An efficient multigrid solver for 3D biharmonic equation with a\n discretization by 25-point difference scheme

2019/01/15 by Kejia Pan, Dongdong He, Pan, Kejia +3
Computer Science · Engineering · Mathematics · #Matrix Theory and Algorithms #Electromagnetic Simulation and Numerical Methods #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1901.05118

Abstract

In this paper, we propose an efficient extrapolation cascadic multigrid\n(EXCMG) method combined with 25-point difference approximation to solve the\nthree-dimensional biharmonic equation. First, through applying Richardson\nextrapolation and quadratic interpolation on numerical solutions on current and\nprevious grids, a third-order approximation to the finite difference solution\ncan be obtained and used as the iterative initial guess on the next finer grid.\nThen we adopt the bi-conjugate gradient (Bi-CG) method to solve the large\nlinear system resulting from the 25-point difference approximation. In\naddition, an extrapolation method based on midpoint extrapolation formula is\nused to achieve higher-order accuracy on the entire finest grid. Finally, some\nnumerical experiments are performed to show that the EXCMG method is an\nefficient solver for the 3D biharmonic equation.\n

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