## Installation of LINSOL

Please read “How to install LINSOL”, before starting the installation process.

Please read “User’s Overview of LINSOL”, before the first use of LINSOL.

## User Interfaces of LINSOL

Please read “**How to use the Unix/Linux interface of LINSOL**” for the useage of LINSOL with a given matrix (and right hand side) without implementation effort.

The matrix can be read in two formats - the well-known Harwell-Boeing (H/B) file format and the LINSOL file format that is optimally suited to the available storage patterns of the program package LINSOL. Please read “**The LINSOL file format**” to get to know the LINSOL file format.

The format of the file storing the right hand sides (rhs) and the initial guesses and the format of the file storing the solutions is described in “**The file format of the rhs, initial guesses and the solutions**”.

Please read “**The matrix structure of LINSOL**” and “**How to use LINSOL in user applications**” to embed the program package LINSOL into your application.

## Papers related to LINSOL from members of the former research group for supercomputers

### The theoretical background of the program package LINSOL is addressed in

Rüdiger Weiss, Hartmut Häfner and Willi Schönauer

**LINSOL (LINear SOLver) - Description and User's Guide for the Parallelized Version** (DRAFT Version 0.96)

Internal Report 61-95 1995 (524 KiloBytes (KB))

### The basic concepts of the program package LINSOL are addressed in

H. Häfner, W. Schönauer, R. Weiss

**The Program Package LINSOL - Basic Concepts and Realization** (62 KB)

Applied Numerical Mathematics, Vol. 30, No. 2-3, 1999, pp. 213-224.

H. Häfner, W. Schönauer, R. Weiss

**The portable and parallel linear solver package LINSOL** (97 KB)

Proceedings of the 4th European SGI/Cray MPP Workshop, IPP R/46, Oct. 1998, Max-Planck-Institut für Plasmaphysik, Garching bei München, Germany, pp. 242-251.

W. Schönauer, H. Häfner, R. Weiss

**LINSOL, a Parallel Iterative Linear Solver Package of Generalized CG-type for Sparse Matrices** (131 KB)

Proceedings of the 8th SIAM Conference on Parallel Processing for Scientific Computing, SIAM, Philadelphia 1997, CD-ROM (ISBN 0-89817-395-1), 8 pages.

H. Häfner, W. Schönauer

**Portable Parallelization of the Iterative Linear Solver Package LINSOL **(58 KB)

in E.H. D’Hollander, G.R. Joubert, F.J. Peters, D. Trystram (Eds.), Parallel Computing: State-of-the-Art and Perspectives, Elsevier, Amsterdam 1996, pp. 625-628.

###

### Different bandwidth optimization algorithms that are integrated in LINSOL are addressed in

D. Zundel

**Implementation and comparison of three bandwidth optimizing algorithms on a distributed memory parallel computer** (441 KB)

Diploma thesis, Internal report 75-01.

D. Zundel and W. Schönauer

**A Fast "Parallelized" Single Pass Bandwidth Optimizer for Sparse matrices** (208 KB)

To appear in: Proceedings of the International Conference on Numerical Algorithms, Marrakesh, Morocco, October 1-5, 2001.

###

### Theoretical and practical aspects of the embedding of the (I)LU preconditioner into the program package LINSOL are addressed in

H. Häfner, W. Schönauer

Embedding of the (I)LU preconditioner into the program package LINSOL (32 KB)

The online paper is a revised version compared to the published version.

Proc. 18th PARS Workshop, Munich, PARS Mitteilungen Nr. 18, Nov. 2001, Gesellschaft für Informatik, Bonn, pp. 77-86.

H. Häfner, W. Schönauer, R. Weiss

**The integration of different variants od the (I)LU algorithm in the LINSOL program package** (137 KB)

Applied Numerical Mathematics 41 (2002), pp. 39-59.

W. Schönauer, H. Häfner, R. Weiss

**Numerical experiments to optimize the (I)LU preconditioning in the iterative linear solver package LINSOL** (103 KB)

Applied Numerical Mathematics 41 (2002), pp. 23-37.

Hartmut Häfner, Willi Schönauer, Rüdiger Weiss

**Parallelization and Integration of the LU and ILU Algorithm in the LINSOL Program Package** (60 KB)

in V. Malyshkin (Ed.), PaCT, Springer Lecture Notes in Computer Science 1662, Berlin 1999, pp. 417-427.

###

### Practical papers on iterative linear solvers and their parallelization are addressed in

R. Weiss, C. Roll, H. Häfner, L. Gross, M. Schmauder, W. Schönauer

Parallelisierung von ODIN-Software für iterative Gleichungslöser

in A. Schreiner, E. Schnepf (Herausgeber), Drittes ODIN-Symposium, Rechenzentrum Universität Karlsruhe, 1994, Seite 117-128.

H. Häfner, W. Schönauer

**Kommunikation auf verschiedenen Parallelrechnern, Auswirkung auf die Programmierung** (82 KB)

in A. Schreiner, E. Schnepf (Herausgeber), Drittes ODIN-Symposium, Rechenzentrum Universität Karlsruhe, 1994, Seite 195-206.

###

### Theoretical papers on iterative linear solvers are addressed in

C. Koschinski

**Properties of Approximate Inverses and Adaptive Control Concepts for Preconditioning** (897 KB)

Doctoral thesis, Internal Report 74-99, 1999.

R. Weiss

**How to Improve Iterative Solvers: Parallelization and Preconditioning**

1999.

R. Weiss, I. Podgajezkaya, H. Häfner, W. Schönauer

**Iterative Sovers for Linear Equations, from the Past to the Future**

1999.

