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The Stefan problem solved via conjugate gradient-like iterative methods on a parallel vector machine

Journal Article · · International Journal of Supercomputer Applications; (United States)

The aim of this paper is to illustrate the validity and efficiency of iterative methods for solving large linear systems arising from the finite element discretization of the equation governing conduction-controlled solidification processes. Starting from the basic enthalpy equation, two alternative formulations are obtained and fixed-grid finite element discretizations are developed. These discretizations yield a set of nonlinear equations that are linearized using the Newton-Raphson scheme. The linearized equations are used as a basis for evaluating different iterative methods of the conjugated gradient type. Symmetric scaling and incomplete factorization preconditioning of the linear equations are used to improve the convergence properties of the iterative methods. Vectorization and parallelization are also employed to make full use of the CRAY-2 supercomputer. The results indicate that the implementation of currently available iterative solvers leads to efficient solution methodologies for phase change problems.

OSTI ID:
5604461
Journal Information:
International Journal of Supercomputer Applications; (United States), Journal Name: International Journal of Supercomputer Applications; (United States) Vol. 5:3; ISSN 0890-2720; ISSN IJSAE
Country of Publication:
United States
Language:
English