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GPU-accelerated discontinuous Galerkin methods on polytopic meshes. (English) Zbl 1528.65105

Summary: Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/polyhedral (henceforth, collectively termed as polytopic) elements have received considerable attention in recent years. Due to the physical frame basis functions used typically and the quadrature challenges involved, the matrix-assembly step for these methods is often computationally cumbersome. To address this important practical issue, this work proposes two parallel assembly implementation algorithms on Compute Unified Device Architecture-enabled graphics cards for the interior penalty dG method on polytopic meshes for various classes of linear PDE problems. We are concerned with both single graphics processing unit (GPU) parallelization, as well as with implementation on distributed GPU nodes. The results included showcase almost linear scalability of the quadrature step with respect to the number of GPU cores used since no communication is needed for the assembly step. In turn, this can justify the claim that polytopic dG methods can be implemented extremely efficiently, as any assembly computing time overhead compared to finite elements on “standard” simplicial or box-type meshes can be effectively circumvented by the proposed algorithms.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65Y10 Numerical algorithms for specific classes of architectures
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
68Q25 Analysis of algorithms and problem complexity
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
65R10 Numerical methods for integral transforms

Software:

Thrust; CUDA; SciPy; Python
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Full Text: DOI arXiv

References:

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