GPU-Accelerated Discontinuous Galerkin Methods on Polytopic Meshes

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