  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 quasi-static 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. By
applying local refinements in the arc-length parameter, the APALM refines
solutions where the non-linearity in the load-response space is maximal. The
concept is easily extended for bifurcation problems. The performance of the
method is demonstrated using isogeometric Kirchhoff-Love shells on problems
with snap-through and pitch-fork instabilities. It can be concluded that the
adaptivity of the method works as expected and that a relatively coarse
approximation of the serial initialization can already be used to produce a
good approximation in parallel.
