NESC0847 DISPL-1.

1. NAME OR DESIGNATION OF PROGRAM:  DISPL-1.

3. DESCRIPTION OF PROBLEM OR FUNCTION

DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed  types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter-  face conditions for problems in an inhomogeneous medium. The spatial domain is one- ot two- dimensional with rectangular Cartesian, cylindrical, or shperical (in one dimension only) geometry.

4. METHOD OF SOLUTION

The numerical method is based on the use of Galerkin's procedure combined with the use of B-splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The spatial domain must be rectangular with sides parallel to the coordinate geometry.  Cross derivative terms are not permitted in the PDE. The order of the B-splines is at most 12. Other parameters such as the number of  mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code.

6. TYPICAL RUNNING TIME

The IBM version required 90 CPU seconds for compilation of the DISPL1 source and 100 CPU seconds for compilation and execution of the sample problems, including the plot creation jobs, on an IBM3033. The CDC version required a total of 66 CP seconds for all compilations and executions on a CDC7600 and 184 CP  seconds on a CDC6600.
The following execution times were required by NEA-DB to execute the test cases on IBM 3033:
MORTRAN preprocessing of the source program: 30 CP seconds;
Test case 1 execution: 34 CP seconds;
Test case 2 execution:  5 CP seconds.

7. UNUSUAL FEATURES OF THE PROGRAM

Mixed-type systems can be treated  (e.g. a parabolic-elliptic system consisting of a parabolic equation coupled with an elliptic equation). General orthogonal coordinate systems can also be treated with an appropriate choice of coefficients. Spatial domains can be heterogeneous with specified physical materials in each subdomain. Continuity or gap interface conditions can be specified. Boundary conditions can be nonlinear and can be of different types for each species and side. They need not be imposed on all sides for all species so that a class of problems larger than parabolic systems can be treated. All user- specified functions (coefficients) of the PDE system can depend on time, position, species concentrations, and, where appropriate, species gradients. The B-splines used in the spatial approximate can be any degree from zero through eleven, and the smoothness of the approximation can vary from zero to maximal smoothness. Moreover, the polynomial degree and smoothness can be different for each coordinate direction. The time-step integration features automatic time-step selection and integration order control to achieve specified local error control. MORTRAN2 preprocessing makes it convenient to customize a compilation to the size of a problem set.
Extensive dump/restart capabilities permit the user to produce intermediate results at specified times. In addition, a dump will automatically occur when the computation time is about to expire. Restarts from these dumps are invoked through input parameters. The  code writes a graphics data set for use with plotting packages.

8. RELATED AND AUXILIARY PROGRAMS

The DISPL1 package must be compiled using the MORTRAN2 preprocessor (NESC Abstract 678).

10. REFERENCES

- Carl DeBoor,
  A Practical Guide to Splines, Springer-Verlag, New York, Inc.,
  1978.
- A.C. Hindmarsh,
  GEAR: Ordinary Differential Equation Systems Solver,
  UCID-30001 Rev. 3, December 1974.
- Summary of Input Parameters for DISPL1, ANL-AMD Note, September
  17, 1979.
- DISPL1, NESC No. 847.370B, DISPL1 IBM370 version Tape Description
  and Implementation Information,
  National Energy Software Center Note 81-41, April 22, 1981.
- DISPL1, NESC No. 847.7600B, DISPL1 CDC7600 Version Tape Descrip-
  tion and Implementation Information,
  National Energy Software Center Note 81-40, April 22, 1981.

-  G.K.Leaf et al.:
   DISPL: A Software Package for One and Two Spatially Dimensioned
   Kinetics-Diffusion Problems
   ANL-77-12 Rev.1 (November 1978)
-  National Energy Software Center Note 80-23
-  A.James Cook and L.J.Shustek:
   MORTRAN2, A Macro-Based Structured FORTRAN Extension
   SLAC-PUB-1527 (January 1975)

