TY - GEN A1 - Seebass, Martin A1 - Beck, Rudolf A1 - Gellermann, Johanna A1 - Nadobny, Jacek A1 - Wust, Peter T1 - Electromagnetic phased arrays for regional hyperthermia -- optimal frequency and antenna arrangement N2 - In this paper we investigate the effects of the three-dimensional arrangement of antennas and frequency on temperature distributions that can be achieved in regional hyperthermia using an electromagnetic phased array. We compare the results of power-based and temperature-based optimization. Thus we are able to explain the discrepancies between previous studies favouring more antenna rings on the one hand and more antennas per ring on the other hand. We analyze the sensitivity of the results with respect to changes in amplitudes and phases as well as patient position. This analysis can be used for different purposes. First, it provides additional criteria for selecting the optimal frequency. Second, it can be used for specifying the required phase and amplitude accuracy for a real phased array system. Furthermore, it may serve as a basis for technological developments in order to reduce both types of sensitivities described above. T3 - ZIB-Report - 00-28 KW - Pelvic heating KW - phased array optimization Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5961 ER - TY - GEN A1 - Burger, Sven A1 - Klose, Roland A1 - Schädle, Achim A1 - Zschiedrich, Lin T1 - HelmPole - A finite element solver for scattering problems on unbounded domains: Implementation based on PML N2 - The solution of scattering problems described by the Helmholtz equation on unbounded domains is of importance for a wide variety of applications, for example in electromagnetics and acoustics. An implementation of a solver for scattering problems based on the programming language Matlab is introduced. The solver relies on the finite-element-method and on the perfectly-matched-layer-method, which allows for the simulation of scattering problems on complex geometries surrounded by inhomogeneous exterior domains. This report gives a number of detailed examples and can be understood as a user manual to the freely accessible code of the solver HelmPole. T3 - ZIB-Report - 03-38 KW - Helmholtz equation KW - finite element method KW - perfectly matched layer Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7609 ER - TY - THES A1 - Schmidt, Frank T1 - A New Approach to Coupled Interior-Exterior Helmholtz-Type Problems: Theory and Algorithms N2 - The work presents a new approach to the numerical solution of time-harmonic and time-dependent scattering problems. We replace Sommerfeld's radiation condition valid for the Helmholtz equation by a more general concept called pole condition. The pole condition is based on the Laplace transform of the exterior solution and allows a characterization of outgoing waves. Both new insight into the analysis of scattering problems as well as new numerical algorithms are obtained. T3 - ZIB-Report - 02-45 KW - Pole condition KW - Helmholtz equation KW - Wide angle one-way equation KW - Schroedinger equation KW - Transparent boundary conditions KW - Unbounded domains KW - Fini Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7128 ER - TY - GEN A1 - Weiser, Martin A1 - Schiela, Anton A1 - Deuflhard, Peter T1 - Asymptotic Mesh Independence of Newton's Method Revisited N2 - The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems. T3 - ZIB-Report - 03-13 KW - mesh independence KW - nonlinear partial differential equations KW - Newton method KW - finite element method KW - collocation method Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7352 ER - TY - GEN A1 - Weiser, Martin A1 - Deuflhard, Peter A1 - Erdmann, Bodo T1 - Affine conjugate adaptive Newton methods for nonlinear elastomechanics N2 - The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. Based on well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning. T3 - ZIB-Report - 04-01 KW - affine conjugate Newton methods KW - nonconvex minimization KW - nonlinear elastomechnics KW - cranio-maxillofacial surgery KW - soft tissue simulation KW - multilev Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7768 ER - TY - GEN A1 - Zschiedrich, Lin A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank T1 - A new Finite Element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D N2 - In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer. T3 - ZIB-Report - 03-44 KW - transparent boundary conditions KW - perfectly matched layer KW - pole condition Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7662 ER - TY - GEN A1 - Oevermann, Michael A1 - Scharfenberg, Carsten A1 - Klein, Rupert T1 - A sharp