Concurrency of three-dimensional refined isogeometric analysis

Abstract We perform the analysis of the concurrency of the parallel refined isogeometric analysis (rIGA) computations. Namely, we consider three-dimensional mesh partitioned into several macro-elements, with tensor product B-spline basis functions, and C° separators introduced between the macro-elements. We partition the computational problem into a sequence of tasks, and we define the dependency relation between the tasks. Next, we use the trace theory approach to identify the sets of tasks that can be executed in concurrent, one set after the other. We also estimate the computational cost of the tasks. To generalize our model for the distributed memory case, we use the Partitioning Communication Agglomeration and Mapping (PCAM) model with tasks and communication channels mapped into the architecture of the parallel distributed memory machine. We perform numerical experiments on the representative three-dimensional meshes partitioned into macro-elements with quadratic and cubic B-splines, and we compare the numerical results with theoretical estimates.

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