@techreport{Deiterding, author = {Deiterding, Ralf}, title = {Simulation of a shock tube experiment with non-equilibirum chemistry}, address = {Cottbus}, abstract = {The ignition process of a hydrogen-oxygen-argon mixture in a shock tube is simulated. The document describes a reactive test case of the DFG high priority research program "Analysis und Numerics of Conservation laws".}, language = {en} } @techreport{Deiterding, author = {Deiterding, Ralf}, title = {Simulation eines Stoßrohrexperiments mit Nichtgleichgewichtschemie}, address = {Cottbus}, abstract = {Der Entz{\"u}ndungsvorgang eines Wasserstoff-Sauerstoff-Argon-Gemisches in einem Stoßrohr wird simuliert. Das Dokument beschreibt einen reaktiven Testfall der DFG-Schwerpunktprogramms "Analysis und Numerik von Erhaltungsgleichungen".}, language = {de} } @inproceedings{Deiterding, author = {Deiterding, Ralf}, title = {Accurate Simulation of Rayleigh-Taylor instabilities}, series = {Proceedings, Colloquium Fluid Dynamics '99, Prague, 19 - 20.10.1999}, booktitle = {Proceedings, Colloquium Fluid Dynamics '99, Prague, 19 - 20.10.1999}, publisher = {Acad. of Sciences of the Czech Republic, Inst. of Thermodynamics}, address = {Prague}, isbn = {80-85918-52-8}, pages = {37 -- 44}, abstract = {We derive a modification of the wave propagation proposed by R. J. LeVeque to accurately capture the behaviour of quasi-steady flows to the case of the Euler equations undergravitational influence and apply it to flows of two nonmixing ideal gases. We present results of a numerical simulation of the behaviour of an instable interface between two gases driven by the standard gravitational field (Rayleigh-Taylor-instability).}, language = {en} } @inproceedings{BaderDeiterding, author = {Bader, Georg and Deiterding, Ralf}, title = {A distributed memory adaptive mesh refinement package for inviscid flow simulations}, series = {Proceedings, Colloquium Fluid Dynamics '99, Prague, 19 - 20.10.1999}, booktitle = {Proceedings, Colloquium Fluid Dynamics '99, Prague, 19 - 20.10.1999}, publisher = {Acad. of Sciences of the Czech Republic, Inst. of Thermodynamics}, address = {Prague}, isbn = {80-85918-52-8}, pages = {9 -- 14}, abstract = {An object-oriented implementation in C++ of the Berger-Oliger adaptive mesh refinement algorithm for hyperbolic conservation laws is described. The software design is tailored especially for distributed memory super-computers. An examplary computation for the standard inviscid Euler equations is shown.}, language = {en} } @inproceedings{Deiterding, author = {Deiterding, Ralf}, title = {Efficient simulation of multi-dimensional detonation phenomena}, abstract = {The paper presents a solution strategy for Euler equations for multiple thermally perfect gaseous species with detailed chemical reaction. Via operator-splitting a high-resolution finite-volume scheme and a stiff ODE solver are coupled. A parallel blockstructured adaptive mesh refinement algorithm is utilized to achieve the required local resolution. A highly resolved computation of regular detonation-cell patterns of the hydrogen-oxygen-argon system demonstrates the efficiency of the entire approach.}, language = {en} } @phdthesis{Berti, author = {Berti, Guntram}, title = {Generic Software Components for Scientific Computing}, publisher = {dissertation.de}, address = {Berlin}, isbn = {3-89825-169-1}, pages = {250 S.}, language = {en} } @inproceedings{Berti, author = {Berti, Guntram}, title = {A calculus for stencils on arbitrary grids with applications to parallel PDE solution}, language = {en} } @inproceedings{Berti, author = {Berti, Guntram}, title = {A Generic Toolbox for the Grid Craftsman}, series = {Proceedings 17. GAMM-Seminar on Construction of Grid Generation Algorithms}, booktitle = {Proceedings 17. GAMM-Seminar on Construction of Grid Generation Algorithms}, editor = {Hackbusch, Wolfgang}, publisher = {Max-Planck-Institute for Mathematics in the Sciences}, address = {Leipzig}, isbn = {3-00-007753-7}, language = {en} } @phdthesis{Kemm, author = {Kemm, Friedemann}, title = {Divergenzkorrekturen und asymptotische Untersuchungen bei der numerischen Simulation idealer magnetohydrodynamischer Str{\"o}mungen}, address = {Stuttgart}, url = {http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-27335}, language = {de} } @article{Kemm, author = {Kemm, Friedemann}, title = {Magnetische Ladungen oder, warum es manchmal sinnvoll ist, etwas mathematisch zu modellieren, was es gar nicht gibt}, language = {de} } @incollection{KemmLeeSchneider, author = {Kemm, Friedemann and Lee, Yong-Joong and Schneider, Rudolf}, title = {Hyperbolic GLM scheme for elliptic constraints in computational electromagnetics and MHD}, language = {en} } @incollection{Bader, author = {Bader, Georg}, title = {High-Resolution Simulation of Detonations with Detailed Chemistry}, language = {en} } @inproceedings{RieperBader, author = {Rieper, Felix and Bader, Georg}, title = {Consistency of the Explicit Roe Scheme for Low Mach number flows in Exterior Domains}, series = {Hyperbolic problems, Proceedings of the XIth International Conference on Hyperbolic Problems held in Ecole Normale Sup{\´e}rieure, Lyon, July 17-21, 2006}, booktitle = {Hyperbolic problems, Proceedings of the XIth International Conference on Hyperbolic Problems held in Ecole Normale Sup{\´e}rieure, Lyon, July 17-21, 2006}, publisher = {Springer}, address = {Heidelberg [u.a.]}, isbn = {3-540-75711-2}, pages = {883 -- 890}, abstract = {We show the consistency of the explicit Roe scheme with the asymptotic Euler equations for low Mach numbers.}, language = {en} } @phdthesis{Rieper, author = {Rieper, Felix}, title = {On the behaviour of numerical schemes in the low mach number regime}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus-5747}, language = {en} } @misc{RieperBader, author = {Rieper, Felix and Bader, Georg}, title = {The influence of cell geometry on the accuracy of upwind schemes in the low mach number regime}, abstract = {AbstractIt is well known, that standard upwind schemes for the Euler equations face a number of problems in the low Mach number regime: stiffness, cancellation and accuracy problems. A new aspect, presented in this paper, is the dependence on the cell geometry: applied on a triangular grid, the accuracy problem disappears, i.e. flows of arbitrarily small Mach numbers can be simulated on a fixed mesh. We give an asymptotic analysis of this, up to date unknown, phenomenon for the first-order Roe scheme and present a number of numerical results.Keywords: Incompressible and compressible flow; Euler equations; Low Mach number flow; Roe scheme; Numerical dissipation; Asymptotic analysisPACS classification codes: 47.11.Df; 47.11.