A survey of parallel solvers for the finite element method in computational electromagnetics <s> Introduction <s> The new trends of parallel electromagnetic fields computation are presented New hardware developments are given. New developments in parallel methods are described: standard iterative and direct solving methods and domain decomposition methods. Special attention is paid to parallel computation using the JAVA language. The current status and properties of two prevailing programming environments (PVM and MPI) are finally given and compared. <s> BIB001 </s> A survey of parallel solvers for the finite element method in computational electromagnetics <s> Introduction <s> A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This paper describes how the modeling of large devices has been made possible using parallel computation. New algorithms are then proposed to implement this formulation on a cluster of workstations (10 DEC ALPHA 300X) and on a CRAY C98. Analysis of the computation efficiency is performed using simple problems. The electromagnetic scattering of a plane wave by a perfect electric conducting airplane is finally given as example. <s> BIB002
Numerical computation is more and more used in engineering sciences to develop new devices or to optimize existing one. Only parallel computers provide the increase in computing performances necessary to solve today's problems. Two reasons may be highlighted: large memory is required because of a large amount of data, or speed is required to obtain the solution  . We have previously presented a survey of the parallelization of numerical techniques used in computational electromagnetics  . In this paper, it is proposed to focus now our attention on numerical solving methods for the parallelized Finite Element Method (FEM) in electromagnetics BIB001 . The objective is actually to describe lately appeared methods which can be useful to solve efficiently linear systems issued from FE discretization. The main characteristic of such systems is that they are generally sparse. The FEM is attractive for modeling 2D and 3D devices because of its adaptability for designing complex systems with highly heterogeneous materials. Modeling realistic devices requires the solution of a large problem which can be afforded only by parallel computation BIB002 . The first section deals with standard numerical solving methods, such as preconditioned conjugate gradient. In the second section, domain decomposition methods (DDM) are described. Since these methods are less known in computational electromagnetics, their basic principle is presented. Special attention is also paid to multilevel methods, which can be seen as a DDM method from a strict mathematical point of view. As example, the last section shows the implementation of a Finite Element Time Domain (FETD) algorithm used for a wave propagation problem. A comparison between the two message passing libraries PVM and MPI is also performed.