Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Comparison of second- and fourth-order discretizations for multigrid Poisson solvers
Journal of Computational Physics
A three-point combined compact difference scheme
Journal of Computational Physics
A three-point sixth-order nonuniform combined compact difference scheme
Journal of Computational Physics
Preconditioned iterative methods and finite difference schemes for convection-diffusion
Applied Mathematics and Computation
A multigrid tutorial: second edition
A multigrid tutorial: second edition
High accuracy multigrid solution of the 3D convection-diffusion equation
Applied Mathematics and Computation
Mathematics and Computers in Simulation
Numerical Mathematics and Computing
Numerical Mathematics and Computing
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Compact optimal quadratic spline collocation methods for the Helmholtz equation
Journal of Computational Physics
A Finite Element Splitting Extrapolation for Second Order Hyperbolic Equations
SIAM Journal on Scientific Computing
A Fourth Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Square
Journal of Scientific Computing
Computers & Mathematics with Applications
An efficient fourth-order low dispersive finite difference scheme for a 2-D acoustic wave equation
Journal of Computational and Applied Mathematics
Hi-index | 31.46 |
We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, multigrid method, Richardson extrapolation technique, and an operator based interpolation scheme. We use multigrid V-Cycle procedure to build our multiscale multigrid algorithm, which is similar to the full multigrid method (FMG). The multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method, compared to Sun-Zhang's sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) method and the standard fourth order compact difference (FOC) scheme using a multigrid method.