%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 }