high performance computing on graphics processing units: hgpu.org

Finite Element Analysis helps designers at the early stages of product design through simulation and behavioral prediction. This thesis is on transient finite element analysis, specifically, structural dynamics, where the behavior of a product due to time-dependent loads is desired. A critical computational challenge in structural dynamics is that it typically requires significant amounts of time and memory. In the present thesis, a fast time-stepping strategy for the Newmark-beta method is developed; the latter is used extensively in modeling structural dynamics. In particular, we speed up the repeated inversion of the linear system of equations in the Newmark-beta method by implementing and merging five distinct but complementary concepts: 1) Voxelization; 2) Assembly-Free FEA; 3) Deflated Conjugate Gradient; 4) Parallelization; 5) Adaptive Sub-Domain Refinement. The resulting Assembly-Free Deflated Conjugate Gradient (AF-DCG) version of the Newmark-beta is well-suited for large-scale problems, and can be easily ported to multi-core architectures. Numerical experiments demonstrate that the proposed method is much faster than the well-known commercial software ANSYS.