion of thevolatility cube. An example is presented in section 4. We conclude by suggestingpossible future research in section 5.
1 Formulation of the Problem
We first review the interest rate market setup before we formulate the problemsolved. European options (calls and puts), being the most basic and liquidlytraded contracts, are the building blocks in the equity world. Central conceptslike implied volatility are defined with respect to equity options and theBlack-Scholes formula for pricing these options. The prices of European putsand calls are frequently quoted as implied volatilities, obtained by invertingthe Black-Scholes formula. Due to their liquidity, the prices of these optionsare available on the market. This is the reason why pricing models for exotic(illiquid) products are usually calibrated in such a way that these liquid callsand puts are priced consistently.
The interest rate world (or fixed income world), on the other hand,is characterized by a large number of diverse products. However, interestrate caps, interest rate floors and swaptions can (to a certain extent) beregarded as the equivalent of Europeans options in the interest rate world (seeBrigo and Mercurio [2]). These are the most liquid and nonlinear products inthe interest rate world and interest rate models are calibrated to consistenlyprice these instruments. In this report we focus on the swaption market.
We now consider swaptions more closely. Let Tm be the option maturityand Tm+1 < Tm+2 < · · · < Tn the payment dates of the swaption, wherem,n ∈ N. Thus, Tn − Tm is the swaption tenor and Tn the total maturity.A swaption with maturity Tm and tenor Tn−Tm is a contract allowing the holderto enter an interest rate swap with maturity Tn at time Tm. Such a swaptionis usually referred to as a Tm (Tn − Tm) swaption. The fixed leg is equal tothe strike K. The swaption is essentially a European call on the underlyinginterest rate swap. We assume that the payment dates are (taking the day countconvention into account) equidistant, ie Ti − Ti−1 = ∆t for i = m + 1, . . . , n.
1
The payoff of the swaption at time Tm is (see Filipovic [3])
N [r(Tm)−K]+∆tn∑
i=m+1
P (Tm, Ti),
where N is the notional, r(Tm) is the swap rate at time Tm and P (t, T ) isthe value (at time t) of a zero-coupon bond with maturity T . It is evidentthat the price of the swaption is the expectation of [r(Tm) −K]+. Therefore,the swaption can be interpreted as a European call on the underlying swap rater(Tm). The fair forward swap rate at time t is (see Brigo and and Mercurio [2],for example)
Smn(t) =P (t, Tm)− P (t, Tn)∆t∑ni=m+1 P (t, Ti)
.
Swaptions are usually priced with the interest rate equivalent of the Black-Scholes formula, namely the Black1 formula (see Black [1]). The swaptionvolatility, defined with respect to the Black formula, is a central quantity inthe interest rate world. Similar to the implied volatility in the equity world,the price of a swaption is frequently quoted in terms of the implied swaptionvolatility for the underlying swap rate.
Denote the implied swaption volatility2 for a Tm (Tn − Tm) swaption withstrike K by σmn(K). Thus the volatility is a function of the option maturity,tenor and strike. It has become common practice to order the implied swaptionvolatilities in a three-dimensional structure known as a volatility cube. The x-,y- and z-dimension of the volatility cube are option maturity, tenor and strikerespectively. Each point of the cube is the implied volatility for these threevalues, ie σmn(K) for Tm, Tn − Tm and K. One does not generally obtain acomplete cube from the market. Typically one would have all the volatilities forthe at-the-money (ATM) strike values. Therefore, the plane σmn(KATM) wouldbe complete for all typical values of Tm and Tn − Tm, where KATM is the ATMstrike. However, for other strike values K only some market quotes of σmn(K)would be available. Completing the volatility cube entails “determining”the missing values of σmn(K). An intuitive approach would be to interpolatebetween the known values. This would not work well in cases where few valuesare available, which is frequently the case (see the discussion in section 3 andthe example in section 4).
The aim of this project is to complete the volatility cube. The first deci-sion to be made is how to model the forward swap rate. The most importantrequirement on the model is that it captures the market smile and the marketskew. This is particularly important in the case of cube completion for tworeasons. The first reason is that the available volatility data contains smilesand skews. The second reason is that the (missing) values needed to completethe cube must also exhibit smiles and skews in order to be consistent with thegiven data, ie the neighboring points.
