DASKR

Preamble

This repository is a mirror of the netlib code of daskr. It is stored here in the hope to be modernized some day. At the moment, as compared to the original code, it has been restructured to be compatible with fpm build system.

TODO list

• Use fpm as build system
• Remove implicite typing
• Remove goto's
• Create explicit interfaces to pass residual, jacobian and krilov solver.
• Split direct and krylov solvers.
• Replace linpack linear solver for Lapack
• Create a modern documentation site

Since the code is a the the moment F77 fixed-form it should be compiled with the option -std=legacy.

fpm build --flag "-std=legacy"

Introduction

   DASKR Package: DAE Solver with Krylov Methods and Rootfinding
                  Version of 8 June 2011

        P. N. Brown, A. C. Hindmarsh, and L. R. Petzold 

DASKR is a solver for systems of differential-algebraic equations (DAEs).
It includes options for both direct and iterative (Krylov) methods for the solution of the linear systems arising at each (implicit) time step. DASKR is a variant of the DASPK package [1]. In addition to all the capabilities of DASPK, DASKR includes the ability to find the roots of a given set of functions while integrating the DAE system.

In contrast to the older DASSL package, DASKR includes a procedure for calculating consistent initial conditions for a large class of problems (which includes semi-explicit index-1 systems) [2]. This procedure includes options for inequality constraints on selected components. The package also includes an option to omit the algebraic components from the local error control.

Along with the solver itself, the DASKR package includes five example programs and a set of general-purpose preconditioner files. These are described in more detail below. The package includes separate single and double precision versions of all source files.

Package Contents

1. The DASKR package is being distributed in the form of a tar file, which expands to a directory, DASKR. The DASKR directory contains this README file and three subdirectories.

2. The subdirectory DASKR/solver contains the following source files:

   ddaskr.f = main solver source, double precision dlinpk.f = required LINPACK/BLAS routines, double precision daux.f = machine constant and error handler, double precision

   sdaskr.f = main solver source, single precision slinpk.f = required LINPACK/BLAS routines, single precision saux.f = machine constant and error handler, single precision

The LINPACK/BLAS files are provided for the sake of completeness, but the target machine/system of interest may already have optimized versions of these routines, which should be used instead for the sake of efficiency.

A complete usage document is included as the initial prologue of each source file ddaskr.f/sdaskr.f.

3. The subdirectory DASKR/examples contains the following files:

   dkrdem.f = small demonstration program, double precision, which solves two small problems with self-checking logic dheat.f = heat equation example program, double precision, using the Krylov option with banded preconditioner dheatilu.f = heat equation example program, double precision, using the Krylov option with sparse ILU preconditioner dweb.f = food web system example program, double precision, using the direct (band) option, and the Krylov option with a product preconditioner based on reaction-transport form dwebilu.f = food web system example program, double precision, using the Krylov option with sparse ILU preconditioner makeddem = Make-file to compile and load dkrdem program makedh = Make-file to compile and load dheat program makedhilu = Make-file to compile and load dheatilu program makedw = Make-file to compile and load dweb program makedwilu = Make-file to compile and load dwebilu program

   skrdem.f = small demonstration program, single precision, which solves two small problems with self-checking logic sheat.f = heat equation example program, single precision, using the Krylov option with banded preconditioner sheatilu.f = heat equation example program, single precision, using the Krylov option with sparse ILU preconditioner sweb.f = food web system example program, single precision, using the direct (band) option, and the Krylov option with a product preconditioner based on reaction-transport form swebilu.f = food web system example program, single precision, using the Krylov option with sparse ILU preconditioner makesdem = Make-file to compile and load skrdem program makesh = Make-file to compile and load sheat program makeshilu = Make-file to compile and load sheatilu program makesw = Make-file to compile and load sweb program makeswilu = Make-file to compile and load swebilu program

   dkrdem.out = output from dheat.f program dheat.out = output from dheat.f program dheatilu.out = output from dheatilu.f program dweb.out = output from dweb.f program dwebilu.out = output from dwebilu.f program

Except for dkrdem/skrdem, all of these examples make use of preconditioner routines, provided in the files described below, when calling DASKR with the Krylov method option. All are heavily commented and intended for use as models for real user applications of DASKR.

