Poisson equation solver with fourth-order accuracy by using interpolated differential operator scheme. (English) Zbl 0999.65114
Summary: A Poisson equation solver with fourth-order spatial accuracy is developed by using the interpolated differential operator (IDO) scheme. The number of grids required for obtaining the results of numerical computation with the same accuracy as that by the second-order center finite difference method is drastically reduced. The consistency is confirmed to the use of the multigrid method and the red-black algorithm. The decrease of the CPU time by the multigrid method and by the parallel computing indicates the applicability of the IDO Poisson solver to large scale problems.
MSC:
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 65Y05 | Parallel numerical computation |
| 65N15 | Error bounds for boundary value problems involving PDEs |
Keywords:
comparison of methods; interpolated differential operator scheme; Hermite interpolation; Poisson equation; finite difference method; consistency; multigrid method; red-black algorithm; parallel computingReferences:
| [1] | Gutknecht, M. H., Variants of Bi-CGSTAB for matrices with complex spectrum, Tech. Report 91-14, IPS Research Report (1991) |
| [2] | Saad, Y.; Schultz, M., Conjugate gradient-like algorithms for solving nonsymmetric linear systems, Math. Comp., 44, 417-424 (1985) · Zbl 0566.65019 |
| [3] | Aoki, T., Interpolated differential operator (IDO) scheme for solving partial differential equations, Comp. Phys. Comm., 102, 132-146 (1996) |
| [4] | Sakurai, K.; Aoki, T., Implicit IDO (interpolated differential operator) scheme, Comp. Fluids Dynamics Journal, 8, 1, 6-12 (1999) |
| [5] | Kondoh, Y.; Hosaka, Y.; Ishii, K., Kernel optimum nearly-analytical discretization (KOND) algorithm applied to parabolic and hyperbolic equations, Comput. Math. Applic., 27, 3, 59-90 (1994) · Zbl 0796.65101 |
| [6] | Brandt, A., Multi-level adaptive solutions to boundary-value problems, Math. Comput., 31, 333-390 (1977) · Zbl 0373.65054 |
| [7] | Qianshun, C., Use of the splitting scheme and multigrid method to compute flow separation, Int. J. Num. Meth. Fluids, 7, 719-731 (1987) · Zbl 0628.76045 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