1Additional to its use in the interest rate world, the Black formula is also used extensivelyin the foreign exchange (FX) and commodity worlds.
2Note that although the implied swaption volatility is defined in the context of the Blackmodel, an implied volatility can also be extracted when a different model is used (as in theequity world). Consequently, the implied swaption volatility is the volatility which, whensubstituted into the Black formula yields the swaption price given by the chosen model.
2
Given the above-mentioned reasons, a stochastic volatility model seems tobe best-suited for modeling the forward swap rate. Such a model takes accountof smiles and skews. Furthermore, there is empirical evidence that the swaptionvolatility is stochastic (see Brigo and Mercurio [2], for example). An importantexample of a stochastic volatility model is the stochastic volatility enhancementof the popular BGM model3 (see Wu and Zhang [10], for example). Brigo andMercurio [2] list and cover several stochastic volatility models for the interestrate world. However, our client, Assenagon GmbH, wanted the SABR stochasticvolatility model. The next section discusses this model.
Before we proceed to present the SABR model, we shortly discuss the prac-tical relevance of the cube completion problem. Why should traders be thatinterested in having a complete volatility cube? There are two main answers tothis question. The first answer is that a complete cube contains valuable infor-mation on the current state of the market. A completed cube enables traders toconsistently quote swaptions different from the liquidly traded ones. The sec-ond answer is of a practical nature: most commercial interest rate software andmodeling tools require a complete cube as input data. Using this cube allowsus to price more exotic interest rate derivatives.
2 The SABR Model
The SABR4 model by Hagan, Kumar, Lesniewski and Woodward [5] (see alsoHagan and Lesniewski [6] and Hagan, Lesniewski and Woodward [7]) involvesthe modeling of the forward swap rate Smn(t).
The forward swap rate in the SABR model is assumed to evolve accordingto the stochastic differential equation (SDE)
dSmn(t) = Vmn(t) (Smn(t))βmn dWmn(t), (1)
where the stochastic volatility is modeled by the driftless SDE
dVmn(t) = σmnVmn(t)dZmn(t). (2)
The initial volatility is
Vmn(0) = v0mn. (3)
The correlation between the Wiener processes Wmn(t) and Zmn(t) is denotedby ρmn. The correlations between Wiener processes corresponding to differentmaturity-tenor pairs are not relevant for the completion of the cube. Therefore,we can consider Smn(t) and Vmn(t) in isolation.
In order to complete the volatility cube, we need an expression for the impliedswaption volatility σmn(K) in the SABR model. The remainder of this sectionis devoted to the derivation of an expression for σmn(K). The first step in doingthis is the derivation of an expression for the option price in the SABR model.
3This model is also known as the LIBOR market model.4SABR stands for Stochastic, Alpha, Beta and Rho (see Brigo and Mercurio [2]).
Note that the value v0mn in (3) is frequently denoted by α.
3
The second step is setting this option price equal to the option price in the Blackmodel and thus obtaining the implied volatility. We only perform the first stepand refer the reader to Hagan, Kumar, Lesniewski and Woodward [5] for thesecond step. The first step can again be divided into two parts. The first partis the derivation of a partial differential equation (PDE) for the call price. Wedo this in somewhat more detail than in [5]. However, the second part of thefirst step (solving the resulting PDE) is quite technical and not needed for theremainder of our analysis. Thus, we also refer the interested reader to Hagan,Kumar, Lesniewski and Woodward [5] for the solution of this PDE (8).
We now derive an expression for the price (at time t) of a European callC(t, T, S, V ) with maturity T . S is the forward rate at time t and V is thevolatility at time t. This is a call on the forward swap rate. As mentionedin section 1, it is market practice to price a swaption with a formula similarto Black’s formula (see Brigo and Mercurio [2]). Therefore, the price of a callon the forward swap rate corresponds to the price of a payer swaption. Thederivation is based on perturbation theory and our approach is similar to thatof Hagan, Kumar, Lesniewski and Woodward [5]. We omit the indices m and nto simplify notation and write the SABR SDEs as
dSt = VtSβt dWt
and
dVt = σVtdZt.
