A Moore-Penrose continuation method based on a Schur complement approach for nonlinear finite element bifurcation problems

Continuation methods have proved to be very powerful tools when solving large finite element problems. However, implementation of these methods often require modifications to the standard finite element method. As a finite element code is already very complex, we would like to implement the continuation method as efficiently as possible. In this paper, we present a new implementation technique based on a Schur complement approach for the Moore-Penrose continuation method. This method facilitates the detection of bifurcation points and also enables branch following. Numerical examples will be presented and analyzed using the proposed approach.