A survey of parallel solvers for the finite element method in computational electromagnetics <s> Other parallel standard iterative methods <s> Recently, a number of researchers have investigated a class of algorithms that are based on multilevel graph partitioning that have moderate computational complexity, and provide excellent graph partitions. However, there exists little theoretical analysis that could explain the ability of multilevel algorithms to produce good partitions. In this paper we present such an analysis. Weshow under certain reasonable assumptions that even if no refinement is used in the uncoarsening phase, a good bisection of the coarser graph is worse than a good bisection of the finer graph by at most a small factor. We also show that for planar graphs, the size of a good vertex-separator of the coarse graph projected to the finer graph (without performing refinement in the uncoarsening phase) is higher than the size of a good vertex-separator of the finer graph by at most a small factor. <s> BIB001 </s> A survey of parallel solvers for the finite element method in computational electromagnetics <s> Other parallel standard iterative methods <s> This paper investigates parallel iterative solvers with preconditioning for the computation of magnetic and electric fields on a printed circuit board (PCB) containing a magnetic film. Special scaled symmetric quasi-minimal residual (QMR) methods and a bi-conjugate gradient stabilized (BICGSTAB) method, preconditioned by an incomplete LU factorization with threshold (ILUT), are presented. The results show that these solvers are well suited for PCB simulations on parallel computers, requiring both real and complex arithmetic. <s> BIB002
Other parallel iterative solvers may be used for the FE method and can be more efficient than the preconditioned CG. As example, the Quasi-Minimal Residual (QMR) method and the BI-Conjugate Gradient STAbilized (BICGSTAB) method are compared in BIB002 for the computation of 2D axisymmetric magnetic and electric fields on printed circuit board (PCB) containing magnetic films. Both solvers and preconditioners are parallelized by matrix and vector partitioning, the mesh partition being obtained by using METIS BIB001 . The results obtained on different parallel machines show the efficiency of this approach (Table II) . 