论文标题
带有前向散射的辐射传输方程的角度多移民预处理
An Angular Multigrid Preconditioner for the Radiation Transport Equation with Forward-Peaked Scatter
论文作者
论文摘要
在上一篇论文（Lathouwers andPerkó，2019年）中，我们为Boltzmann传输方程开发了一种有效的角度multigrid预处理，并具有由Fokker-Planck近似模型的前向峰散射。离散化基于空间和角度的完全不连续的盖尔金有限元方案。发现该方案在各向同性和各向异性的角度网眼上非常有效。本文的目的是将方法扩展到非fokker-Planck模型，该模型描述了一般的Legendre扩展。由于使用了标准源迭代，因此使用了标准源的迭代，而在最高的角网格上的解决方案是通过特殊的扫描程序来实现的，该过程能够仅使用少量迭代来用高度各向异性散射解决此问题。通过降低多式预科器中的散射顺序获得有效的方案。提出了一组测试问题，以说明该方法的有效性，即，比单网格情况更少的迭代效果，更重要的是，计算工作减少。
In a previous paper (Lathouwers and Perkó, 2019) we have developed an efficient angular multigrid preconditioner for the Boltzmann transport equation with forward-peaked scatter modeled by the Fokker-Planck approximation. The discretization was based on a completely discontinuous Galerkin finite element scheme both for space and angle. The scheme was found to be highly effective on isotropically and anisotropically refined angular meshes. The purpose of this paper is to extend the method to non-Fokker-Planck models describing the forward scatter by general Legendre expansions. As smoother the standard source iteration is used whereas solution on the coarsest angular mesh is effected by a special sweep procedure that is able to solve this problem with highly anisotropic scatter using only a small number of iterations. An efficient scheme is obtained by lowering the scatter order in the multigrid preconditioner. A set of test problems is presented to illustrate the effectivity of the method, i.e. in less iterations than the single-mesh case and more importantly with reduced computational effort.
