Parallel scanning of implicit surfaces with the simplex algorithm

Abstract

Solution of mechanical problems often requires the analytical or numerical calculation of equilibrium paths, while solution sets of other dimension than one are rare. From this requirement emerged numerous method for the calculation of bifurcation diagrams. Two large group of the solution methods are the continuation methods and the scanning methods (however hybrid algorithm exists as well). The Simplex Algorithm is a robust approximative technique based on the Piecewise Linearization (PL-)algorithm, which has its application as a continuation and as a scanning algorithm as well. In this paper we will show the extension of the method for finding a 2-dimensional manifold (i.e. surface) with the scanning of the parameter space. We analyze the performance of the algorithm and its parallelization through two simple examples.