The correlation between the Wiener processes Wt and Zt is denoted by ρ. Weuse the perturbation parameter ε and define
σ :=σ
ε
and
Vt :=Vtε.
The SDEs now become
dSt = εVtSβt dWt
and
dVt = εσVtdZt.
We rewrite these SDEs in terms of independent Wiener processes Wt and Zt as
dSt = εVtSβt dWt (4)
and
dVt = εσVt
(ρdWt +
√1− ρ2dZt
). (5)
4
Let the transition probability density function be γ, then
γ(u,w, x1, x2, y1, y2)dy1dy2 =
P(y1 < Sw < y1 + dy1, y2 < Vw < y2 + dy2
∣∣∣ Su = x1, Vu = x2
),
where u ≤ w. γ satisfies the forward Kolmogorov equation (see Karartzas andShreve [8], for example)
∂
∂wγ(u,w, x1, x2, y1, y2) =
12∂2
∂y21
[ε2y2β
1 y22γ(u,w, x1, x2, y1, y2)
]+
12∂2
∂y22
[ε2σ2y2
2γ(u,w, x1, x2, y1, y2)]
+
∂2
∂y1∂y2
[ε2σyβ1 y
22ργ(u,w, x1, x2, y1, y2)
]=
12ε2y2
2
∂2
∂y21
[y2β1 γ(u,w, x1, x2, y1, y2)
]+
12ε2σ2 ∂
2
∂y22
[y22γ(u,w, x1, x2, y1, y2)
]+
ε2σρ∂2
∂y1∂y2
[yβ1 y
22γ(u,w, x1, x2, y1, y2)
], (6)
where we have used (4) and (5). We now turn to the call price, which is givenby
C(t, T, S, V ) = E(
[ST −K]+∣∣∣ St = S, Vt = V
)=∫ ∞−∞
∫ ∞K
(y1 −K)γ(t, T, S, V , y1, y2)dy1dy2
= [S −K]++∫ ∞−∞
∫ ∞K
∫ T
t
(y1 −K)∂
∂wγ(t, w, S, V , y1, y2)dwdy1dy2,
where we have used the fact that5
γ(u,w, x1, x2, y1, y2) = δ(y1 − x1)δ(y2 − x2) +∫ w
u
∂
∂sγ(u, s, x1, x2, y1, y2)ds.
However, since
0 =∫ ∞−∞
∂2
∂y22
[y22γ(u,w, x1, x2, y1, y2)
]dy2
and
0 =∫ ∞−∞
∂2
∂y1∂y2
[yβ1 y
22γ(u,w, x1, x2, y1, y2)
]dy2
5
(see Wu [11] or note that γ vanishes at infinity) we obtain
C(t, T, S, V ) = [S −K]++
12ε2∫ ∞−∞
∫ ∞K
∫ T
t
(y1 −K)y22
∂2
∂y21
[y2β1 γ(t, w, S, V , y1, y2)
]dwdy1dy2
by substituting (6) into the equation for the call price. Furthermore, integrationby parts yields
y22K
2βγ(u,w, x1, x2,K, y2) =∫ ∞K
y22(y1 −K)
∂2
∂y21
[y2β1 γ(u,w, x1, x2, y1, y2)
]dy1.
Therefore, the call price is given by
C(t, T, S, V ) = [S −K]++
12ε2K2β
∫ ∞−∞
∫ T
t
y22γ(t, w, S, V ,K, y2)dwdy2,
where we have changed the order of integration. Let
Γ(u,w, x1, x2) :=∫ ∞−∞
y22γ(u,w, x1, x2,K, y2)dy2(
= E(V 2w | Su = x1, . . .
)),
where u ≤ w, then the call price can be expressed as
C(t, T, S, V ) = [S −K]+ +12ε2K2β
∫ T
t
Γ(t, w, S, V )dw, (7)
where we have again changed the order of integration. Γ satisfies the Feynman-Kac formula (see Karartzas and Shreve [8], for example)
− ∂
∂uΓ(u, t, x1, x2) =
12ε2x2β
1 x22
∂2
∂x21
Γ(u, t, x1, x2)+
12ε2σ2x2
2
∂2
∂x22
Γ(u, t, x1, x2)+
ε2σρxβ1x22
∂2
∂x1∂x2Γ(u, t, x1, x2) (8)
with the boundary condition
Γ(t, t, x1, x2) = x22δ(x1 −K).
