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 …

Discontinuous Galerkin (dG) methods are powerful tools for solving complex partial
differential equations (PDEs), in particular those involving irregular geometries. Their key
advantages include handling complex geometries and the ability to resolve localised
features efficiently with adaptable meshes and/or variable local polynomial degrees.
However, matrix assembly in dG implementations presents a challenge due to the use of
physical frame basis functions and expensive quadratures over polytopic elements. This …