\%26\#8722;j; 47.15.G\%26\#8722;; 47.15.km}, language = {en} } @inproceedings{Kemm, author = {Kemm, Friedemann}, title = {A carbuncle free Roe-type solver for the Euler equations}, series = {Hyperbolic problems, proceedings of the Eleventh International Conference on Hyperbolic Problems, held in Ecole Normale Sup{\´e}rieure, Lyon, July 17 - 21, 2006}, booktitle = {Hyperbolic problems, proceedings of the Eleventh International Conference on Hyperbolic Problems, held in Ecole Normale Sup{\´e}rieure, Lyon, July 17 - 21, 2006}, editor = {Benzoni-Gavage, Sylvie}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {3-540-75711-2}, pages = {601 -- 608}, abstract = {Based on the idea of the HLLEM scheme, we propose a novel ansatz to cure the well known carbuncle instability. Instead of testing all neighboring cells for strong shocks we test the Riemann problem for contact and shear waves. As an indicator we suggest the residual of the Rankine-Hugoniot condition for the linear waves. By using known approaches, we can apply a well tempered amount of viscosity for the contact and shear waves of the Roe and HLLEM methods. The resulting Riemann solver approximates contact and shear waves exactly. However, according to the chosen value of a parameter, the Carbuncle phenomenon can be completely avoided.}, language = {en} } @misc{KleefeldReissel, author = {Kleefeld, Andreas and Reißel, Martin}, title = {The Levenberg-Marquardt method applied to a parameter estimation problem arising from electrical resistivity tomography}, series = {Journal of Applied Mathematics and Computation}, volume = {217}, journal = {Journal of Applied Mathematics and Computation}, number = {9}, issn = {0096-3003}, pages = {4490 -- 4501}, abstract = {An efficient and robust electrical resistivity tomographic inversion algorithm based on the Levenberg-Marquardt method is considered to obtain quantities like grain size, source discrimination and particle size distribution. The corresponding model in two-dimensions is based on the Maxwell equations and leads to a partial differential equation with mixed Dirichlet-Neumann boundary conditions. The forward problem is solved numerically with the finite-difference method. However, the inverse problem at hand is a classic nonlinear and ill-posed parameter estimation problem. Linearizing it and applying the Tikhonov regularization method yields an iterative scheme, the Levenberg-Marquardt method. Several systems of equations of large size have to be solved efficiently in each iteration step which is accomplished by the conjugate gradient method without setting up the corresponding matrix. Instead fast matrix-vector multiplications are performed directly. Therefore, the derivative and its adjoint for the parameter-to-solution map are needed. Numerical results demonstrate the performance of our method as well as the possibility to reconstruct some of the desired parameters.}, language = {en} } @inproceedings{Kemm, author = {Kemm, Friedemann}, title = {Discrete Involutions, Resonance, and the Divergence Problem in MHD}, series = {Hyperbolic problems, proceedings of the 12th international conference on hyperbolic problems, June 9-13, 2008}, booktitle = {Hyperbolic problems, proceedings of the 12th international conference on hyperbolic problems, June 9-13, 2008}, editor = {Tadmor, Eitan}, publisher = {American Mathematical Society}, address = {Providence, RI}, isbn = {978-0-8218-4730-5}, pages = {725 -- 735}, language = {en} } @misc{KleefeldBrazauskas, author = {Kleefeld, Andreas and Brazauskas, Vytaras}, title = {Folded and log-folded-t distributions as models for insurance loss data}, doi = {http://www.tandfonline.com/doi/abs/10.1080/03461230903424199}, abstract = {A rich variety of probability distributions has been proposed in the actuarial literature for fitting of insurance loss data. Examples include: lognormal, log-t, various versions of Pareto, loglogistic, Weibull, gamma and its variants, and generalized beta of the second kind distributions, among others. In this paper, we supplement the literature by adding the log-folded-normal and log-folded-t families. Shapes of the density function and key distributional properties of the ‘folded’ distributions are presented along with three methods for the estimation of parameters: method of maximum likelihood; method of moments; and method of trimmed moments. Further, large and small-sample properties of these estimators are studied in detail. Finally, we fit the newly proposed distributions to data which represent the total damage done by 827 fires in Norway for the year 1988. The fitted models are then employed in a few quantitative risk management examples, where point and interval estimates for several value-at-risk measures are calculated.}, language = {en} } @misc{Kleefeld, author = {Kleefeld, Andreas}, title = {Linear Fredholm integral equations of the first kind over surfaces in 3D}, abstract = {Linear Fredholm integral equations of the first kind over surfaces are less familiar than those of the second kind, although they arise in many applications like computer tomography, heat conduction and inverse scattering. This article emphasizes their numerical treatment, since discretization usually leads to ill-conditioned linear systems. Strictly speaking, the matrix is nearly singular and ordinary numerical methods fail. However, there exists a numerical regularization method - the Tikhonov method - to deal with this ill-conditioning and to obtain accurate numerical results.