New Methods to Speed-up the Boundary Element Method in LS-DYNA

Abstract

LS-DYNA is a general purpose explicit and implicit finite element program used to analyse the non linear dynamic response of three-dimensional solids and fluids. It is developed by Livermore Software Technology Corporation (LSTC). An electromagnetism (EM) module has been added to LS-DYNA for coupled mechanical/thermal/electromagnetic simulations, which have been extensively performed and benchmarked against experimental results for Magnetic Metal Forming (MMF) and Welding (MMW) applications. These simulations are done using a Finite Element Method (FEM) for the conductors coupled with a Boundary Element Method (BEM) for the surrounding air. The BEM has the advantage that it does not require an air mesh, which can be difficult to build when the gaps between conductors are very small, and to adapt when the conductors are moving, with contact possibly arising. Besides, the BEM does not require the introduction of infinite boundary conditions which are somehow artificial and can create discrepancies. On another hand, it generates dense matrices which take time to assemble and solve, and require a lot of memory. In LS-DYNA, the memory issue is handled by using low rank approximations on the off diagonal sub-blocks of the BEM matrices, creating a so-called Block Low Rank (BLR) matrix structure. The issue of the assembly and solve time is now being studied, and we present the so called “Multi-Center” (MC) method where the computation of the far-field submatrices is greatly reduced and the solve time somehow reduced. We will present the method as well as some first results.