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- Irfan Altas, Jonathan Dym, Murli M. Gupta, Ram P. Manohar
- SIAM J. Scientific Computing
- 1998

In this work, we use a symbolic algebra package to derive a family of nite diierence approximations for the biharmonic equation on a 9 point compact stencil. The solution and its rst derivatives are carried as unknowns at the grid points. Dirichlet boundary conditions are thus incorporatednaturally. Since the approximations use the 9 point compact stencil,â€¦ (More)

We combine a compact high-order diierence approximation with multigrid V-cycle algorithm to solve the two dimensional Poisson equation with Dirichlet boundary conditions. This scheme, along with several diierent orderings of grid space and projection operators, is compared with the ve-point formula to show the dramatic improvement in computed accuracy, onâ€¦ (More)

- Jun Zhang, Lixin Ge, Murli M. Gupta
- Neural Parallel & Scientific Comp.
- 2000

We present a fourth order compact nite diierence scheme for a general three dimensional convection diiusion equation with variable coeecients on a uniform cubic grid. This high order compact diierence scheme is used to solve convection diiusion equation with boundary layers on a three dimensional nonuniform grid. We compare the computed accuracy andâ€¦ (More)

In this paper, we propose a new paradigm for solving Navierâ€“Stokes equations. The proposed methodology is based on a streamfunctionâ€“velocity formulation of the two-dimensional steady-state Navierâ€“Stokes equations representing incompressible fluid flows in two-dimensional domains. Similar formulations are also possible for three-dimensional fluid flows. Theâ€¦ (More)

diffusion equations using a nine-point compact difference scheme. implementation with multigrid, and carry out a Fourier We test the efficiency of the algorithm with various smoothers and smoothing analysis of the Gaussâ€“Seidel operator. In Secintergrid transfer operators. The algorithm displays a grid-indepention 3 we present numerical experiments thatâ€¦ (More)

- Givi Berikelashvili, Murli M. Gupta, Manana Mirianashvili
- SIAM J. Numerical Analysis
- 2007

- Irfan Altas, Jocelyne Erhel, Murli M. Gupta
- Numerical Algorithms
- 2002

In this paper, we consider several finite-difference approximations for the three-dimensional biharmonic equation. A symbolic algebra package is utilized to derive a family of finite-difference approximations for the biharmonic equation on a 27 point compact stencil. The unknown solution and its first derivatives are carried as unknowns at selected gridâ€¦ (More)

- Murli M. Gupta, Jun Zhang
- Applied Mathematics and Computation
- 2000

We present an explicit fourth-order compact nite diierence scheme for approximating the three dimensional convection-diiusion equation with variable coeecients. This 19-point formula is deened on a uniform cubic grid. Fourier smoothing analysis is performed to show that the smoothing factor of certain relaxation techniques used with the scheme is smallerâ€¦ (More)

- Murli M. Gupta, Jun Zhang
- 1998

We present an explicit fourth-order compact nite diierence scheme for approximating the three dimensional convection-diiusion equation with variable coeecients. This 19-point formula is deened on a uniform cubic grid. Fourier smoothing analysis is performed to show that the smoothing factor of some relaxation techniques with our scheme is smaller than 1. Weâ€¦ (More)