论文标题
自适应稀疏网格不连续的Galerkin方法：审核和软件实施
Adaptive sparse grid discontinuous Galerkin method: review and software implementation
论文作者
论文摘要
本文回顾了自适应稀疏网格不连续的Galerkin（ASG-DG）方法，用于计算高维偏微分方程（PDE）及其软件实现。 c \ texttt {++}软件包称为adam-dg，实现ASG-DG方法，可在\ url {https://github.com/juntaaohuang/adaptive-multirestolution-dg}上获得。该软件包能够处理一类大的高维线性和非线性PDE。我们回顾了算法的基本组件和软件的功能，包括所使用的多波管，双线性操作员的组装，具有分层结构的数据的快速矩阵向量产品。我们通过报告几个基准测试的数值错误和CPU成本，包括线性传输方程，波浪方程和汉密尔顿 - 雅各比方程，进一步证明了包装的性能。
This paper reviews the adaptive sparse grid discontinuous Galerkin (aSG-DG) method for computing high dimensional partial differential equations (PDEs) and its software implementation. The C\texttt{++} software package called AdaM-DG, implementing the aSG-DG method, is available on Github at \url{https://github.com/JuntaoHuang/adaptive-multiresolution-DG}. The package is capable of treating a large class of high dimensional linear and nonlinear PDEs. We review the essential components of the algorithm and the functionality of the software, including the multiwavelets used, assembling of bilinear operators, fast matrix-vector product for data with hierarchical structures. We further demonstrate the performance of the package by reporting numerical error and CPU cost for several benchmark test, including linear transport equations, wave equations and Hamilton-Jacobi equations.