11. MACHINE REQUIREMENTS

The IBM version DISPL1 source requires 600K bytes of storage for compilation. Compilation and execution of the DISPL1 sample problems, including the plot creation jobs, requires a maximum of 350K bytes. The CDC version requires a maximum of 121,000 (octal) words of executable storage for the CDC7600, 140,000 (octal) words for the CDC6600, and 135,000 (octal) words for the CYBER175 execution. In the MORTRAN2 preprocessing stage, the user can easily  adjust the storage requirements to the optimum for a current problem. In addition to the standard input and print files, the program requires files assigned to logical unit 10 for reading restart data, logical unit 11 for writing data for a later restart,  and logical unit 12 for writing plotting data.
Main storage requirements for execution on IBM 3033 are:
MORTRAN preprocessing: 188K bytes;
test case 1:           340K bytes
test case 2:           312K bytes.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

MORTRAN2 (80%) and FORTRAN (20%). By use of the MORTRAN2 preprocessor %F control card, the FORTRAN component is passed through the MORTRAN2 pre- processor along with the MORTRAN component.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

OS/370
(IBM370/195,3033), SCOPE 2.1.3 (CDC7600), SCOPE 3.4.4. (CDC6600), NOS1.3 (CDC CYBER175).

15. NAME AND ESTABLISHMENT OF AUTHOR

G.K. Leaf and M. Minkoff
Applied Mathematics Division
Argonne National Laboratory
9700 South Cass Avenue
Argonne, Illinois 60439

File name	File description	Records
NESC0847_01.002	DISPL-1 INFORMATION	43
NESC0847_01.003	DISPL-1 SOURCE MORTRAN-2	7413
NESC0847_01.004	DISPL-1 MORTRAN MACROS	233
NESC0847_01.005	MORTRAN-2 PRECOMPILER FORTRAN-4 IBM 3033	792
NESC0847_01.006	MORTRAN-2 MACROS	87
NESC0847_01.007	JCL FOR MORTRAN-2 LOAD MODULE GENERATION	40
NESC0847_01.008	DISPL-1 JCL FOR MORTRAN-2 PREPROCESSING	13
NESC0847_01.009	DISPL-1 SOURCE FORTRAN-4 IN CARD IMAGES	8673
NESC0847_01.010	DRIVER-1 SOURCE MORTRAN-2 FOR TEST CASE 1	554
NESC0847_01.011	DRIVER-1 JCL FOR MORTRAN-2 PREPROCESSING	11
NESC0847_01.012	DRIVER-1 SOURCE FORTRAN-4 FOR TEST CASE 1	243
NESC0847_01.013	INPUT FOR TEST CASE 1	36
NESC0847_01.014	OUTPUT OF TEST CASE 1	467
NESC0847_01.015	JCL FOR TEST CASE 1	83
NESC0847_01.016	DRIVER-2 SOURCE MORTRAN2 FOR TEST CASE 2	658
NESC0847_01.017	DRIVER-2 JCL FOR MORTRAN-2 PREPROCESSING	13
NESC0847_01.018	DRIVER-2 SOURCE FORTRAN-4	347
NESC0847_01.019	INPUT FOR TEST CASE 2	36
NESC0847_01.020	OUTPUT OF TEST CASE 2	489
NESC0847_01.021	JCL FOR TEST CASE 2	83
NESC0847_01.022	CONTOUR PLOT DRIVERS SOURCE (MORTRAN-2)	615
NESC0847_01.023	CONTOUR PLOT DRIVERS SOURCE (FORTRAN-4)	647
NESC0847_01.024	CONTOUR PLOT INPUT FOR TEST CASE	10
NESC0847_01.025	CONTOUR BLACKBOX INPUT	31
NESC0847_01.026	3-D PLOT DRIVERS SOURCE (MORTRAN-2)	689
NESC0847_01.027	3-D PLOT DRIVERS SOURCE (FORTRAN-4)	717
NESC0847_01.028	3-D PLOT INPUT FOR TEST CASE	14
NESC0847_01.029	X-SEC PLOT DRIVERS SOURCE (MORTRAN-2)	1154
NESC0847_01.030	X-SEC PLOT DRIVERS SOURCE (FORTRAN-4)	1105
NESC0847_01.031	X-SEC PLOT INPUT FOR TEST CASE	13
NESC0847_01.032	DISPL-1 ORIGINAL JCL FROM NESC	612