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

Journal Article · Tue Jan 01 04:00:00 EST 1991 · International Journal of Supercomputer Applications; (United States)

DOI:https://doi.org/10.1177/109434209100500307· OSTI ID:5604461

Chronopoulos, A T; Swaminathan, C R; Voller, V R ^[1]

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1. Univ. of Minnesota, Minneapolis, MN (US)

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

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
COMPUTERS
CRAY COMPUTERS
DIGITAL COMPUTERS
ENTHALPY
FINITE ELEMENT METHOD
ITERATIVE METHODS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARALLEL PROCESSING
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
PROGRAMMING
SOLIDIFICATION
SUPERCOMPUTERS
THERMODYNAMIC PROPERTIES
VECTOR PROCESSING