Unfitted hybrid high-order methods for the wave equation

A High Order Approximation of the Two Dimensional Acoustic Wave Equation with Discontinuous Coefficients

This paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. The method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions. The construction of the nonstandard method is based on the special treatment of the interface using suitable jump conditio...

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein’s equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on ...

Stable and high order accurate difference methods for the elastic wave equation in discontinuous media

Article history: Received 5 December 2013 Received in revised form 26 August 2014 Accepted 28 August 2014 Available online 6 September 2014

High Order Unfitted Finite Element Methods for Interface Problems and PDEs on Surfaces

High Order Stable Finite Difference Methods for the Schrödinger Equation

In this paper we extend the Summation–by–parts–simultaneous approximation term (SBP–SAT) technique to the Schrödinger equation. Stability estimates are derived and the accuracy of numerical approximations of interior order 2m, m = 1, 2, 3, are analyzed in the case of Dirichlet boundary conditions. We show that a boundary closure of the numerical approximations of order m lead to global accuracy...