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Implicit FEM Solver on GPU for Interactive Deformation Simulation

Hadrien Courtecuisse, Jérémie Allard, François Faure
GPU Computing Gems Vol. 2.


We present a set of methods to implement an implicit Finite Element solver on the GPU. In contrast to previous FEM implementations on the GPU which only address explicit time integration, our method allows large time steps for arbitrarily stiff objects. Unlike previous GPU-based sparse solvers, we avoid the assembly of the system matrix, and parallelize the matrix operations directly on the original object mesh. This considerably reduces the number of operations required, and more importantly the consumed bandwidth, enabling the method to be fast enough for highly complex interactive stiff body simulations. The presented methods can be applied in game and visual effects simulations, as well as medical and physics applications, where FEM is well established but currently limited by its computational cost. The core of the method can also be applied to many other scientific applications where a large irregular sparse system of equations is solved using an iterative method.

Article (Pdf)

BibTex :
author = "Allard, J\'er\'emie and Courtecuisse, Hadrien and Faure, Fran\c{c}ois",
title = "Implicit FEM Solver on GPU for Interactive Deformation Simulation",
booktitle = "Computing Gems Jade Edition",
chapter = "21",
year = "2011",
month = sep,
publisher = "NVIDIA/Elsevier",
url = ""