DeepAI
Log In Sign Up

An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form

04/18/2020
by   Juntao Huang, et al.
0

In this paper, we propose a class of adaptive multiresolution (also called adaptive sparse grid) discontinuous Galerkin (DG) methods for simulating scalar wave equations in second order form in space. The two key ingredients of the schemes include an interior penalty DG formulation in the adaptive function space and two classes of multiwavelets for achieving multiresolution. In particular, the orthonormal Alpert's multiwavelets are used to express the DG solution in terms of a hierarchical structure, and the interpolatory multiwavelets are further introduced to enhance computational efficiency in the presence of variable wave speed or nonlinear source. Some theoretical results on stability and accuracy of the proposed method are presented. Benchmark numerical tests in 2D and 3D are provided to validate the performance of the method.

READ FULL TEXT

page 29

page 30

page 32

page 33

01/27/2020

An energy-based discontinuous Galerkin method for semilinear wave equations

We generalize the energy-based discontinuous Galerkin method proposed in...
07/03/2020

An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations

This paper develops a high order adaptive scheme for solving nonlinear S...
10/11/2020

Discontinuous Galerkin methods for a dispersive wave hydro-sediment-morphodynamic model

A dispersive wave hydro-sediment-morphodynamic model developed by comple...
03/05/2019

An interior penalty discontinuous Galerkin method for the time-domain acoustic-elastic wave interaction problem

In this paper, we consider numerical solutions of a time domain acoustic...
11/03/2022

Adaptive sparse grid discontinuous Galerkin method: review and software implementation

This paper reviews the adaptive sparse grid discontinuous Galerkin (aSG-...
11/25/2022

Discontinuous Galerkin method for linear wave equations involving derivatives of the Dirac delta distribution

Linear wave equations sourced by a Dirac delta distribution δ(x) and its...