We omit the detail of solving this PDE since the solution steps are quite tech-nical and do not contribute to understanding the model. See Hagan, Kumar,Lesniewski and Woodward [5] for the solution details. Substituting the solutionof (8) into (7), one obtains
C(t, T, S, V ) = [S −K]+ +|S −K|
4√π
∫ ∞a
q−32 e−qdq,
6
where
a := − ln(S1−β −K1−β
(S −K)(1− β)(KS)
β2
)− ln b−
14ε2ρV σc+
d
2T.
The expressions for b, c and d are quite involved and since they are not directlyneeded in the remainder of this report, we refer the reader to Hagan, Kumar,Lesniewski and Woodward [5].
Using the same technique to derive the option price in the Black setup, onecan equate the call prices in the two models (SABR and Black) to obtain anapproximate expression for σ. Re-introducing the indices m and n and stressingthe strike-dependence K, one obtains the formula
σmn(K) ≈ v0mn
[1 +
(1− β)2
24
(lnSmn(0)K
)2
+(1− β)4
1920
(lnSmn(0)K
)4]−1
·
(Smn(0)K)−1−β
2z
x(z)
{1 +
[(1− β)2
(v0mn
)224 (Smn(0)K)1−β
+
ρmnβmnσmnv0mn
4 (Smn(0)K)1−β
2
+ σ2mn
2− 3ρ2mn
24
]Tm
}, (9)
where
z :=σmnv0mn
(Smn(0)K)1−β
2 lnSmn(0)K
and
x(z) := ln
√1− 2ρmnz + z2 + z − ρmn
1− ρmn.
Note that only terms of order O(ε2) have been included. Furthermore, ε wasset to one to recover Vt and σ from Vt and σ. The formula above is the versionfound in Mercurio and Pallavicini [9].
Although (9) is an approximate formula, we shall ignore the approximatesign and consider the expression on the right-hand side of (9) as the impliedvolatility. In order to distinguish between the model implied volatility σmn(K)and the market-quoted implied volatility, we shall denote the latter by σmn(K)(not to be confused with the perturbation volatility σ without indices).
3 Calibrating the Model and Completing theCube
The aim of this project is to complete the volatility cube. As pointed out insection 1, the x-, y- and z-dimension of the volatility cube are option maturity,
5δ denotes the Dirac delta.
7
tenor and strike respectively. Each point of the cube is the implied volatilityfor these three values, ie σmn(K) (from equation (9)) for Tm, Tn − Tm and Kin the case of the SABR model. As pointed out in section 1, one generally onlyhas a complete σmn(KATM)-plane for all typical values of Tm and Tn−Tm. Onereason why one cannot simply interpolate between the given volatility valuesto find the missing ones, is the sparseness of the given cube. For many strikevalues K there are so few points σmn(K) known that it defeats the concept ofinterpolation. A second reason is the nonlinear structure. For fixed values of mand n, the mapping K 7→ σmn(K) is anything but flat. It is rather parabolic.This is known as the volatility smile. One can also view it on a surface level.Each plane σmn(K) (where K remains fixed) can be mapped onto a volatilitysurface6. The x- and y-dimension of the surface are the option maturity andtenor respectively. The z-dimension is the value σmn(K). The volatility surfaceis usually far from being flat. The modeling of the volatility surface is anactive area of research and there are entire books (see Gatheral [4], for example)devoted to this topic. The volatility surface is basically a “landscape” withmountains and valleys. Therefore, interpolation will (in most cases) deliverbad results. Knowing only a few points of this landscape, it is impossible todeduce exactly where the mountains and valleys start and end or how highthe mountains are and how low the valleys are. Consequently, interpolationmakes no sense at all. Therefore, we have decided to calibrate an entire SABRmodel for each pair (m,n) corresponding to fixed values of Tm and Tn − Tmand all values of K. In the landscape analogy this means that we fix the x-and y-coordinates of a point and calibrate its “height” in all the landscapessimultaneously.
