Vectorization techniques for explicit arbitrary Lagrangian-Eulerian calculations

Abstract

Vectorization techniques for explicit arbitrary Lagrangian-Eulerian (ALE) calculations are described. Explicit finite element codes provide an efficient means for solving dynamic problems involving large deformations. The size of the timestep in an explicit calculation is restricted by the smallest dimension in the mesh. As a calculation progresses, the large deformations severely distort the elements and decrease the timestep size. ALE formulations are used to reduce the distortion in the mesh, which improves the accuracy of the solution while allowing a larger timestep size. Although Lagrangian calculations are readily vectorized, the Vectorization of ALE calculations is complicated. Material is transported between adjacent elements, and the standard finite element data structures do not contain the required connectivity data. This paper describes the necessary extensions to the finite element data structure, a method for vectorizing the assembly of the Lagrangian force vector (which is usually not vectorized in finite element programs), and recent work on the advection of momentum.