Parallel isogeometric boundary element analysis with T-splines on CUDA

Abstract

We present a framework for parallel isogeometric boundary element analysis (BEA) of elastic solids on CUDA. To deal with traction discontinuities, we propose a BEA model that supports multiple nodes and semi-discontinuous elements. The multiplicity of a node is defined by the number of regions containing any element influenced by the node. A region is a group of connected elements delimited by a closed crease curve. The default shape function of an element is determined by a linear operator applied to a set of basis functions. A BEA model is supposed to be generated from a watertight boundary representation of a solid. In this paper, we employ bicubic analysis-suitable T-splines. In this case, the shape of an element is defined by its Bézier extraction operator applied to the tensor product of Bernstein polynomials of degree 3. We describe the data structures of the BEA model and the main algorithms of the analysis pipeline on CUDA. In particular, we describe two strategies for parallel assembling of the linear system of equations. We also introduce a novel approach for inside integration based on the subdivision of the singular region in triangles with constant aspect ratio. In the T-splines context, we extend the Bézier extraction to handle unstructured T-meshes with crease edges. Moreover, we propose a scheme for embedding the influence of linked tangency handles on the shape of an element directly into the Bézier extraction operator. Such an embedding enables the removal of the corresponding nodes from the BEA model and the application of an alternative collocation method we discuss in the paper. We present several experiments to evaluate the accuracy and efficiency of the proposed framework. The results demonstrate that the GPU can be advantageously employed for parallelizing T-spline-based isogeometric analysis using boundary elements, achieving a speedup of up to 29x compared to the sequential code on a current laptop. We make the BEA code available in a prototype in MATLAB with a graphical interface that allows users to apply boundary conditions and visualize analysis results on the boundary.