International Journal of High Performance Computing Applications
A conservative phase field method for solving incompressible two-phase flows
Journal of Computational Physics
Matrix decomposition algorithms for elliptic boundary value problems: a survey
Numerical Algorithms
A Fourth Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Square
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
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In this paper, a fast direct solver for the Poisson equation on the half-staggered grid is presented. The Poisson equation results from the projection method of the finite difference solution of the incompressible Navier--Stokes equations. To achieve our goal, new algorithms for diagonalizing a semidefinite pair are developed. The fast solver can also be extended to the three-dimensional case. The motivation and related issues in using this half-staggered grid are also discussed.