}, language = {en} } @misc{KleefeldLin, author = {Kleefeld, Andreas and Lin, Tzu-Chu}, title = {The nonlinear Landweber method applied to an inverse scattering problem for sound-soft obstacles in 3D}, abstract = {The inverse scattering problem for sound-soft obstacles is considered for both smooth and piecewise smooth surfaces in 3D. The nonlinear and ill-posed integral equation of the first kind is solved by the nonlinear Landweber method. It is an iterative regularization scheme to obtain approximations for the unknown boundary of the obstacle. It is stable with respect to noise and essentially no extra work is required to incorporate several incident waves. So far, it has only been applied to the two dimensional case. Two different integral equations are presented to obtain far-field data. Furthermore, the domain derivative and its adjoint are characterized. The integral equations of the second kind are approximated by a boundary element collocation method. The two-grid method is used to solve the large and dense linear systems. Numerical examples are illustrated to show that both smooth and piecewise smooth obstacles can be reconstructed with this method, where the latter case has not yet been reported.}, language = {en} } @misc{KleefeldLin, author = {Kleefeld, Andreas and Lin, Tzu-Chu}, title = {Boundary element collocation method for solving the exterior Neumann problem for Helmholtz's equation in three dimensions}, series = {Electronic transactions on numerical analysis}, volume = {39}, journal = {Electronic transactions on numerical analysis}, issn = {1068-9613}, pages = {113 -- 143}, abstract = {We describe a boundary integral equation that solves the exterior Neumann problem for the Helmholtz equation in three dimensions. The unique solution is found by approximating a Fredholm integral equation of the second kind with the boundary element collocation method. We prove uperconvergence at the collocation points, distinguishing the cases of even and odd interpolation. Numerical examples demonstrate the performance of the method solving the integral equation and confirm the superconvergence.}, language = {en} } @misc{Kleefeld, author = {Kleefeld, Andreas}, title = {The transmission problem for the Helmholtz equation in R³}, series = {Computational Methods in Applied Mathematics}, volume = {12}, journal = {Computational Methods in Applied Mathematics}, number = {3}, issn = {1609-4840}, pages = {330 -- 350}, abstract = {The problem under consideration is the three-dimensional transmission problem for time harmonic acoustic waves for two homogeneous media. A simply-connected and bounded region with sufficiently smooth boundary is immersed in an infinite medium. Each medium is c haracterized by the space independent wave number κ and the density μ. The system of boundary integral equations is reviewed as well as an existence and uniqueness result. The system is approximated by the boundary element collocation method and consistency, stability, and convergence is proved. In addition, superconvergence is proved and numerical results illustrate the agreement with these theoretical results. No numerical results seem to be reported for this method yet.}, language = {en} } @misc{Kleefeld, author = {Kleefeld, Andreas}, title = {A modified boundary integral equation for solving the exterior Robin problem for the Helmholtz equation in three dimensions}, series = {Applied Mathematics and Computation}, volume = {2012}, journal = {Applied Mathematics and Computation}, number = {219}, issn = {0096-3003}, doi = {10.1016/j.amc.2012.08.055}, pages = {2114 -- 2123}, abstract = {A boundary integral equation with modified fundamental solution to solve the exterior Robin problem for Helmholtz's equation is considered. A specific choice of the coefficients of these added terms ensure the unique solvability and, in addition, they can be chosen to ensure the minimization of the least-squares difference of the modified and the exact Green's function or the minimization of the condition number. Numerical results are reported showing the robustness and the superconvergence of the new method.}, language = {en} } @misc{Kemm, author = {Kemm, Friedemann}, title = {A comparative study of TVD limiters - well known limiters and an introduction of new ones}, series = {International Journal for Numerical methods in Fluids}, volume = {67}, journal = {International Journal for Numerical methods in Fluids}, number = {4}, doi = {10.1002/fld.2357}, pages = {404 -- 440}, abstract = {This paper gives a comparative study of TVD-limiters for standard explicit Finite Volume schemes. In contrast to older studies it includes also unsymmetrical limiter functions which depend on the local CFL-number. We classify the limiters and show how to extend these families of limiters. We introduce a new member of the Superbee family, which is adapted to Roe's linear third-order scheme. Based on an idea by Serna and Marquina, new smooth limiters are introduced, which turn the van~Leer and van~Albada limiters into complete classes of limiters. The comparison of the limiters is done with some standard test cases. The results clarify the influence of the chosen limiter on the quality of the numerical results. Compared to ENO or WENO schemes, they also show the high resolution, which can be obtained by a CFL-number dependent limiter when the grid is not highly refined.}, language = {en} } @misc{KleefeldBrazauskas, author = {Kleefeld, Andreas and Brazauskas, Vytaras}, title = {A statistical application of the quantile mechanics approach: MTM estimators for the parameters of t and gamma distribution}, series = {European Journal of Applied Mathematics}, volume = {23}, journal = {European Journal of Applied Mathematics}, number = {5}, issn = {0956-7925}, doi = {10.1017/S0956792512000137}, pages = {593 -- 610}, abstract = {In this paper, we revisit the quantile mechanics approach, which was introduced by Steinbrecher and Shaw (Steinbrecher, G. \& Shaw, W. T. (2008) Quantile mechanics. European. J. Appl. Math. 19, 87-112). Our objectives are (i) to derive the method of trimmed moments (MTM) estimators for the parameters of gamma and Student's t distributions, and (ii) to examine their large- and small-sample statistical properties. Since trimmed moments are defined through the quantile function of the distribution, quantile mechanics seems like a natural approach for achieving objective (i). To accomplish the second goal, we rely on the general large sample results for MTMs, which were established by Brazauskas et al. (Brazauskas, V., Jones, B. L. \& Zitikis, R. (2009) Robust fitting of claim severity distributions and the method of trimmed moments. J. Stat. Plan. Inference 139, 2028-2043), and then use Monte Carlo simulations to investigate small-sample behaviour of the newly derived estimators. We find that, unlike the maximum likelihood method, which usually yields fully efficient but non-robust estimators, the MTM estimators are robust and offer competitive trade-offs between robustness and efficiency. These properties are essential when one employs gamma or Student's t distributions in such outlier-prone areas as insurance and finance.