An Adaptive Multiresolution Interior Penalty Discontinuous Galerkin Method for Wave Equations in Second Order Form
An Adaptive Multiresolution Interior Penalty Discontinuous Galerkin Method for Wave Equations in Second Order Form
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DOI：
10.1007/s10915-020-01322-w
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发表时间：
2020-04
影响因子：
2.5
通讯作者：
Juntao Huang;Yuan Liu;Wenting Guo;Zhanjing Tao;Yingda Cheng
中科院分区：
文献类型：
--
作者：
Juntao Huang;Yuan Liu;Wenting Guo;Zhanjing Tao;Yingda Cheng
本文提出了一类自适应多分辨率间断Galerkin（DG）方法，用于数值模拟空间二阶标量波动方程。该方案的两个关键组成部分包括自适应函数空间中的内部惩罚DG公式和两类用于实现多分辨率的多小波。特别是，正交Alpert的多小波被用来表示DG解的层次结构，并进一步引入插值多小波，以提高计算效率的存在下，可变的波速或非线性源。文中给出了该方法的稳定性和精度的一些理论结果。通过二维和三维的基准数值试验验证了该方法的有效性。
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.