interface finite volume method for elliptic equations on Cartesian grids N2 - We present a second order sharp interface finite volume method for the solution of the three-dimensional poisson equation with variable coefficients on Cartesian grids. In particular, we focus on interface problems with discontinuities in the coefficient, the source term, the solution, and the fluxes across the interface. The method uses standard piecewiese trilinear finite elements for normal cells and a double piecewise trilinear ansatz for the solution on cells intersected by the interface resulting always in a compact 27-point stencil. Singularities associated with vanishing partial volumes of intersected grid cells are removed by a two-term asymptotic approach. In contrast to the 2D method presented by two of the authors in [M.~Oevermann, R.~Klein: A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces, J.~Comp.~Phys.~219 (2006)] we use a minimization technique to determine the unknown coefficients of the double trilinear ansatz. This simplifies the treatment of the different cut-cell types and avoids additional special operations for degenerated interface topologies. The resulting set of linear equations has been solved with a BiCGSTAB solver preconditioned with an algebraic multigrid. In various testcases -- including large coefficient ratios and non-smooth interfaces -- the method achieves second order of accuracy in the L_inf and L_2 norm. T3 - ZIB-Report - 08-38 KW - elliptische Gleichungen KW - Finite Volumen KW - eingebettete Ränder KW - variable und diskontinuierliche Koeffizienten KW - diskontinuierliche Lösung KW - Elliptic equations KW - finite volume methods KW - embedded interface KW - variable and discontinuous coefficients KW - discontinuous solution Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10900 SN - 1438-0064 ER - TY - GEN A1 - Oevermann, Michael A1 - Klein, Rupert T1 - A cartesian grid finite volume method for the solution of the Poisson equation with variable coefficients and embedded interfaces N2 - We present a finite volume method for the solution of the two-dimensional Poisson equation $ \nabla\cdot( \beta( {\mbox{\boldmath $x$}}) \nabla u({\mbox{\boldmath $x$}})) = f(\mbox{\boldmath $x$}) $ with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution $u({\mbox{\boldmath $x$})$ resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the $L^\infty$ and $L^2$ norm. T3 - ZIB-Report - 06-05 KW - Poisson equation KW - finite volume methods KW - embedded interface KW - ariable and discontinuous coefficients KW - discontinuous solution Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8996 ER - TY - GEN A1 - Braess, Dietrich A1 - Deuflhard, Peter A1 - Lipnikov, Konstantin T1 - A Subspace Cascadic Multigrid Method for Mortar Elements N2 - A cascadic multigrid (CMG) method for elliptic problems with strong material jumps is proposed and analyzed. Non--matching grids at interfaces between subdomains are allowed and treated by mortar elements. The arising saddle point problems are solved by a subspace confined conjugate gradient method as smoother for the CMG. Details of algorithmic realization including adaptivity are elaborated. Numerical results illustrate the efficiency of this CMG algorithm. T3 - ZIB-Report - SC-99-07 KW - Finite Elements KW - Rayleigh-Ritz and Galerkin Methods KW - Multigrid Methods KW - Domain Decomposition Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3954 ER - TY - GEN A1 - Deuflhard, Peter T1 - Differential Equations in Technology and Medicine. Computational Concepts, Adaptive Algorithms, and Virtual Labs N2 - This series of lectures has been given to a class of mathematics postdocs at a European summer school on Computational Mathematics Driven by Industrial Applications in Martina Franca, Italy (organized by CIME). It deals with a variety of challenging real life problems selected from clinical cancer therapy, communication technology, polymer production, and pharmaceutical drug design. All of these problems from rather diverse application areas share two common features: (a) they have been modelled by various differential equations -- elliptic, parabolic, or Schrödinger--type partial differential equations, countable ordinary diffential equations, or Hamiltonian systems, (b) their numerical solution has turned out to be real challenge to computational mathematics. T3 - ZIB-Report - SC-99-34 KW - differential equations: KW - ordinary KW - partial KW - countable KW - hamiltonian KW - finite element methods: KW - adaptive KW - multilevel KW - grid generation KW - medical t Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4223 ER -