}, language = {en} } @misc{KleefeldKirsch, author = {Kleefeld, Andreas and Kirsch, Andreas}, title = {The factorization method for a conductive boundary condition}, series = {Journal of Integral Equations and Applications}, volume = {24}, journal = {Journal of Integral Equations and Applications}, number = {4}, issn = {0897-3962}, doi = {10.1216/JIE-2012-24-4-575}, pages = {575 -- 601}, abstract = {In this article, the inverse scattering problem for obstacles with conductive boundary conditions is considered. The problem at hand is solved with the Factorization Method; that is, the operator and its factorization is derived. To obtain generic far field data for several obstacles the boundary element method is employed to solve the integral equation numerically. The far field data are highly accurate due to superconvergence. Finally, we show that we are able to reconstruct several obstacles and thus confirm the validity of the new operator factorization.}, language = {en} } @inproceedings{Kemm, author = {Kemm, Friedemann}, title = {CFL-Number-dependent TVD-Limiters}, series = {Numerical Methods for Hyperbolic Equations: Theory and Applications}, booktitle = {Numerical Methods for Hyperbolic Equations: Theory and Applications}, editor = {V{\´a}zquez-Cend{\´o}n, Elena and Hidalgo, Arturo and Garc{\´i}a-Navarro, Pilar and Cea, Luis}, publisher = {CRC Press, Taylor \& Francis Group}, address = {London}, isbn = {978-0-415-62150-2}, pages = {277 -- 283}, abstract = {In this paper, we show how algebraic limiting and limiters which take into account the local CFL-number lead to a significant increase in accuracy. Furthermore, we show how these limiters can be easily adapted to the nonlinear TVD-condition by Jeng and Payne.}, language = {en} } @misc{Kleefeld, author = {Kleefeld, Andreas}, title = {The exterior problem for the Helmholtz equation with mixed boundary conditions in three dimensions}, series = {International Journal of Computer Mathematics}, volume = {89}, journal = {International Journal of Computer Mathematics}, number = {17}, issn = {0020-7160}, doi = {10.1080/00207160.2012.709932}, pages = {2392 -- 2409}, abstract = {In this article, a new integral equation is derived to solve the exterior problem for the Helmholtz equation with mixed boundary conditions in three dimensions, and existence and uniqueness is proven for all wave numbers. We apply the boundary element collocation method to solve the system of Fredholm integral equations of the second kind, where we use constant interpolation. We observe superconvergence at the collocation nodes and illustrate it with numerical results for several smooth surfaces.}, language = {en} } @incollection{KleefeldBurgeth, author = {Kleefeld, Andreas and Burgeth, Bernhard}, title = {Morphology for Color Images via Loewner Order for Matrix Fields}, series = {Mathematical Morphology and Its Applications to Signal and Image Processing}, booktitle = {Mathematical Morphology and Its Applications to Signal and Image Processing}, editor = {Hendriks, Cris L. Luengo and Borgefors, Gunilla and Strand, Robin}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-38293-2}, doi = {10.1007/978-3-642-38294-9_21}, pages = {243 -- 254}, abstract = {Mathematical morphology is a very successful branch of image processing with a history of more than four decades. Its fundamental operations are dilation and erosion, which are based on the notion of a maximum and a minimum with respect to an order. Many operators constructed from dilation and erosion are available for grey value images, and recently useful analogs of these processes for matrix-valued images have been introduced by taking advantage of the so-called Loewner order. There has been a number of approaches to morphology for vector-valued images, that is, colour images based on various orders, however, each with its merits and shortcomings. In this article we propose an approach to (elementary) morphology for colour images that relies on the existing order based morphology for matrix fields of symmetric 2×2-matrices. An RGB-image is embedded into a field of those 2×2-matrices by exploiting the geometrical properties of the order cone associated with the Loewner order. To this end a modification of the HSL-colour model and a relativistic addition of matrices is introduced. The experiments performed with various morphological elementary operators on synthetic and real images demonstrate the capabilities and restrictions of the novel approach.}, language = {en} } @misc{Kemm, author = {Kemm, Friedemann}, title = {On the origin of divergence errors in MHD simulations and consequences for numerical schemes}, series = {Communications in Applied Mathematics and Computational Science}, volume = {8}, journal = {Communications in Applied Mathematics and Computational Science}, number = {1}, issn = {2157-5452}, doi = {10.2140/camcos.2013.8.1}, pages = {1 -- 38}, abstract = {This paper investigates the origin of divergence errors in MHD simulations. For that purpose, we introduce the concept of discrete involutions for discretized conservation laws. This is done in analogue to the concept of involutions for hyperbolic conservation laws, introduced by Dafermos. By exploring the connection between discrete involutions and resonance, especially for constrained transport like MHD, we identify the lack of positive central viscosity and the assumption of one-dimensional physics in the calculation of intercell fluxes as the main sources of divergence errors. As an example of the consequences for numerical schemes, we give a hint how to modify Roe-type schemes in order to decrease the divergence errors considerably and, thus, stabilize the scheme.