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ESTS0847 PDASAC.

PDASAC, Partial Differential Sensitivity Analysis of Stiff System

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1. NAME OR DESIGNATION OF PROGRAM:  PDASAC.
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2. COMPUTERS
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Program name Package id Status Status date
PDASAC ESTS0847/01 Arrived 09-MAR-2001

Machines used:

Package ID Orig. computer Test computer
ESTS0847/01 Many Computers
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3. DESCRIPTION OF PROGRAM OR FUNCTION

PDASAC solves stiff, nonlinear  initial-boundary-value problems in a timelike dimension t and a space dimension x. Plane, circular cylindrical or spherical boundaries can be handled. Mixed-order systems of partial differential and algebraic equations can be analyzed with members of order or 0 or 1 in t, 0, 1 or 2 in x. Parametric sensitivities of the calculated states are computed simultaneously on request, via the Jacobian of the state equations. Initial and boundary conditions are efficiently reconciled. Local error control (in the max-norm or  the 2-norm) is provided for the state vector and can include the parametric sensitivities if desired.
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4. METHOD OF SOLUTION

The method of lines is used, with a user- selected x-grid and a minimum-bandwith finite-difference approximations of the x-derivatives. Starting conditions are reconciled with a damped Newton algorithm adapted from Bain and Stewart (1991). Initial step selection is done by the first-order algorithms of Shampine (1987), extended here to differential- algebraic equation systems. The solution is continued with the DASSL predictor-corrector algorithm (Petzold 1983, Brenan et al. 1989) with the initial acceleration phase deleted and with row scaling of  the Jacobian added. The predictor and corrector are expressed in divided-difference form, with the fixed-leading-coefficient form of  corrector (Jackson and Sacks-Davis 1989; Brenan et al. 1989). Weights for the error tests are updated in each step with the user's tolerances at the predicted state. Sensitivity analysis is performed directly on the corrector equations of Caracotsios and Stewart (1985) and is extended here to the initialization when needed.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

This algorithm, like DASSL, performs well on differential-algebraic equation systems of index 0 and 1 but not on higher-index systems; see Brenan et al. (1989). The user assigned the work array lengths and the output unit. The machine number range and precision are determined at run time by a call to the LAPACK subroutine DLAMCH.
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6. TYPICAL RUNNING TIME

Each example has been run in less than one minute on a 486/33 personal computer.
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7. UNUSUAL FEATURES OF THE PROGRAM

Variable coefficient matrices are  available for the t and d-derivatives through the user's subroutines Esub and CDsub. These matrices may be diagonal, dense, banded or identity; when variable they may vary with t, x, state vector u and  a vector of parameters. The code includes parametric sensitivity analysis; automatic reconciliation of initial states and derivatives; row scaling of the Jacobian to improve numerical stability; and accurate stopping at a designated value of a functional of the state vector. The latter feature allows repeated stopping on a value of a solution component or t-derivative to generate a Poincari map of the solution.
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8. RELATED AND AUXILIARY PROGRAMS

This code is developed from DASSL (Petzold 1983) and its extension DDASAC (Caracotsios (1985)). The linear algebra computations are done with selected LAPACK and BLAS codes, provided in the file LAPACK.FOR on the same diskettes.
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9. STATUS
Package ID Status date Status
ESTS0847/01 09-MAR-2001 Masterfiled Arrived
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10. REFERENCES:
ESTS0847/01, included references:
- W.E. Stewart, M. Caracotsios and J.P. Sorensen:
  Appendix C. PDASAC Software Package Documentation
  (February 8, 1995)
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11. MACHINE REQUIREMENTS:  No special hardware is required.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
ESTS0847/01 FORTRAN
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

PDASAC is in use  on a wide variety of machines and operating systems.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

All
floating-point numbers are expressed in double precision. The Filename.FOR on the diskette denotes a Fortran source file, and Filename.DAT denotes an output data file. The .FOR files, when compiled and linked, suffice for execution of the four test problems given in the users' manual, APPENDIX C. The .DAT files correspond to the printed outputs of the four examples, given in Appendix C. These results were computed on a VAXstation 3200.
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15. NAME AND ESTABLISHMENT OF AUTHORS

     M. Caracotsios
     Amoco Chemical Company, Naperville, IL (United States)
     W.E. Stewart
     University of Wisconsin-Madison, Madison, WI (United States)
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16. MATERIAL AVAILABLE
ESTS0847/01
source program   mag tapeLAPACK.FOR Source code                     SRCTP
source program   mag tapePDASAC.FOR Source code                     SRCTP
source program   mag tapeAPPCXMP1.FOR Test problem source code      SRCTP
test-case output mag tapeAPPCXMP1.DAT Output of test problem        OUTTP
source program   mag tapeAPPCXMP2.FOR Test problem source code      SRCTP
test-case output mag tapeAPPCXMP2.DAT Output of test problem        OUTTP
source program   mag tapeAPPCXMP3.FOR Test problem source code      SRCTP
test-case output mag tapeAPPCXMP3.DAT Output of test problem        OUTTP
source program   mag tapeAPPCXMP4.FOR Test problem source code      SRCTP
test-case output mag tapeAPPCXMP4.DAT Output of test problem        OUTTP
report                   Appendix C PDASAC Doc. (February 8, 1995)  REPPT
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: partial differential equations, sensitivity analysis.