NESC9576 CPDES3.

1. NAME OR DESIGNATION OF PROGRAM:  CPDES3.

3. DESCRIPTION OF PROGRAM OR FUNCTION

CPDES3 solves the linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximation employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils, permits general couplings between all of the component PDE's, and automatically generates the matrix structures needed to perform the  algorithm.

4. METHOD OF SOLUTION

The resulting sparse matrix equation with a complicated sub-band structure and generally asymmetric is solved by either the prEconditioned conjugate gradient (CG) method or the preconditioned biconjugate gradient (BCG) algorithm. BCG enjoys faster convergence in most cases but in rare instances diverges. Then, CG iterations must be used.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The discretization of the coupled three-dimensional PDE's and their boundary conditions must result in an operator stencil which fits in the Cray2 memory. In addition, the matrix must possess a reasonable amount of diagonal dominance for the preconditioning technique to be effective.

6. TYPICAL RUNNING TIME

Execution times are problem dependent because ill-conditionel matrices require more iterations than well- conditioned ones. The sample problems converged to relative errors of 1.0E-10 in 10 to 90 seconds on the Cray2.

7. UNUSUAL FEATURES OF THE PROGRAM

All inner loops are arranged to vectorize on the Cray2. A switch is included to allow the user to choose between the biconjugate (BCG) or conjugate (CG) gradient algorithm.

8. RELATED AND AUXILIARY PROGRAMS

The preconditioning technique is the same as that used in ILUCG3 (NESC 9927). CPDES2 (NESC 9577) is a preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled PDE's in two dimensions.

10. REFERENCES:

- D.V. Anderson, A.E. Koniges, and D.E. Shumaker:
  CPDES3 - A Preconditioned Conjugate Gradient Solver for Linear
  Asymmetric Matrix Equations Arising from Coupled Partial
  Differential Equations in Three Dimensions
  UCRL-96618 Preprint (May 1987).

11. MACHINE REQUIREMENTS

From 24*n*m to (256*n-76)*m words of the memory depending on the matrix sparsity pattern, where n is the number of coupled partial differential equations and m is the number of linear equations.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  CTSS.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

All COMMON and NAMELIST declarations are set in macros, and PARAMETER statements are used. The CPDES3 source is processed by a pre-compiler to obtain standard CFT FORTRAN source; the pre-compiler is not included.

15. NAME AND ESTABLISHMENT OF AUTHORS

          D.V. Anderson, A.E. Koniges, D.E. Shumaker
          National MFE Computer Center
          Lawrence Livermore National Laboratory

File name	File description	Records
NESC9576_01.001	Information file	38
NESC9576_01.002	CPDES3 LRLTRAN source program	1137