Authors

Abstract

We propose an Exponential DG framework for partial differential equations. We decompose7 governing equations into linear and nonlinear parts to which we apply the discontinuous Galerkin 8 (DG) spatial discretization. In particular, we construct the linear part using Jacobian that effectively 9 capture stiff characteristics in the system. The former is integrated analytically, whereas the latter10 is approximated. This approach i) is stable with a large Courant number (Cr > 1); ii) supports11 high-order solutions both in time and space; iii) is computationally favorable compared to IMEX12 DG methods with no preconditioner; iv) becomes comparable to explicit RKDG methods on uniform13 mesh and beneficial on non-uniform grid for Euler equations; v) is scalable in a modern massively14 parallel computing architecture due to its explicit nature of exponential time integrators and com15 pact communication stencil of DG method. Numerical results demonstrate the performance of our16 proposed methods through various examples. We also discuss the stability and convergence analysis17 for our exponential DG scheme in the context of Burgers equation.