It is evident from the SABR model description (1), (2) and (3), that fourparameters need to be calibrated. Hagan and Lesniewski [6] suggest fixing oneof the parameters ρmn (or βmn) and calibrating the remaining three parametersσmn, v0
mn and βmn (or ρmn). We have experimented with this approach andobtained the best results when βnm was fixed at 0.5.
The first step is to determine the pair (m,n) with the largest number ofmarket-quoted volatilities. That is the swaption with option maturity Tm andtenor Tn−Tm for which σmn(K) is available for the largest number of differentstrikes K. Once this pair (m′, n′) has been found, σm′n′ , v0
m′n′ and ρm′n′ arecalibrated by means of the least-squares method7.
The second step is to calibrate the entire maturity-tenor grid, keeping thematurity fixed and calibrating for each tenor. For each maturity we start bycalibrating the tenor with the largest number of quoted volatilities. The startingvalues of σmn, v0
mn and ρmn for each pair (m,n) are the values calibrated forthe previous pair. The values σm′n′ , v0
m′n′ and ρm′n′ are used for calibratingthe very first pair.
A smoothness parameter is applied to the calibration of each pair (m,n)for which few quotes are available. These are typically the pairs for which weonly have ATM market volatilities. The smoothness parameter prevents thecalibrated parameters from moving too far away from the initial values.
We have also implemented a second approach which differs from the ap-6This volatility surface is not the same as the volatility surface in the equity world where
the x- and y-dimension of the surface are the strike and maturity.7This implies that the volatilies calculated using (9) are fitted to the market volatilitieseσmn(K).
8
proach above in the calibration of the pairs (m,n) for which several marketquotes are available. The parameters for such a pair are calibrated severaltimes. Thus, we calibrate the parameters and then calibrate again using thecurrent values as the starting values.
4 Example
We now apply the procedure from section 3 to fictituous data resembling actualmarket data from September 2010. The payment frequency is quarterly, ie∆t = 0.25. Figure 1 is a plot the ATM (fictituous) market volatility surface.The z-dimension is the volatility in percentage. We have the complete ATMvolatility surface, which is frequently the case.
1020304050
1m
20y 1y
30y
Option Maturity
Tenor
Figure 1: The Market ATM Volatility Surface
We calibrate the data using the second approach described in section 3. Fig-ure 2 is a plot of the ATM volatility surface resulting from our cube completion.As mentioned in section 3, we fix a point (m,n) and calibrate the SABR modelon all strikes simultaneously. Thus, after having considered every point (m,n)all volatility surfaces have been calibrated. Therefore, the ATM volatility sur-face (which we also have as input data) is a “by-product” of the calibrationprocedure. Since we know what it should look like (figure 1), the calibratedATM surface is a good test of our calibration ansatz. Comparing figures 1 and2, one observes that the two surfaces are almost identical. We can conclude thatour calibration procedure can fit the ATM volatilities very accurately.
We now turn to one of the volatility surfaces for which we have very few
9
1020304050
1m
20y 1y
30y
Option Maturity
Tenor
Figure 2: The Calibrated ATM Volatility Surface
points (volatility values). Figure 3 is a plot of the completed volatility surface(produced by our method) for a strike which is 25 basis points from the ATMstrike. Although the shape is plausible, this surface is not as smooth as the ATMsurface in figure 2. The reason for this is that our client wanted a completedvolatility cube to use as the input to existing valuation software. The accuracy ofthe volatility values is more important than the smoothness of the surface in thiscase. A smoother surface be obtained by using stricter smoothing parameters.
5 Conclusion
The method described in this report has been implemented in Matlab. Acorresponding Excel sheet, which communicates with Matlab via the ExLinkadd-in, has also been created. An important trade-off in the implementation isbetween the smoothness of the resulting volatility surfaces and the accuracy ofthe calibration. Accuracy in this context refers to the extent to which the knownvolatilities are matched by the calibrated surfaces. We have mainly stressed thequality in the example of section 4. An interesting area of future research mightbe determining an optimal trade-off between smoothness and accuracy.
