Nonlinear Finite Element Problems on Parallel Computers

VECFEM is a black-box solver for the solution of a large class of nonlinear functional equations by finite element methods. It uses very robust solution methods for the linear FEM problem to compute reliably the Newton-Raphson correction and the error indicator. Kernel algorithms are conjugate gradient methods (CG) for the solution of the linear system. In this paper we present the optimal data structures on parallel computers for the matrix-vector multiplication, which is the key operation in the CG iteration, the principles of the element distribution onto the processors and the mounting of the global matrix over all processors as transformation of optimal data structures. VECFEM is portably implemented for message passing systems. Two examples with unstructured and structured grids will show the efficiency of the data structures. Keywords: parallel computers, finite element method, black-box solver The solution of nonlinear functional equations, e.g. arising from elliptic and parab..