典型文献
Energy-Based Discontinuous Galerkin Difference Methods for Second-Order Wave Equations
文献摘要：
We combine the newly constructed Galerkin difference basis with the energy-based dis-continuous Galerkin method for wave equations in second-order form.The approximation properties of the resulting method are excellent and the allowable time steps are large com-pared to traditional discontinuous Galerkin methods.The one drawback of the combined approach is the cost of inversion of the local mass matrix.We demonstrate that for constant coefficient problems on Cartesian meshes this bottleneck can be removed by the use of a modified Galerkin difference basis.For variable coefficients or non-Cartesian meshes this technique is not possible and we instead use the preconditioned conjugate gradient method to iteratively invert the mass matrices.With a careful choice of preconditioner we can dem-onstrate optimal complexity,albeit with a larger constant.
文献关键词：
中图分类号：
作者姓名：
Lu Zhang;Daniel Appel?;Thomas Hagstrom
作者机构：
Department of Applied Physics and Applied Mathematics,Columbia University,New York,NY 10027,USA;Department of Computational Mathematics,Science and Engineering and Department of Mathematics,Michigan State University,East Lansing,MI 48824,USA;Department of Mathematics,Southern Methodist University,Dallas,TX 75275,USA
文献出处：
引用格式：
[1]Lu Zhang;Daniel Appel?;Thomas Hagstrom-.Energy-Based Discontinuous Galerkin Difference Methods for Second-Order Wave Equations)[J].应用数学与计算数学学报,2022(03):855-879
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Energy,Based,Discontinuous,Galerkin,Difference,Methods,Second,Order,Wave,Equations,We,newly,constructed,difference,basis,energy,wave,equations,second,order,form,approximation,properties,resulting,excellent,allowable,steps,pared,traditional,discontinuous,methods,drawback,combined,approach,cost,inversion,local,mass,matrix,demonstrate,that,constant,problems,Cartesian,meshes,this,bottleneck,can,removed,by,use,modified,For,variable,coefficients,technique,not,possible,we,instead,preconditioned,conjugate,gradient,iteratively,invert,matrices,With,careful,choice,preconditioner,optimal,complexity,albeit,larger
AB值：
0.624463
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