论文标题
小波坐标中非局部操作员的快速直接求解器
A fast direct solver for nonlocal operators in wavelet coordinates
论文作者
论文摘要
在本文中，我们考虑了非本地运营商的快速直接求解器。关键的想法是将系统矩阵的小波表示结合，产生准sparse矩阵，并与嵌套的解剖序列方案结合。后者分别通过cholesky分解或LU分解分别分解系统矩阵的分解过程中大大降低了填充。这样，我们最终以压缩系统矩阵的确切倒数，仅矩阵中的非零条目数量适度增加。 为了说明方法的疗效，我们为非局部运算符的不同高度相关应用进行数值实验：我们考虑（i）三个空间维度的边界积分方程的直接解决方案，从可极化的持续模型发出，（ii）在集成形式和（iii iii and（iii iii simus）中，是一个随机范围的抛物性偏置式问题。
In this article, we consider fast direct solvers for nonlocal operators. The pivotal idea is to combine a wavelet representation of the system matrix, yielding a quasi-sparse matrix, with the nested dissection ordering scheme. The latter drastically reduces the fill-in during the factorization of the system matrix by means of a Cholesky decomposition or an LU decomposition, respectively. This way, we end up with the exact inverse of the compressed system matrix with only a moderate increase of the number of nonzero entries in the matrix. To illustrate the efficacy of the approach, we conduct numerical experiments for different highly relevant applications of nonlocal operators: We consider (i) the direct solution of boundary integral equations in three spatial dimensions, issuing from the polarizable continuum model, (ii) a parabolic problem for the fractional Laplacian in integral form and (iii) the fast simulation of Gaussian random fields.
