Coarse space orthogonalization for indefinite linear systems of equations arising in geometrically nonlinear elasticity

Abstract

This paper is concerned with the solution of indefinite linear systems arising in the course of Newton iterations for problems of geometrically nonlinear elasticity by Krylov subspace methods. The convergence of these methods often slows down considerably due to the ill-conditioning or even indefiniteness of the matrix near simple limit or bifurcation points. We illustrate that orthogonalizing against a low-dimensional coarse finite element space is a key ingredient to get satisfactory convergence in all parameter ranges. This approach is combined with the usual hierarchical and multilevel preconditioners and implementation issues are discussed in some detail. Computational experiments performed for a realistic example from planar elasticity using isoparametric finite elements illustrate the effectiveness of the coarse space orthogonalization approach.