Work

Leapfrog time-stepping for Hermite methods

Year: 2018

Type: preprint

Abstract: We introduce Hermite-leapfrog methods for first order wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors. The new schemes stagger field variables in both time and space and are high-order accurate. We provide a detailed description of the method and demonstrate that the method conserves variable quantities in one-space dimension. Higher dimensional versions of the method are constructed via a tensor product construction. Numerical evidence and rigorous analysis in one space dimension establish stability and high-order convergence. Experiments demonstrating efficient implementations on a graphics processing unit are also presented.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1808.10481

Authors: Vargas, Arturo, Hagstrom, Thomas, Chan, Jesse, Warburton, Tim

Institutions: Lawrence Livermore National Laboratory, Southern Methodist University, Rice University, Virginia Tech

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, Lawrence Livermore National Laboratory

Awards: G1088636562, Collaborative Research: Improved Algorithms for Multiwave Imaging in Complex Media: Theory and Computation, G2145270357, Robust High-Order Methods for Wave Equations in the Time Domain, G3669113783, Bernstein-Bezier Techniques for High Order Time-Domain Discontinuous Galerkin Methods, G991281326

OpenAlex ID: W2952756700

Cites: 10

Cited by:

Related to: 20