}, language = {en} } @misc{KleefeldLin, author = {Kleefeld, Andreas and Lin, Tzu-Chu}, title = {A Global Galerkin Method for Solving the Exterior Neumann Problem for the Helmholtz Equation Using Panich's Integral Equation Approach}, series = {SIAM Journal on Scientific Computing}, volume = {35}, journal = {SIAM Journal on Scientific Computing}, number = {3}, issn = {1064-8275}, doi = {10.1137/120873066}, pages = {A1709 -- A1735}, abstract = {We describe a boundary integral equation that solves the exterior Neumann problem for the Helmholtz equation in three dimensions for smooth obstacles that can be described globally in spherical coordinates. The unique solution is found by approximating the Fredholm integral equation of the second kind with the Galerkin method, where the basis functions are spherical harmonics. This leads to a fast method for small and medium wave numbers, since the system of equations is of size smaller than 64. To smooth the integrand a new map is introduced which significantly improves the accuracy. Numerical results for several smooth surfaces are presented.}, language = {en} } @misc{Kleefeld, author = {Kleefeld, Andreas}, title = {A numerical method to compute interior transmission eigenvalues}, series = {Inverse Problems}, journal = {Inverse Problems}, number = {29}, issn = {0266-5611}, doi = {10.1088/0266-5611/29/10/104012}, pages = {104012}, abstract = {In this paper the numerical calculation of eigenvalues of the interior transmission problem arising in acoustic scattering for constant contrast in three dimensions is considered. From the computational point of view existing methods are very expensive, and are only able to show the existence of such transmission eigenvalues. Furthermore, they have trouble finding them if two or more eigenvalues are situated closely together. We present a new method based on complex-valued contour integrals and the boundary integral equation method which is able to calculate highly accurate transmission eigenvalues. So far, this is the first paper providing such accurate values for various surfaces different from a sphere in three dimensions. Additionally, the computational cost is even lower than those of existing methods. Furthermore, the algorithm is capable of finding complex-valued eigenvalues for which no numerical results have been reported yet. Until now, the proof of existence of such eigenvalues is still open. Finally, highly accurate eigenvalues of the interior Dirichlet problem are provided and might serve as test cases to check newly derived Faber-Krahn type inequalities for larger transmission eigenvalues that are not yet available.}, language = {en} } @misc{AnagnostōpulosCharalambopoulosKleefeld, author = {Anagnostōpulos, Kōnstantinos N. and Charalambopoulos, Antonios and Kleefeld, Andreas}, title = {The factorization method for the acoustic transmission problem}, series = {Inverse Problems}, volume = {29}, journal = {Inverse Problems}, number = {11}, issn = {0266-5611}, doi = {10.1088/0266-5611/29/11/115015}, pages = {115015}, abstract = {In this work, the shape reconstruction problem of acoustically penetrable bodies from the far-field data corresponding to time-harmonic plane wave incidence is investigated within the framework of the factorization method. Although the latter technique has received considerable attention in inverse scattering problems dealing with impenetrable scatterers and it has not been elaborated for inverse transmission problems with the only exception being a work by the first two authors and co-workers. We aim to bridge this gap in the field of acoustic scattering; the paper on one hand focuses on establishing rigorously the necessary theoretical framework for the application of the factorization method to the inverse acoustic transmission problem. The main outcome of the investigation undertaken is the derivation of an explicit formula for the scatterer's characteristic function, which depends solely on the far-field data feeding the inverse scattering scheme. Extended numerical examples in three dimensions are also presented, where a variety of different surfaces are successfully reconstructed by the factorization method, thus, complementing the method's validation from the computational point of view.}, language = {en} } @inproceedings{KleefeldJuTozzaetal., author = {Kleefeld, Andreas and Ju, Yong Chul and Tozza, Silvia and Breuß, Michael and Bruhn, Andr{\´e}s}, title = {Generalised Perspective Shape from Shading with Oren-Nayar Reflectance}, series = {Proceedings 24th British Machine Vision Conference, BMVC 2013, Bristol, UK, September 2013}, booktitle = {Proceedings 24th British Machine Vision Conference, BMVC 2013, Bristol, UK, September 2013}, editor = {Burghardt, Tilo and Damen, Dima and Mayol-Cuevas, Walterio and Mirmehdi, Majid}, publisher = {BMVA Press}, doi = {10.5244/C.27.42}, pages = {42.1 -- 42.11}, abstract = {In spite of significant advances in Shape from Shading (SfS) over the last years, it is still a challenging task to design SfS approaches that are flexible enough to handle a wide range of input scenes. In this paper, we address this lack of flexibility by proposing a novel model that extends the range of possible applications. To this end, we consider the class of modern perspective SfS models formulated via partial differential equations (PDEs). By combining a recent spherical surface parametrisation with the advanced non-Lambertian Oren-Nayar reflectance model, we obtain a robust approach that allows to deal with an arbitrary position of the light source while being able to handle rough surfaces and thus more realistic objects at the same time. To our knowledge, the resulting model is currently the most advanced and most flexible approach in the literature on PDE-based perspective SfS. Apart from deriving our model, we also show how the corresponding set of sophisticated Hamilton-Jacobi equations can be efficiently solved by a specifically tailored fast marching scheme. Experiments with medical real-world data demonstrate that our model works in practice and that is offers the desired flexibility.