An asynchronous parallel explicit solver based on scaled boundary finite element method using octree meshes

Abstract

Explicit time integration methods are an integral part of solving structural dynamics problems such as the propagation of elastic and acoustic waves, impact scenarios including crash tests and many more. One common limitation of this class of time integrators is, however, their conditional stability, meaning that highly distorted, small, or stiff finite elements typically govern the critical time step size. That is to say, even a small number of such elements will result in a significantly decrease of the feasible time step, which in turn drastically increases the computational costs of solving the semi-discrete equations of motion. This is especially true for non-uniform and unstructured meshes. Therefore, an asynchronous explicit solver in parallel is proposed in this article. The idea is to assign different time step sizes to different parts of the mesh, such that the overall computational effort is minimized. To improve the performance of the proposed solver, it is combined with a sophisticated octree meshing framework, where the balanced octrees are used, meaning that the ratio of the element sizes of adjacent elements cannot exceed a value of two. Thus, the critical time step of each element can be estimated straightforwardly. To avoid issues with hanging nodes, a special polyhedral element formulation, the scaled boundary finite element method, is employed. Since there are only a limited number of cell patterns in a balanced octree, the stiffness and mass matrices are pre-computed, significantly reducing the computational cost. Moreover, exploiting an element-by-element technique, the assembly of global stiffness matrices can be avoided. The main advantage of the described methodology is that the asynchronous explicit solver can be easily implemented in a high-performance computing environment. By means of several numerical examples, the accuracy and efficiency of the proposed method are demonstrated, as well as its versatility in handling complex engineering problems.