Hermite Methods for the Scalar Wave Equation

TL;DR

This paper introduces high-order Hermite methods for solving the scalar wave equation, providing stability, error analysis, and implementation strategies for efficient computation in multiple dimensions.

Contribution

It presents novel arbitrary order dissipative and conservative Hermite methods with detailed stability and error analyses for the scalar wave equation.

Findings

Achieves $ ext{O}(2m)$ accuracy with $ ext{O}(m^d)$ degrees of freedom per node.

Provides stability and error analyses for the proposed methods.

Includes implementation strategies suitable for accelerators.

Abstract

Arbitrary order dissipative and conservative Hermite methods for the scalar wave equation achieving $\mathcal{O}(2m)$ orders of accuracy using $\mathcal{O}(m^d)$ degrees of freedom per node in $d$ dimensions are presented. Stability and error analyses as well as implementation strategies for accelerators are also given.