ESTS0169: ILUCG2, 2-D Partial Differential Equations Assymmetric Matrix Solver

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ESTS0169 ILUCG2. (Abstract last modified 17-JUN-2001)

ILUCG2, 2-D Partial Differential Equations Assymmetric Matrix Solver

Abstract Table of Contents:

1. NAME OR DESIGNATION OF PROGRAM - ILUCG2.

2. COMPUTER FOR WHICH PROGRAM IS DESIGNED AND OTHER MACHINE VERSION PACKAGES AVAILABLE -

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Explanation of the status codes.

Program-name Package-ID Status ILUCG2 ESTS0169/01 Arrived

Machines used: Package-ID Orig.Computer Test Computer ESTS0169/01 CRAY 1

3. DESCRIPTION OF PROGRAM OR FUNCTION - ILUCG2 (Incomplete LU factorized Conjugate Gradient algorithm for 2-D problems) was developed to solve a linear asymmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as plasma diffusion, equilibria, and phase space transport (Fokker-Planck equation) problems. These equations share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE's are discretized with finite-difference or finite-element methods, the resulting matrix system is frequently of block-tridiagonal form. To use ILUCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. A generalization of the incomplete Cholesky conjugate gradient algorithm is used to solve the matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For problems having a symmetric matrix ICCG2 should be used since it runs up to four times faster and uses approximately 30% less storage. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source, containing extensions and macros, which must be processed by a precompiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The precompiler is not included, but precompilation may be performed by a text editor as described in the UCRL-88746 Preprint.

4. METHOD OF SOLUTION -

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM -

6. TYPICAL RUNNING TIME -

7. UNUSUAL FEATURES OF THE PROGRAM -

8. RELATED AND AUXILIARY PROGRAMS -

9. STATUS
ESTS0169/01: 17-JUN-2001 Masterfiled Arrived

10. REFERENCES  -
- D.V. Anderson,
  ICCG3: Subprograms for the Solution of a Linear Symmetric Matrix
  Equation Arising from 7, 15, 19, or 27 Point 3D Discretization,
Computer Physics Communications, Vol. 30, No. 1, pp. 51-57 (1983) also available as UCRL-88746 Preprint (February 1983).
ESTS0169/01:
- A.I. Shestakon and D.V. Anderson:
  ILUCG2 - Subprograms for the Solution of a Linear Asymmetry Matrix
  Equation Arising from a 9-Point Discretization
  UCRL-88743 Preprint (February 1983).

11. MACHINE REQUIREMENTS - At least 22*mn, where mn is the number of linear equations.

12. PROGRAMMING LANGUAGE(S) USED -
ESTS0169/01: FORTRAN

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

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS -

15. NAME AND ESTABLISHMENT OF AUTHORS -
- Anderson, D.V.
Lawrence Livermore National Lab., CA
United States

16. MATERIAL AVAILABLE -
ESTS0169/01:
ILUCG2 General Source
ILUCG2 FORTRAN Source
report                   UCRL-88743 Preprint (February 1983)        REPPT

17. CATEGORIES -

- P. General Mathematical and Computing System Routines
- X. Magnetic Fusion Research

Keywords: DIFFERENTIAL EQUATIONS, ITERATIVE METHODS, NUMERICAL SOLUTION, PHASE SPACE, PLASMA, TRANSPORT THEORY