Real-Time Nonlinear Finite Element Computations on GPU: Handling of Different Element Types

Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers, we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different nonlinear material models, finite deformations and brain-skull contacts) in less than 5 s on a personal computer using a Graphics Processing Unit (GPU) for models having up to 50,000 degrees of freedom. In this chapter, we compare several approaches for implementing different element types on the GPU using the NVIDIA Compute Unified Device Architecture. Our results can be used as a guideline for selecting the best GPU implementation approach for finite element algorithms which require mixed meshes or even for meshless methods.