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Manuscript Title: Determination of SSOR-SI iteration parameters.
Authors: J.B. Campbell
Program title: MUCALC
Catalogue identifier: ABUM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 10(1975)194
Programming language: Fortran.
Computer: IBM 360/67.
Operating system: TSS/360.
RAM: 26K words
Word size: 32
Peripherals: magnetic tape.
Keywords: General purpose, Differential equations, Laplace, Dirichlet problem, Eigenvalue, Fixed membrane, Dinite difference.
Classification: 4.3.

Nature of problem:
In this communication, an efficient method for the determination of iteration parameters for symmetric successive overrelaxation iteration with semi-iterative refinement as applied to the solution of the discrete laplacian is described. SSOR-SI is one of the iterative techniques used for the solution of finite difference equations and is described by Young. The program may also be used to calculate at least one eigenvalue of the fixed membrane problem.

Solution method:
The spectral radius of the Jacobi matrix associated with the difference equations is determined by the power method described by Faddeev and Faddeeva. This value can be used for a determination of SSOR iteration parameters.

Restrictions:
The iteration parameters are determined only for a region where there are no irregular difference approximations and where a square mesh is used.

Unusual features:
Integer arithmetic is used throughout the determination. Integer multiplication and division occur in key parts of the program only when the multiplier or divisor is a power of 2.

Running time:
The first eigenvalue of the fixed membrane problem for an L-shaped region was calculated to 3 significant digits in 10 s. When assembler language versions of two small subroutines of the program were used, the computing time was reduced to 5 sec. An accuracy of 3 digits in the first eigenvalue is sufficient for the determination of iteration parameters.