Multiple right-hand side techniques for the numerical simulation of quasistatic electric and magnetic fields
M. Clemens, M. Helias, T. Steinmetz, and G. Wimmer. Journal of Computational and Applied Mathematics, 215 (2):
328–338(2008)Proceedings of the Third International Conference on Advanced Computational Methods in Engineering (ACOMEN 2005)..
DOI: 10.1016/j.cam.2006.04.072
Abstract
The simulation of slowly varying transient electric high-voltage fields and magnetic fields requires the repeated and successive solution of high-dimensional linear algebraic systems of equations with identical or near-identical system matrices and different right-hand side vectors. For these solution processes which are required within implicit time integration schemes and nonlinear (quasi-)Newton–Raphson methods an iterative multiple right-hand side (mrhs) scheme is used which recycles vector subspaces resulting from previous preconditioned conjugate gradient iteration runs. The combination of this scheme with a subspace projection extrapolation start value generation scheme is discussed. Numerical results for three-dimensional electric and magnetic field simulations are presented and the efficiency of the new schemes re-using eigenvector information from previous iteration processes with different tolerance criteria are compared to those of standard conjugate gradient iterations.
%0 Journal Article
%1 CLEMENS2008328
%A Clemens, Markus
%A Helias, Moritz
%A Steinmetz, Thorsten
%A Wimmer, Georg
%D 2008
%J Journal of Computational and Applied Mathematics
%K 65f10-iterative-methods-for-linear-systems 78m10-optics-electromagnetism-finite-element-method
%N 2
%P 328–338
%R 10.1016/j.cam.2006.04.072
%T Multiple right-hand side techniques for the numerical simulation of quasistatic electric and magnetic fields
%U http://www.sciencedirect.com/science/article/pii/S0377042706007436
%V 215
%X The simulation of slowly varying transient electric high-voltage fields and magnetic fields requires the repeated and successive solution of high-dimensional linear algebraic systems of equations with identical or near-identical system matrices and different right-hand side vectors. For these solution processes which are required within implicit time integration schemes and nonlinear (quasi-)Newton–Raphson methods an iterative multiple right-hand side (mrhs) scheme is used which recycles vector subspaces resulting from previous preconditioned conjugate gradient iteration runs. The combination of this scheme with a subspace projection extrapolation start value generation scheme is discussed. Numerical results for three-dimensional electric and magnetic field simulations are presented and the efficiency of the new schemes re-using eigenvector information from previous iteration processes with different tolerance criteria are compared to those of standard conjugate gradient iterations.
@article{CLEMENS2008328,
abstract = {The simulation of slowly varying transient electric high-voltage fields and magnetic fields requires the repeated and successive solution of high-dimensional linear algebraic systems of equations with identical or near-identical system matrices and different right-hand side vectors. For these solution processes which are required within implicit time integration schemes and nonlinear (quasi-)Newton–Raphson methods an iterative multiple right-hand side (mrhs) scheme is used which recycles vector subspaces resulting from previous preconditioned conjugate gradient iteration runs. The combination of this scheme with a subspace projection extrapolation start value generation scheme is discussed. Numerical results for three-dimensional electric and magnetic field simulations are presented and the efficiency of the new schemes re-using eigenvector information from previous iteration processes with different tolerance criteria are compared to those of standard conjugate gradient iterations.},
added-at = {2019-07-02T02:20:45.000+0200},
author = {Clemens, Markus and Helias, Moritz and Steinmetz, Thorsten and Wimmer, Georg},
biburl = {https://www.bibsonomy.org/bibtex/22a280ba0d61bb60142c1c2f0cd4c378c/gdmcbain},
doi = {10.1016/j.cam.2006.04.072},
interhash = {d0c3eaad316bb8948ef62f8b1b41d70c},
intrahash = {2a280ba0d61bb60142c1c2f0cd4c378c},
issn = {0377-0427},
journal = {Journal of Computational and Applied Mathematics},
keywords = {65f10-iterative-methods-for-linear-systems 78m10-optics-electromagnetism-finite-element-method},
note = {Proceedings of the Third International Conference on Advanced Computational Methods in Engineering (ACOMEN 2005).},
number = 2,
pages = {328–338},
timestamp = {2019-07-02T02:20:45.000+0200},
title = {Multiple right-hand side techniques for the numerical simulation of quasistatic electric and magnetic fields},
url = {http://www.sciencedirect.com/science/article/pii/S0377042706007436},
volume = 215,
year = 2008
}