An efficient multigrid solver for 3D biharmonic equation with a discretization by 25-point difference scheme
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| Format: | Preprint |
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2019
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| _version_ | 1866916533209399296 |
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| author | Pan, Kejia He, Dongdong Ni, Runxin |
| author_facet | Pan, Kejia He, Dongdong Ni, Runxin |
| contents | In this paper, we propose an efficient extrapolation cascadic multigrid (EXCMG) method combined with 25-point difference approximation to solve the three-dimensional biharmonic equation. First, through applying Richardson extrapolation and quadratic interpolation on numerical solutions on current and previous grids, a third-order approximation to the finite difference solution can be obtained and used as the iterative initial guess on the next finer grid. Then we adopt the bi-conjugate gradient (Bi-CG) method to solve the large linear system resulting from the 25-point difference approximation. In addition, an extrapolation method based on midpoint extrapolation formula is used to achieve higher-order accuracy on the entire finest grid. Finally, some numerical experiments are performed to show that the EXCMG method is an efficient solver for the 3D biharmonic equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1901_05118 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | An efficient multigrid solver for 3D biharmonic equation with a discretization by 25-point difference scheme Pan, Kejia He, Dongdong Ni, Runxin Numerical Analysis 65N06, 65N55 In this paper, we propose an efficient extrapolation cascadic multigrid (EXCMG) method combined with 25-point difference approximation to solve the three-dimensional biharmonic equation. First, through applying Richardson extrapolation and quadratic interpolation on numerical solutions on current and previous grids, a third-order approximation to the finite difference solution can be obtained and used as the iterative initial guess on the next finer grid. Then we adopt the bi-conjugate gradient (Bi-CG) method to solve the large linear system resulting from the 25-point difference approximation. In addition, an extrapolation method based on midpoint extrapolation formula is used to achieve higher-order accuracy on the entire finest grid. Finally, some numerical experiments are performed to show that the EXCMG method is an efficient solver for the 3D biharmonic equation. |
| title | An efficient multigrid solver for 3D biharmonic equation with a discretization by 25-point difference scheme |
| topic | Numerical Analysis 65N06, 65N55 |
| url | https://arxiv.org/abs/1901.05118 |