An important advantage of this approach is that the produced volatilitysurface is free of arbitrage for fixed tenor and maturity. This means that foreach volatility curve (m,n), the mapping K 7→ σmn(K) is arbitrage-free andtherefore traders can safely quote prices along this curve. The input values wehave used in the example were arbritrage-free. However, frequently market data
10
102030405060
1m
20y 1y
30y
Option Maturity
Tenor
Figure 3: The Calibrated Volatility Surface (Strike = 25 bps)
contains arbitrage.Another interesting area for future research is exploring arbitrage opportu-
nities accross maturities and tenors in order to implement restrictions on themodel which result in a completely arbitrage-free cube.
11
References
[1] F Black. The Pricing of Commodity Contracts. Journal of Financial Eco-nomics, 3:167–179, 1976.
[2] D Brigo and F Mercurio. Interest Rate Models – Theory and Practice: WithSmile, Inflation and Credit. Springer-Verlag, Berlin, 2006.
[3] D Filipovic. Term-Structure Models – A Graduate Course. Springer-Verlag,Berlin, 2009.
[4] J Gatheral. The Volatility Surface. John Wiley & Sons, Hoboken, NewJersey, 2006.
[5] PS Hagan, D Kumar, AS Lesniewski, and DE Woodward. Managing SmileRisk. Wilmott, 2002.
[6] PS Hagan and AS Lesniewski. LIBOR Market Model with SABR StyleStochastic Volatility. Working Paper, 2006.
[7] PS Hagan, AS Lesniewski, and DE Woodward. Probability Distribution inthe SABR Model of Stochastic Volatility. 2005.
[8] I Karatzas and SE Shreve. Brownian Motion and Stochastic Calculus.Springer-Verlag, New York, 1991.
[9] F Mercurio and A Pallavicini. Swaption, Skews and Convexity Adjust-ments. Working Paper, 2005.
[10] L Wu and F Zhang. LIBOR Market Model with Stochastic Volatility.Journal of Industrial and Management Optimization, 2(2):199–227, 2006.
[11] Q Wu. Series Expansion of the SABR Joint Density. Working Paper, 2010.
12
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The PDF-files of the following reports are available under: www.itwm.fraunhofer.de/de/zentral__berichte/berichte
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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, 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. Mladenovic , 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-GamaThe capacitated single-allocation hub loca-tion problem revisited: A note on a classical formulationKeywords: 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)
194. M. Burger, M. Speckert, K. DreßlerOptimal control methods for the calculation of invariant excitation signals for multibody systemsKeywords: optimal control, optimization, mbs simula-tion, invariant excitation(9 pages, 2010)
195. A. Latz, J. ZauschThermodynamic consistent transport theory of Li-Ion batteriesKeywords: Li-Ion batteries, nonequilibrium thermody-namics, thermal transport, modeling(18 pages, 2010)
196. S. DesmettreOptimal investment for executivestockholders with exponential utilityKeywords: portfolio choice, executive stockholder, work effort, exponential utility(24 pages, 2010)
197. W. Arne, N. Marheineke, J. Schnebele, R. Wegener
Fluid-fiber-interactions in rotational spin-ning process of glass wool productionKeywords: Rotational spinning process, viscous thermal jets, fluid-fiber-interactions, two-way coupling, slender-body theory, Cosserat rods, drag models, boundary value problem, continuation method(20 pages, 2010)
198. A. Klar, J. Maringer, R. WegenerA 3d model for fiber lay-down in nonwovenproduction processesKeywords: fiber dynamics, Fokker-Planck equations, diffusion limits(15 pages, 2010)
199. Ch. Erlwein, M. MüllerA regime-switching regression model for hedge fundsKeywords: switching regression model, Hedge funds, optimal parameter estimation, filtering(26 pages, 2011)
200. M. DalheimerPower to the people – Das Stromnetz der ZukunftKeywords: Smart Grid, Stromnetz, Erneuerbare Ener-gien, Demand-Side Management(27 pages, 2011)
201. D. Stahl, J. HauthPF-MPC: Particle Filter-Model Predictive ControlKeywords: Model Predictive Control, Particle Fil-ter, CSTR, Inverted Pendulum, Nonlinear Systems, Sequential Monte Carlo(40 pages, 2011)
202. G. Dimitroff, J. de KockCalibrating and completing the volatility cube in the SABR ModelKeywords: stochastic volatility, SABR, volatility cube, swaption(12 pages, 2011)
Status quo: February 2011