}, language = {en} } @incollection{KleefeldBurgeth, author = {Kleefeld, Andreas and Burgeth, Bernhard}, title = {Order based morphology for color images via matrix fields}, series = {Visualization and Processing of Tensor Fields and Higher Order Descriptors for Multi-Valued Data}, booktitle = {Visualization and Processing of Tensor Fields and Higher Order Descriptors for Multi-Valued Data}, editor = {Burgeth, Bernhard and Vilanova, Anna and Westin, Carl-Fredrik}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-54300-5}, doi = {10.1007/978-3-642-54301-2_4}, pages = {75 -- 95}, abstract = {Mathematical morphology is a successful branch of image processing with a history of more than four decades. Its fundamental operations are dilation and erosion, which are based on the notion of supremum and infimum with respect to an order. From dilation and erosion one can build readily other useful elementary morphological operators and filters, such as opening, closing, morphological top-hats, derivatives, and shock filters. Such operators are available for grey value images, and recently useful analogs of these processes for matrix-valued images have been introduced by taking advantage of the so-called Loewner order. There is a number of approaches to morphology for vector-valued images, that is, color images based on various orders, however, each with its merits and shortcomings. In this chapter we propose an approach to (elementary) morphology for color images that relies on the existing order based morphology for matrix fields of symmetric 2 × 2-matrices. An RGB-image is embedded into a field of those 2 × 2-matrices by exploiting the geometrical properties of the order cone associated with the Loewner order. To this end a modification of the HSL-color model and a relativistic addition of matrices is introduced. The experiments performed with various morphological elementary operators on synthetic and real images provide results promising enough to serve as a proof-of-concept.}, language = {en} } @misc{KleefeldBurgeth, author = {Kleefeld, Andreas and Burgeth, Bernhard}, title = {An approach to color-morphology based on Einstein addition and Loewner order}, series = {Pattern Recognition Letters}, volume = {47}, journal = {Pattern Recognition Letters}, issn = {0167-8655}, doi = {10.1016/j.patrec.2014.01.018}, pages = {29 -- 39}, abstract = {In this article, a new method to process color images via mathematical morphology is presented. Precisely, each pixel of an image contained in the rgb-space is converted into a 2 x 2-matrix representing a point in a color bi-cone. The supremum and infimum needed for dilation and erosion, respectively, are calculated with respect to the Loewner order. Since the result can be outside the bi-cone, a map is proposed to ensure the algebraic closure in the bi-cone. A new addition and subtraction based on Einstein's Relativity Theory is used to define morphological operation such as top-hats, gradients, and morphological Laplacian. Since the addition and subtraction is defined in the unit ball, a suitable mapping between those two spaces is constructed. A comparison with the component-wise approach and the full ordering using lexicographical cascades approach demonstrate the feasibility and capabilities of the proposed approach.}, language = {en} } @misc{KleefeldBrazauskas, author = {Kleefeld, Andreas and Brazauskas, Vytaras}, title = {Authors 'Reply to' Letter to the Editor regarding folded models and the paper by Brazauskas and Kleefeld (2011)}, series = {Scandinavian Actuarial Journal}, journal = {Scandinavian Actuarial Journal}, number = {8}, issn = {0346-1238}, doi = {10.1080/03461238.2013.798070}, pages = {753 -- 757}, language = {en} } @incollection{KleefeldBreussWelketal., author = {Kleefeld, Andreas and Breuß, Michael and Welk, Martin and Burgeth, Bernhard}, title = {Adaptive Filters for Color Images: Median Filtering and Its Extensions}, series = {Computational Color Imaging}, booktitle = {Computational Color Imaging}, editor = {Tr{\´e}meau, Alain and Schettini, Raimondo and Tominaga, Shoji}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-15978-2}, doi = {10.1007/978-3-319-15979-9_15}, pages = {149 -- 158}, abstract = {In this paper we are concerned with robust structure-preserving denoising filters for color images. We build on a recently proposed transformation from the RGB color space to the space of symmetric 2×2 matrices that has already been used to transfer morphological dilation and erosion concepts from matrix-valued data to color images. We investigate the applicability of this framework to the construction of color-valued median filters. Additionally, we introduce spatial adaptivity into our approach by morphological amoebas that offer excellent capabilities for structure-preserving filtering. Furthermore, we define color-valued amoeba M-smoothers as a generalization of the median-based concepts. Our experiments confirm that all these methods work well with color images. They demonstrate the potential of our approach to define color processing tools based on matrix field techniques.}, language = {en} } @inproceedings{SharifiBoroujerdiBreussBurgethetal., author = {Sharifi Boroujerdi, Ali and Breuß, Michael and Burgeth, Bernhard and Kleefeld, Andreas}, title = {PDE-Based Color Morphology Using Matrix Fields}, series = {Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, L{\`e}ge-Cap Ferret, France, May 31 - June 4, 2015, Proceedings}, booktitle = {Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, L{\`e}ge-Cap Ferret, France, May 31 - June 4, 2015, Proceedings}, editor = {Aujol, Jean-Fran{\c{c}}ois and Nikolova, Mila and Papadakis, Nicolas}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-18460-9}, doi = {10.1007/978-3-319-18461-6_37}, pages = {461 -- 473}, abstract = {In this work, we propose a novel way for performing operations of mathematical morphology on color images. To this end, we convert pixelwise the rgb-values into symmetric 2x2 matrices. The new color space can be interpreted geometrically as a biconal color space structure. Motivated by the formulation of the fundamental morphological operations dilation and erosion in terms of partial differential equations (PDEs), we show how to define finite difference schemes making use of the matrix field formulation. The computation of a pseudo supremum and a pseudo infimum of three color matrices is a crucial step for setting up advanced PDE-based methods. We show that this can be achieved for our goal by an algebraic technique. We investigate our approach by dedicated experiments and confirm useful properties of the new PDE-based color morphology operations.