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ESTS0170 ILUCG3.

ILUCG3, 3-D Partial Differential Equations Linear Asymmetric Matrix Solver

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1. NAME OR DESIGNATION OF PROGRAM:  ILUCG3.
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2. COMPUTERS
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Program name Package id Status Status date
ILUCG3 ESTS0170/01 Arrived 17-APR-2001

Machines used:

Package ID Orig. computer Test computer
ESTS0170/01 CRAY 1
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3. DESCRIPTION OF PROGRAM OR FUNCTION

ILUCG3 (Incomplete LU factorized Conjugate Gradient algorithm for 3-D asymmetric matrix system arising from discretization of three-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 problems 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 ILUCG3, the discretization of the three-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal matrix. Its element in turn are block-tridiagonal  sub-matrices composed of elementary sub-sub-matrices that are also tridiagonal. A generalization of the incomplete Cholesky conjugate gradient (ICCG) algorithm is used to solve the linear asymmetric 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, ICCG3 should be used since it runs up to  four times faster and uses approximately 30% less storage. Similar methods in two dimensions are available in ILUCG2 and ICCG2.
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4. METHOD OF SOLUTION:
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:
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6. TYPICAL RUNNING TIME:
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7. UNUSUAL FEATURES OF THE PROGRAM:
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8. RELATED AND AUXILIARY PROGRAMS:
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9. STATUS
Package ID Status date Status
ESTS0170/01 17-APR-2001 Masterfiled Arrived
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10. REFERENCES:
ESTS0170/01, included references:
- D.V. Anderson:
  ILUCG3 - Subprograms for the Solution of a Linear Asymmetric
  Matrix Equation Arising from A7, 15, 19, or 27 Point 3D
  Discretization
  UCRL-88745 Preprint (February 1983).
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11. MACHINE REQUIREMENTS

At least 15*mn to 59*mn, depending on user parameters, where mn is the number of linear equations.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
ESTS0170/01 FORTRAN
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  CTSS.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHORS

- Anderson, D.V.
  Lawrence Livermore National Lab., CA
  United States
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16. MATERIAL AVAILABLE
ESTS0170/01
source program   mag tapeILUCG3 Generalized Source                  SRCTP
source program   mag tapeILUCG3 FORTRAN Source                      SRCTP
report                   UCRL-88745 Preprint (February 1983)        REPPT
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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.