A domain-decomposed fast poisson solver on a rectangle
SIAM Journal on Scientific and Statistical Computing - Papers from the Second Conference on Parallel Processing for Scientific Computin
Local mesh refinement multilevel techniques
SIAM Journal on Scientific and Statistical Computing
Fast Fourier transforms for direct solution of Poisson's equation with staggered boundary conditions
Journal of Computational Physics
Computational techniques for fluid dynamics
Computational techniques for fluid dynamics
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A fast Poisson solver for complex geometries
Journal of Computational Physics
Accurate finite difference methods for time-harmonic wave propagation
Journal of Computational Physics
A compact multigrid solver for convection-diffusion equations
Journal of Computational Physics
A GMRES-based plane smoother in multigrid to solve 3D anisotropic fluid flow problems
Journal of Computational Physics
Comparison of second- and fourth-order discretizations for multigrid Poisson solvers
Journal of Computational Physics
Fast and high accuracy multigrid solution of the three dimensional Poisson equation
Journal of Computational Physics
Preconditioned iterative methods and finite difference schemes for convection-diffusion
Applied Mathematics and Computation
High accuracy multigrid solution of the 3D convection-diffusion equation
Applied Mathematics and Computation
Mathematics and Computers in Simulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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A high-order compact (HOC) difference scheme is proposed to solve the three-dimensional (3D) Poisson equation on nonuniform orthogonal Cartesian grids involving no coordinate transformation from the physical space to the computational space. Theoretically, the proposed scheme has third to fourth-order accuracy; its fourth-order accuracy is achieved under uniform grid settings. Then, a multigrid method is developed to solve the linear system arising from this HOC difference scheme and the corresponding multigrid restriction and interpolation operators are constructed using the volume law. Numerical experiments are conducted to show the computed accuracy of the HOC scheme and the computational efficiency of the multigrid method.