An adaptive parallel arc-length method

Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational mechanics to decompose spatial problems into multiple subproblems that can be solved in parallel, advancing solution schemes for dynamics or quasi -statics are inherently serial processes. For quasistatic simulations, however, there is no accumulating 'time' discretization error, hence an alternative approach is required. In this paper, we present an Adaptive Parallel Arc -Length Method (APALM). By using a domain parametrization of the arc -length instead of time, the multi -level error for the arc -length parametrization is formed by the load parameter and the solution norm. Given coarse approximations of arc -length intervals, finer corrections enable the parallelization of the presented method. This results in an arc -length method that is parallel within a branch and inherently adaptive. This concept is easily extended for bifurcation problems. The performance of the method is demonstrated using isogeometric Kirchhoff -Love shells on problems with snapthrough and pitch -fork instabilities and applied to the problem of a snapping meta -material. These results show that parallel corrections are performed in a fraction of the time of the serial initialization, achievable on desktop scale.