@article{PowellWeiser2000, author = {Powell, Gary and Weiser, Martin}, title = {Views, A new form of container adaptors}, volume = {18}, journal = {C/C++ Users Journal}, number = {4}, pages = {40 -- 51}, year = {2000}, abstract = {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.}, language = {en} } @misc{Sali2016, type = {Master Thesis}, author = {Sali, Adrian}, title = {Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology}, pages = {63}, year = {2016}, abstract = {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.}, language = {en} } @article{WeiserGhosh2018, author = {Weiser, Martin and Ghosh, Sunayana}, title = {Theoretically optimal inexact SDC methods}, journal = {Communications in Applied Mathematics and Computational Science}, number = {13-1}, doi = {10.2140/camcos.2018.13.53}, pages = {53 -- 86}, year = {2018}, abstract = {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.}, language = {en} } @article{SchenkWaechterWeiser2008, author = {Schenk, O. and W{\"a}chter, Andreas and Weiser, Martin}, title = {Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization}, volume = {31}, journal = {SIAM J. Sci. Comp.}, number = {2}, pages = {939 -- 960}, year = {2008}, language = {en} } @article{WeiserDeuflhard2007, author = {Weiser, Martin and Deuflhard, Peter}, title = {Inexact central path following algorithms for optimal control problems}, volume = {46}, journal = {SIAM J. Control Opt.}, number = {3}, pages = {792 -- 815}, year = {2007}, language = {en} } @article{BergmannGraichenRohlmannetal.2008, author = {Bergmann, G. and Graichen, F. and Rohlmann, A. and Bender, Alwina and Ehrig, Rainald and Westerhoff, P. and Heinlein, B.}, title = {Design and calibration of load sensing orthopaedic implants}, journal = {Journal Biomech. Eng.}, pages = {02109 -- 1-02109-9}, year = {2008}, language = {en} } @article{ColliFranzoneDeuflhardErdmannetal.2006, author = {Colli Franzone, Piero and Deuflhard, Peter and Erdmann, Bodo and Lang, Jens and Pavarino, Luca Franco}, title = {Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology}, volume = {28}, journal = {SIAM J. Sc. Comp.}, pages = {942 -- 962}, year = {2006}, language = {en} } @article{DahlkeSteidlTeschke2004, author = {Dahlke, S. and Steidl, G. and Teschke, G.}, title = {Coorbit Spaces and Banach Frames on Homogeneous Spaces with Applications to Analyzing Functions on Spheres}, volume = {1-2}, journal = {Adv. Comput.Math.}, number = {21}, pages = {147 -- 180}, year = {2004}, language = {en} } @article{DahlkeSteidlTeschke2004, author = {Dahlke, S. and Steidl, G. and Teschke, G.}, title = {Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces}, volume = {5}, journal = {Journal of Fourier Analysis and Applications}, number = {10}, pages = {507 -- 539}, year = {2004}, language = {en} } @book{DeuflhardWeiser2011, author = {Deuflhard, Peter and Weiser, Martin}, title = {Numerische Mathematik 3}, publisher = {de Gruyter, Berlin}, year = {2011}, language = {de} }