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ESTS0168 ICCG3.

ICCG3, 3-D Partial Differential Equations Linear Symmetric Matrix Solver

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1. NAME OR DESIGNATION OF PROGRAM:  ICCG3.
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2. COMPUTERS
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Program name Package id Status Status date
ICCG3 ESTS0168/01 Arrived 17-APR-2001

Machines used:

Package ID Orig. computer Test computer
ESTS0168/01 CRAY 1
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3. DESCRIPTION OF PROGRAM OR FUNCTION

ICCG3 (Incomplete Cholesky factorized Conjugate Gradient algorithm for 3d symmetric problems) was developed to solve a linear symmetric matrix system arising from discretization of three-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as resistive MHD, spatial diffusive transport, 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 ICCG3, the discretization of the three-dimensional partial differential equation and its boundary conditions must result in a block- tridiagonal matrix. Its elements 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 algorithm is used to solve the linear symmetric matrix equation. Loops are arranged to vectors on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For problems having an asymmetric matrix, ILUCG3 (NESC 9927) should be used. Similar methods in two dimensions are available in ILUCG2 (NESC 9929) and ICCG2 (NESC 9928).
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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
ESTS0168/01 17-APR-2001 Masterfiled Arrived
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10. REFERENCES:
ESTS0168/01, included references:
- D.V. Anderson:
  ICCG3 - Subprogramm for the Solution of a Linear Symmetric Matrix
  Equation Arising from A7, 15, 19, or 27 Point 3D Discretization
  UCRL-88746 Preprint (February 1983).
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11. MACHINE REQUIREMENTS

At least 13*mn to 33*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
ESTS0168/01 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
ESTS0168/01
source program   mag tapeICCG3 Generalized Source FORTRAN           SRCTP
source program   mag tapeICCG3 Generalized Source Example           SRCTP
report                   UCRL-88746 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.