}, language = {en} } @phdthesis{Kleefeld, author = {Kleefeld, Andreas}, title = {Numerical methods for acoustic and electromagnetic scattering: Transmission boundary-value problems, interior transmission eigenvalues, and the factorization method}, pages = {165}, language = {en} } @inproceedings{KleefeldVeste, author = {Kleefeld, Andreas and Veste, Maik}, title = {Robuste und strukturerhaltende Bildentrauschung via Medianfilterung und Bildsegmentierung}, series = {20. und 21. Workshop Computer-Bildanalyse in der Landwirtschaft, 26. Mai 2014, Osnabr{\"u}ck}, booktitle = {20. und 21. Workshop Computer-Bildanalyse in der Landwirtschaft, 26. Mai 2014, Osnabr{\"u}ck}, publisher = {Leibniz-Institut f{\"u}r Agrartechnik Potsdam-Bornim e.V.}, address = {Potsdam}, issn = {0947-7314}, pages = {92 -- 100}, abstract = {Ein Medianfilter ist ein Werkzeug, das benutzt werden kann, um Bilder zu entrauschen. Allerdings verschwimmen vorhandene Strukturen, und eine gute Bildsegmentierung gestaltet sich schwierig. Daher wird hier ein Medianfilteralgorithmus vorgestellt, der in der Lage ist, Bilder zu entrauschen und gleichzeitig vorhandene Strukturen beizubehalten. Wir zeigen die Anwendbarkeit dieser Methode auf Bilder, die durch ein automatisches Minirhizotronsystem aufgenommen worden sind. Dieses dient zur zerst{\"o}rungsfreien Observierung von Wurzelwachstum. Die verbesserten Bilder werden dann zur Bildsegmentierung benutzt, um automatisch die Wurzeln in den Bildern zu entdecken.}, language = {de} } @incollection{WelkKleefeldBreuss, author = {Welk, Martin and Kleefeld, Andreas and Breuß, Michael}, title = {Non-adaptive and Amoeba Quantile Filters for Colour Images}, series = {Mathematical Morphology and Its Applications to Signal and Image Processing}, booktitle = {Mathematical Morphology and Its Applications to Signal and Image Processing}, editor = {Benediktsson, J{\´o}n Atli and Chanussot, Jocelyn and Najman, Laurent and Talbot, Hugues}, publisher = {Springer International Publishing}, address = {Berlin}, isbn = {978-3-319-18719-8}, doi = {10.1007/978-3-319-18720-4_34}, pages = {398 -- 409}, abstract = {Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of the input image within neighbourhoods as output image values. Combining a multivariate quantile definition developed in matrix-valued morphology with a recently introduced mapping between the RGB colour space and the space of symmetric 2×2 matrices, we state a class of colour image quantile filters, along with a class of morphological gradient filters derived from these. Using amoeba structuring elements, we devise image-adaptive versions of both filter classes. Experiments demonstrate the favourable properties of the filters.}, language = {en} } @incollection{KleefeldMeyerBaeseBurgeth, author = {Kleefeld, Andreas and Meyer-Baese, Anke and Burgeth, Bernhard}, title = {Elementary Morphology for SO(2)- and SO(3)-Orientation Fields}, series = {Mathematical Morphology and Its Applications to Signal and Image Processing}, booktitle = {Mathematical Morphology and Its Applications to Signal and Image Processing}, editor = {Benediktsson, J{\´o}n Atli and Chanussot, Jocelyn and Najman, Laurent and Talbot, Hugues}, publisher = {Springer International Publishing}, address = {Berlin}, isbn = {978-3-319-18719-8}, doi = {10.1007/978-3-319-18720-4_39}, pages = {458 -- 469}, abstract = {In this article, techniques to process fields of special orthogonal matrices by means of mathematical morphology are proposed. Since the group structure of SO(2)- resp. SO(3)-fields is not suitable to establish useful notions of infimum and supremum, they are transformed into scalar resp. Sym(2)-fields utilizing a matrix-valued version of the Cayley transform. However, for symmetric 2×2 matrices, that is for Sym(2)-fields, elementary morphological operations are available, see [6] and [7]. Several examples and numerical results are presented to show the merits and the limitations of this novel approach. Additionally, the series of transformations utilized in the proposed methods open up possibilities to visualize SO(2)- and SO(3)-fields.}, language = {en} } @inproceedings{MeyerBaeseBarbuLobbesetal., author = {Meyer-Baese, Anke and Barbu, Adrian and Lobbes, Marc and Hoffmann, Sebastian and Burgeth, Bernhard and Kleefeld, Andreas and Meyer-Baese, Uwe}, title = {Computer-aided diagnosis of breast MRI with high accuracy optical flow estimation}, series = {Independent Component Analyses, Compressive Sampling, Large Data Analyses (LDA), Neural Networks, Biosystems, and Nanoengineering XIII}, booktitle = {Independent Component Analyses, Compressive Sampling, Large Data Analyses (LDA), Neural Networks, Biosystems, and Nanoengineering XIII}, editor = {Szu, Harold H. and Dai, Liyi and Zheng, Yufeng}, publisher = {SPIE}, address = {Bellingham, Wash.}, doi = {10.1117/12.2181815}, abstract = {Non-mass enhancing lesions represent a challenge for the radiological reading. They are not well-defined in both morphology (geometric shape) and kinetics (temporal enhancement) and pose a problem to lesion detection and classification. To enhance the discriminative properties of an automated radiological workflow, the correct preprocessing steps need to be taken. In an usual computer-aided diagnosis (CAD) system, motion compensation plays an important role. To this end, we employ a new high accuracy optical flow based motion compensation algorithm with robustification variants. An automated computer-aided diagnosis system evaluates the atypical behavior of these lesions, and additionally considers the impact of non-rigid motion compensation on a correct diagnosis.