B. Heise and M. Jung
Comparison of parallel solvers for nonlinear elliptic problems based on domain decomposition ideas
Institutsbericht Nr. 494, Institut für Mathematik, Johannes Kepler Universität Linz
In the present paper, the solution of nonlinear elliptic boundary value problems (b.v.p.) on parallel machines with Multiple Instruction Multiple Data (MIMD) architecture is discussed. Especially, we consider electro-magnetic field problems the numerical solution of which is based on finite element discretizations and a nested Newton solver. For solving the linear systems of algebraic finite element equations in each Newton step, parallel conjugate gradient methods with a Domain Decomposition preconditioner (DD PCG) as well as parallelized global multigrid methods are applied. The implementation of the whole algorithm, i.e. the mesh generation, the generation of the finite element equations, the nested Newton algorithm, the DD PCG method and the global multigrid method, is based on a non-overlapping DD data structure. The efficiency of the parallel DD PCG methods and the parallelized global multigrid methods, which are embedded in the nested Newton solver, are compared. Furthermore, the performance of the parallel nested Newton solver on different machines (GC Power Plus, Multicluster with transputers T805, and workstation cluster) is demonstrated by numerical results.