4. The subdirectory DASKR/preconds contains the following source files:

   dbanpre.f = preconditioner for banded problems, double precision drbdpre.f = routines for a reaction-based block-diagonal precond- itioner for DAEs arising from a reaction-transport system, without block-grouping, double precision drbgpre.f = routines for a reaction-based block-diagonal precond- itioner for DAEs arising from a reaction-transport system, with block-grouping, double precision dilupre.f = preconditioner routines for sparse ILU preconditioning, double precision, intended for general DAE problems. dsparsk.f = routines from SPARSKIT, Y. Saad (Univ. of Minnesota), double precision, used by dilupre.f

   sbanpre.f = preconditioner for banded problems, single precision srbdpre.f = routines for a reaction-based block-diagonal precond- itioner for DAEs arising from a reaction-transport system, without block-grouping, single precision srbgpre.f = routines for a reaction-based block-diagonal precond- itioner for DAEs arising from a reaction-transport system, with block-grouping, single precision silupre.f = preconditioner routines for sparse ILU preconditioning, single precision, intended for general DAE problems. ssparsk.f = routines from SPARSKIT, Y. Saad (Univ. of Minnesota), single precision, used by silupre.f

At the beginning of each of these source files is a prologue which documents the contents of the file and the usage of the routines in it.

Installation and Usage Notes

1. The single and double precision versions of the SPARSKIT subset, in the files ssparsk.f and dsparsk.f in DASKR/preconds, cannot be installed together as a single library, because of name duplications among the individual routines. If such a combined installation is desired, first change the names of all precision-dependent subroutines in either ssparsk.f or dsparsk.f, so as to have unique names across the two files. Then make the same name changes in the corresponding file silupre.f or dilupre.f which calls those SPARSKIT routines.

2. The five example problems can be compiled and loaded using the appropriate make-file in DASKR/examples. First check the compiler and flags in the make-file, however. Each make-file finds the required solver and preconditioner source or object files in ../solver and ../preconds. The output files for all five examples, as run in double precision on a Sun Sparc-10 Workstation, are provided in the files d*.out. The results on other systems may differ slightly.

3. The example programs that use ILU preconditioning, if altered to use the option JACOUT = 1, write an additional output file containing the initial Jacobian and residual vector in Boeing-Harwell format. A map of the Jacobian as a postscript file can then be generated using the SPARSKIT routines readmt and pspltm.

4. Users of DASKR with a sparse ILU preconditioner are encouraged to experiment with the many options available in the SPARSKIT package, as accessed through the dilupre.f/silupre.f modules provided. See the prologue in those files, and the two examples that use ILU.

5. Important Note: The use of single precision on a 32-bit machine is strongly discouraged. The amplification of roundoff errors by the integration and linear system solution algorithms is such that double precision is generally required on short-wordlength machines. In particular, the small demonstration program and the food web example programs provided here do not run on a 32-bit machine in single precision, with even the moderate tolerance values of 1.0e-5.

References

[1] P. N. Brown, A. C. Hindmarsh, and L. R. Petzold, Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems, SIAM J. Sci. Comp., 15 (1994), pp. 1467-1488.

[2] P. N. Brown, A. C. Hindmarsh, and L. R. Petzold, Consistent Initial Condition Calculation for Differential-Algebraic Systems, SIAM J. Sci. Comp. 19 (1998), pp. 1495-1512.

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Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract number W-7405-Eng-48.

Copyright (c) 2002, The Regents of the University of California. UCRL-CODE-2002-058 All rights reserved. This file is part of DASKR. For details, see DASKR/LICENSE