}, language = {en} } @incollection{KleefeldBurgeth, author = {Kleefeld, Andreas and Burgeth, Bernhard}, title = {Processing Multispectral Images via Mathematical Morphology}, series = {Visualization and Processing of Higher Order Descriptors for Multi-Valued Data}, booktitle = {Visualization and Processing of Higher Order Descriptors for Multi-Valued Data}, editor = {Hotz, Ingrid and Schultz, Thomas}, publisher = {Springer International Publishing}, address = {Berlin}, isbn = {978-3-319-15089-5}, doi = {10.1007/978-3-319-15090-1}, pages = {129 -- 148}, language = {en} } @misc{DelourmeSchmidtSemin, author = {Delourme, B{\´e}rang{\`e}re and Schmidt, Kersten and Semin, Adrien}, title = {On the homogenization of thin perforated walls of finite length}, series = {Asymptotic Analysis}, volume = {97}, journal = {Asymptotic Analysis}, number = {3-4}, issn = {0921-7134}, doi = {10.3233/ASY-151350}, pages = {211 -- 264}, abstract = {The present work deals with the resolution of the Poisson equation in a bounded domain made of a thin and periodic layer of finite length placed into a homogeneous medium. We provide and justify a high order asymptotic expansion which takes into account the boundary layer effect occurring in the vicinity of the periodic layer as well as the corner singularities appearing in the neighborhood of the extremities of the layer. Our approach combines the method of matched asymptotic expansions and the method of periodic surface homogenization.}, language = {en} } @misc{SchmidtSemin, author = {Schmidt, Kersten and Semin, Adrien}, title = {Absorbing boundary conditions for the viscous acoustic wave equation}, series = {Mathemtatical Methods in the Applied Sciences}, volume = {39}, journal = {Mathemtatical Methods in the Applied Sciences}, number = {17}, issn = {1099-1476}, doi = {10.1002/mma.3755}, pages = {5043 -- 5065}, abstract = {We consider different acoustic models with viscosity in a semi-infinite waveguide with rigid walls, for which we propose and analyse absorbing boundary conditions on a truncated subdomain. The considered models are (i) the viscous acoustic equations in a stagnant mean flow, which exhibit for small viscosities boundary layers on the infinite walls, (ii) the limit equations for vanishing viscosity and (iii) a first-order approximation for low viscosity. The limit model (i) is well known as the Helmholtz equation for the pressure with homogeneous Neumann boundary conditions. For each of these models, the absorbing conditions appear as Dirichlet-to-Neumann (DtN) maps. The DtN boundary conditions for the singularly perturbed model (i) and the approximative model (iii) tend to the DtN boundary conditions of the limit problem (ii) if the viscosity approaches zero, and, hence, provide a uniform accuracy in the viscosity. The convergence of truncated DtN boundary conditions and the behaviour for viscosities tending to zero are shown in numerical experiments.}, language = {en} } @misc{FlissKlindworthSchmidt, author = {Fliss, Sonia and Klindworth, Dirk and Schmidt, Kersten}, title = {Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides}, series = {BIT Numerical Mathematics}, volume = {55}, journal = {BIT Numerical Mathematics}, number = {1}, issn = {0006-3835}, doi = {10.1007/s10543-014-0521-1}, pages = {81 -- 115}, abstract = {The efficient and reliable computation of guided modes in photonic crystal wave-guides is of great importance for designing optical devices. Transparent boundary conditions based on Dirichlet-to-Neumann operators allow for an exact computation of well-confined modes and modes close to the band edge in the sense that no modelling error is introduced. The well-known super-cell method, on the other hand, introduces a modelling error which may become prohibitively large for guided modes that are not well-confined. The Dirichlet-to-Neumann transparent boundary conditions are, however, not applicable for all frequencies as they are not uniquely defined and their computation is unstable for a countable set of frequencies that correspond to so called Dirichlet eigenvalues. In this work we describe how to overcome this theoretical difficulty introducing Robin-to-Robin transparent boundary conditions whose construction do not exhibit those forbidden frequencies. They seem, hence, well suited for an exact and reliable computation of guided modes in photonic crystal wave-guides.}, language = {en} } @misc{ThoensZuevaSeminSchmidt, author = {Th{\"o}ns-Zueva, Anastasia and Semin, Adrien and Schmidt, Kersten}, title = {Multiharmonic analysis for nonlinear acoustics with different scales}, series = {ArXiv.org}, journal = {ArXiv.org}, pages = {20}, abstract = {The acoustic wave-propagation without mean flow and heat flux can be described in terms of velocity and pressure by the compressible nonlinear Navier-Stokes equations, where boundary layers appear at walls due to the viscosity and a frequency interaction appears, i.e. sound at higher harmonics of the excited frequency ω is generated due to nonlinear advection. We use the multiharmonic analysis to derive asymptotic expansions for small sound amplitudes and small viscosities both of order ε2 in which velocity and pressure fields are separated into far field and correcting near field close to walls and into contributions to the multiples of ω. Based on the asymptotic expansion we present approximate models for either the pressure or the velocity for order 0, 1 and 2, in which impedance boundary conditions include the effect of viscous boundary layers and contributions at frequencies 0 and 2⋅ω depend nonlinearly on the approximation at frequency ω. In difference to the Navier-Stokes equations in time domain, which has to be resolved numerically with meshes adaptively refined towards the wall boundaries and explicit schemes require the use of very small time steps, the approximative models can be solved in frequency domain on macroscopic meshes. We studied the accuracy of the approximated models of different orders in numerical experiments comparing with reference solutions in time-domain.}, language = {en} }