A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients
A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients
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用于具有不连续系数的 3D 各向异性扩散方程的新 FV 方案和快速单元中心多重网格求解器
DOI：
10.1016/j.jcp.2021.110794
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发表时间：
2022
影响因子：
4.1
通讯作者：
Li Zhilin
中科院分区：
文献类型：
--
作者：
Pan Kejia;Wu Xiaoxin;Hu Hongling;Yu Yunlong;Li Zhilin
本文提出了一种高效的网格中心外推级联多重网格(CEXCMG)方法，用于求解三维间断系数各向异性扩散方程有限体积(FV)离散所产生的大型线性方程组。对于以单元格为中心的FV方案，顶点处的值通常需要由相邻单元格中心值的线性组合来近似。在文献中，加权系数是通过求解局部线性方程组来获得的，这在三维中是昂贵的。本文的创新点之一是提出了一种新的方法，通过对以单元为中心的顶点进行内插来获得顶点值，该方法避免了在具有任意扩散张量的情况下求解局部线性方程组。本文的另一个主要创新点是基于延拓算子的级联多重网格求解器、新发展的显式梯度传递方法和求解具有间断系数的三维各向异性扩散方程的分裂外推算子。数值实验证明了CEXCMG方法在网格尺寸和各向异性扩散张量系数对比度方面的有效性和稳健性。
In this paper, an efficient cell-centered extrapolation cascadic multigrid (CEXCMG) method is proposed for solving large linear system of equations resulting from finite volume (FV) discretizations of three dimensional (3D) anisotropic diffusion equations with discontinuous coefficients. For cell-centered FV schemes, the values at vertex need to be approximated often by a linear combination of neighboring cell-centered values. In the literature, the weighted coefficients are obtained by solving local linear system of equations which is costly in 3D. One of the novelties of this paper is a new approach for obtaining vertex values by interpolating the cell-centered ones, which avoids solving local linear system of equations even with arbitrary diffusion tensors. Another main novelty of this paper is a new cascadic multigrid solver based on a prolongation operator, the newly developed explicit gradient transfer method, and a splitting extrapolation operator for solving 3D anisotropic diffusion equations with discontinuous coefficients. Numerical experiments are presented to demonstrate the efficiency and robustness of the CEXCMG method in terms of the mesh size and the contrast in the coefficients of the anisotropic diffusion tensor.
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影响因子：
4
作者：
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