Reduced storage nodal discontinuous Galerkin methods on semi-structured prismatic meshes

TL;DR

This paper introduces a high-order nodal discontinuous Galerkin method for wave problems on hybrid meshes with wedges and tetrahedra, featuring energy stability and GPU efficiency improvements.

Contribution

It presents a novel energy-stable mass lumping technique for vertically mapped wedges and demonstrates high-order convergence and GPU performance on layered domains.

Findings

Energy stability achieved with the new mass lumping method.

High-order convergence demonstrated on hybrid meshes.

Efficient GPU implementation evaluated.

Abstract

We present a high order time-domain nodal discontinuous Galerkin method for wave problems on hybrid meshes consisting of both wedge and tetrahedral elements. We allow for vertically mapped wedges which can be deformed along the extruded coordinate, and present a simple method for producing quasi-uniform wedge meshes for layered domains. We show that standard mass lumping techniques result in a loss of energy stability on meshes of vertically mapped wedges, and propose an alternative which is both energy stable and efficient. High order convergence is demonstrated, and comparisons are made with existing low-storage methods on wedges. Finally, the computational performance of the method on Graphics Processing Units is evaluated.