Implementation of a symmetric boundary element method on distributed memory computers for 3D maxwell equations

Abstract

The severe computational requirements for the numerical simulation of high frequency electromagnetism problems led to a strong interest for parallel processing in this domain. This chapter focuses on the design and analysis of a parallel implementation for finite element approximations of such problems on multiple instructions, multiple data (MIMD) distributed-memory computers. Single process, multiple data (SPMD) programming model was used with a message passing mechanism for communications. The algorithm works in two steps. During the first step, the assembly constructs the linear system associated with the approximation method; and during the second step, it solves the system created. These two steps are sequentially performed and use the same distributed data structure to store the matrix of the linear system. The parallelisms induced by each of these two steps are discussed in the chapter. The choice of a symmetric variational formulation allows one to reduce the total amount of elementary computation and the storage. However, it is more difficult to achieve a good parallel efficiency in this context of symmetry for 3D problems; this chapter mainly focuses on this difficulty and in particular optimizes the first step (load balancing and communication) with respect to a well suited distribution of data for the linear solver chosen in the second step.