ESTS0169 ILUCG2.
ILUCG2, 2-D Partial Differential Equations Asymmetric Matrix Solver
NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES
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| Program name | Package id | Status | Status date |
|---|---|---|---|
| ILUCG2 | ESTS0169/01 | Arrived | 17-JUN-2001 |
Machines used:
| Package ID | Orig. computer | Test computer |
|---|---|---|
| ESTS0169/01 | CRAY 1 |
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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.
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.
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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).
- 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, included references:
- 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).
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ESTS0169/01
source program mag tapeILUCG2 General Source SRCTPsource program mag tapeILUCG2 FORTRAN Source SRCTP
report UCRL-88743 Preprint (February 1983) REPPT
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- P. General Mathematical and Computing System Routines
- X. Magnetic Fusion Research
Keywords: differential equations, iterative methods, numerical solution, phase space, plasma, transport theory.