TY - JOUR
T1 - Parallel Hierarchical Matrix Preconditioners for the Curl-Curl Operator
AU - Mario Bebendorf & Joerg Ostrowski
JO - Journal of Computational Mathematics
VL - 5
SP - 624
EP - 641
PY - 2009
DA - 2009/10
SN - 27
DO - http://doi.org/10.4208/jcm.2009.27.5.014
UR - https://global-sci.org/intro/article_detail/jcm/8593.html
KW - Computational electromagnetism, Preconditioners, Hierarchical matrices, Parallelization.
AB - <p style="text-align: justify;">This paper deals with the preconditioning of the curl-curl operator. We use</p><p style="text-align: justify;">$\boldsymbol{H}$(<strong>curl</strong>)-conforming finite elements for the discretization of our corresponding magnetostatic model problem. Jumps in the material parameters influence the condition of the problem. We will demonstrate by theoretical estimates and numerical experiments that hierarchical matrices are well suited to construct efficient parallel preconditioners for the fast and robust iterative solution of such problems.</p>