A Real-Time Multigrid Finite Hexahedra Method for Elasticity

July 11th, 2010

A 30,000-hexahedron FEM model.

Abstract:

In this paper we present a GPU-based multigrid approach for simulating elastic deformable objects in real time. Our method is based on a finite element discretization of the deformable object using hexahedra. It draws upon recent work on multigrid schemes for the efficient numerical solution of partial differential equations on such discretizations. Due to the regular shape of the numerical stencil induced by the hexahedral regime, and since we use matrix-free formulations of all multigrid steps, computations and data layout can be restructured to avoid execution divergence and to support memory access patterns which enable the hardware to coalesce multiple memory accesses into single memory transactions. This enables to effectively exploit the GPU’s parallel processing units and high memory bandwidth via the CUDA parallel programming API. We demonstrate performance gains of up to a factor of 12 compared to a highly optimized CPU implementation. By using our approach, physics-based simulation at an object resolution of 64^3 is achieved at interactive rates.

(Christian Dick, Joachim Georgii and Rüdiger Westermann: “A Real-Time Multigrid Finite Hexahedra Method for Elasticity”http://wwwcg.in.tum.de/Research/Publications/CompMechanics)