GPU-based Parallel Computing for Nonlinear Finite Element Deformation Analysis

Ramin Mafi
McMaster University
McMaster University, 2014


   title={GPU-based Parallel Computing for Nonlinear Finite Element Deformation Analysis},

   author={Mafi, Ramin},


   publisher={McMaster University Library}


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Computer-based surgical simulation and non-rigid medical image registration in image-guided interventions are examples of applications that would benefit from real-time deformation simulation of soft tissues. The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models which then can be discretized by the Finite Element Method (FEM) for a numerical solution. Computational complexity of nonlinear FEM-based models has limited their use in real-time applications. The data-parallel nature and intense arithmetic operations in nonlinear FEM models are suitable for massive parallelization of the computations, in order to meet the response time requirements in such applications. This thesis is concerned with computational aspects of complex nonlinear deformation analysis problems with an emphasis on the speed of response using a parallel computing philosophy. It proposes a fast, accurate and scalable Graphic Processing Unit (GPU)-based implementation of the total Lagrangian FEM using implicit time integration for dynamic nonlinear deformation analysis. This is a general formulation valid for large deformations and strains and can account for material nonlinearities. A penalty method is used to satisfy the physical boundary constraints due to contact between deformable objects. The proposed set of optimized GPU kernels for computing the FEM matrices achieves more than 100 GFLOPS on a GTX 470 GPU device. The use of a novel vector assembly kernel and memory optimization strategies result in a performance gain of up to 25 GFLOPS in the PCG computations.
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