TY - JOUR A1 - Powell, Gary A1 - Weiser, Martin T1 - Views, A new form of container adaptors JF - C/C++ Users Journal N2 - The C++ standard template library has many useful containers for data. The standard library includes two adpators, queue, and stack. The authors have extended this model along the lines of relational database semantics. Sometimes the analogy is striking, and we will point it out occasionally. An adaptor allows the standard algorithms to be used on a subset or modification of the data without having to copy the data elements into a new container. The authors provide many useful adaptors which can be used together to produce interesting views of data in a container. Y1 - 2000 VL - 18 IS - 4 SP - 40 EP - 51 ER - TY - THES A1 - Sali, Adrian T1 - Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology N2 - The primary goal of this paper is to study the coupling of monodomain and eikonal models for the numerical simulation of cardiac electrophysiology. Eikonal models are nonlinear elliptic equations describing the excitation time of the cardiac tissue. They are often used as very fast approximations for monodomain or bidomain models - parabolic reaction-diffusion systems describing the excitation wavefront in terms of ionic currents. The excitation front is a thin region with high gradients, whereas excitation times vary over larger domains. Hence, eikonal equations can be solved on much coarser grids than monodomain equations. Moreover, as eikonal models are not time-dependent, no time integration is needed. Eikonal models are derived from monodomain models making additional assumptions and using certain approximations. While generally the approximation is rather good, several specific situations are not well captured by eikonal models. We consider coupling the two models, i.e. using the monodomain model in regions where more accurate results or the shape of the wavefront are needed, and the eikonal model in the remaining parts of the domain, where the excitation time is sufficient. Restricting the monodomain simulation to a small subdomain reduces the computational effort considerably. Numerical methods for the simulation of the individual models are presented, with the finite element method as the main ingredient. Coupling conditions as well as algorithms for implementing the coupling are explained. The approximation quality and efficiency of the coupled model is illustrated on simple geometries using an Aliev-Panfilov membrane model. Y1 - 2016 ER - TY - JOUR A1 - Weiser, Martin A1 - Ghosh, Sunayana T1 - Theoretically optimal inexact SDC methods JF - Communications in Applied Mathematics and Computational Science N2 - In several inital value problems with particularly expensive right hand side evaluation or implicit step computation, there is a trade-off between accuracy and computational effort. We consider inexact spectral deferred correction (SDC) methods for solving such initial value problems. SDC methods are interpreted as fixed point iterations and, due to their corrective iterative nature, allow to exploit the accuracy-work-tradeoff for a reduction of the total computational effort. On one hand we derive error models bounding the total error in terms of the evaluation errors. On the other hand, we define work models describing the computational effort in terms of the evaluation accuracy. Combining both, a theoretically optimal local tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance. The properties of optimal local tolerances and the predicted efficiency gain compared to simpler heuristics, and a reasonable practical performance, are illustrated on simple numerical examples. Y1 - 2018 U6 - https://doi.org/10.2140/camcos.2018.13.53 IS - 13-1 SP - 53 EP - 86 ER - TY - JOUR A1 - Schenk, O. A1 - Wächter, Andreas A1 - Weiser, Martin T1 - Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization JF - SIAM J. Sci. Comp. Y1 - 2008 VL - 31 IS - 2 SP - 939 EP - 960 ER - TY - JOUR A1 - Weiser, Martin A1 - Deuflhard, Peter T1 - Inexact central path following algorithms for optimal control problems JF - SIAM J. Control Opt. Y1 - 2007 VL - 46 IS - 3 SP - 792 EP - 815 ER - TY - JOUR A1 - Bergmann, G. A1 - Graichen, F. A1 - Rohlmann, A. A1 - Bender, Alwina A1 - Ehrig, Rainald A1 - Westerhoff, P. A1 - Heinlein, B. T1 - Design and calibration of load sensing orthopaedic implants JF - Journal Biomech. Eng. Y1 - 2008 SP - 02109 EP - 1–02109–9 ER - TY - JOUR A1 - Colli Franzone, Piero A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Pavarino, Luca Franco T1 - Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology JF - SIAM J. Sc. Comp. Y1 - 2006 VL - 28 SP - 942 EP - 962 ER - TY - JOUR A1 - Dahlke, S. A1 - Steidl, G. A1 - Teschke, G. T1 - Coorbit Spaces and Banach Frames on Homogeneous Spaces with Applications to Analyzing Functions on Spheres JF - Adv. Comput.Math. Y1 - 2004 VL - 1-2 IS - 21 SP - 147 EP - 180 ER - TY - JOUR A1 - Dahlke, S. A1 - Steidl, G. A1 - Teschke, G. T1 - Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces JF - Journal of Fourier Analysis and Applications Y1 - 2004 VL - 5 IS - 10 SP - 507 EP - 539 ER - TY - BOOK A1 - Deuflhard, Peter A1 - Weiser, Martin T1 - Numerische Mathematik 3 Y1 - 2011 PB - de Gruyter, Berlin ER -