Uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems

AbstractThis paper deals with discrete monotone iterative methods for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform convergence of the monotone iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented

Iterative algorithms of domain decomposition for the solution of a quasilinear elliptic problem

AbstractThis paper deals with iterative algorithms for domain decomposition applied to the solution of a quasilinear elliptic problem. Two iterative algorithms are examined: the first one is the Schwarz alternating procedure and the second algorithm is suitable for parallel computing. Convergence results are established in the two-domain and multidomain decomposition cases. Some issues of parallel implementation of these algorithms are discussed

A finite-volume Navier-Stokes solver for multiblock structured meshes.

In this thesis numerical solution of 2D steady laminar incompressible viscous Navier-Stokes equations has been considered. For such flows a problem occurs with preserving mass flow through the system. Primitive variables were chosen to perform computations. The solver is based on the finite-volume approach with artificial compressibility. The code was written to accomplish numerical computations based on the suggested approach. This code is capable of handling multiblock meshes and does not require coordinate transformations, due to the finite-volume approach. The artificial compressibility approach allows the calculation of pressure and at the same time preserves mass flow through the system at the steady-state. This code was validated against known results for the driven cavity problem and rapidly expanding channel problem. The problem of a moving road vehicle was studied for different mesh arrangements to investigate the influence of boundary conditions together with mesh quality on the computational results. The results of these calculations were also compared to those obtained by STARCD and found to be in reasonably good agreement.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1996 .B63. Source: Masters Abstracts International, Volume: 34-06, page: 2458. Adviser: R. Barron. Thesis (M.Sc.)--University of Windsor (Canada), 1996