R. Weiss

**Where Have We Been and Where Do We Go to**

1999.

R. Weiss

**Duality between Solvers for Ordinary Equations and Linear Systems**

1998.

R. Weiss, H. Häfner, W. Schönauer

**Overview on Solves for Linear Equations**

in RIMS Symposium, Kyoto University, Japan, Vol. 98, No. 115, 1998, pp. 213 - 224.

W. Schönauer

Experiments with Search Directions for a Generalized CG Method

Proceedings 15th IMACS World Congress 1997 on Scientific Computation, Modelling and Applied Mathematics, IMACS, New Brunswick 1997, Vol. II, pp. 515-520 (all volumes in one CD-ROM available). Extended version in Applied Numerical Mathematics, Vol. 30, No. 2-3, 1999, pp. 241-256.

R. Weiss

**Transformations of and Relations between Iterative Linear Solvers** (24 KB)

Internal Report, 1995.

T. Wälde

Genetisch evolutionäre Algorithmen zur Lösung linearer Gleichungssysteme (in German, English abstract)

Diploma thesis, Internal Report 64-96, 1996.

M. Rozloznik, R. Weiss

On the Stable Implementation of the Generalized Minimal Error Method

Internal Report 56-95, 1995.

M. Zimmermann

Projektionsmethoden zur Präkonditionierung von verallgemeinerten CG-Verfahren (in German, English abstract)

Diploma thesis, Internal Report 55-95, 1995.

R. Weiss

**A Theoretical Overview of Krylov Subspace Methods** (154 KB)

Applied Numerical Mathematics, 1995.

B. Wagner

**Kurze Rekursionen bei präkonditionierten CKS-Verfahren** (249 KB, in German)

Internal Report 54-95, 1995.

R. Weiss

**Relations between Smoothing and QMR** (59 KB)

Internal Report 53-94, 1994.

R. Weiss

**Orthogonalization Methods** (156 KB)

Internal Report 52-94, 1994.

R. Weiss

**Minimization Properties and Short Recurrences for Krylov Subspace Methods** (75 KB)

Electronic Transactions on Numerical Analysis, 1994.

W. Schönauer, R. Weiss

**An engineering approach to generalized conjugate gradient methods and beyond** (291 KB)

in W.F. Ames (Ed.), Proceedings 14th IMACS World Congress on Computation and Applied Mathematics, IMACS, New Brunswick 1994, Vol. 3, pp. 1462-1465. Extended version in Applied Numerical Mathematics 19 (1995), pp. 175-206.

R. Weiss, W. Schönauer

Black box solvers for partial differential equations

in H. Küsters, E. Stein, W. Werner (Eds.), Proc. of the Joint International Conference on Mathematical Methods and Supercomputing in Nuclear Applications, M & C + SNA 1993, Kernforschungszentrum Karlsruhe, 1993, Vol. 2, pp. 29-40.

R. Weiss, W. Schönauer

Preconditioned Generalized Conjugate Gradient Methods: What Do We Have and What Do We Need?

in R. Vichnevetsky, D. Knight, G. Richter (Eds.), Advances in Computer Methods for Partial Differential Equations -VII, IMACS, New Brunswick 1992, pp. 806-812.

R. Weiss, W. Schönauer

Accelerating Generalized Conjugate Gradient Methods by Smoothing

in R. Beauwens and P. de Groen (Eds.), Iterative Methods in Linear Algebra, North-Holland, Amsterdam 1992, pp. 283-292.

W. Schönauer, R. Weiss, P. Sternecker

Polyalgorithms with automatic method selection for the iterative solution of linear equations and eigenproblems

in P.W. Gaffney, E.N. Houstis (Eds.), Programming Environments for High-Level Scientific Problem Solving, North-Holland, Amsterdam 1992, pp. 57-67.

P. Sternecker, L. Gross, W. Schönauer

A polyalgorithm for the solution of large symmetric general eigenproblems

in R. Beauwens and P. de Groen (Eds.), Iterative Methods in Linear Algebra, North-Holland, Amsterdam 1992, pp. 423-432.

R. Weiss, W. Schönauer

Solution of partial differential equations by means of data reduction (DARE)

in Multigrid Methods Special Topics and Applications II, edited by W. Hackbusch, U. Trottenberg, GMD-Studien Nr. 189, GMD, St. Augustin, 1991, pp. 361-372.

R. Weiss, W. Schönauer

Solvers for partial differential equations on vector computers

in J. Halin, Treffen des ASIM-Arbeitskreises “Simulationssoftware und -hardware”, Zürich, ASIM-Mitteilungen Heft Nr. 19, pp. 162-169.

R. Weiss, W. Schönauer

Data reduction (DARE) preconditioning for generalized conjugate gradient methods

in O. Axelsson, L.Yu. Kolotilina (Eds.), Preconditioned Conjugate Gradient Methods, Lecture Notes in Mathematics 1457, Springer, Berlin, 1990, pp. 137-153.

R. Weiss, H. Häfner, W. Schönauer

Tuning the matrix-vector-multiplication in diagonal form

in D.J. Evans et al. (Eds.), Parallel Computing ‘89, Amsterdam 1990, pp. 93-98. W. Schönauer, R. Weiss, M. Schlichte

The basic ideas of the data reduction (DARE) method for the solution of large linear systems on vector computers

ZAMM 69 (1989), pp. T184-T185.

W. Schönauer, M. Schlichte, R. Weiss

Numerical experiments with data reduction (DARE) methods for the solution of large linear systems on vector computers

Proceedings 12th IMACS World Congress on Scientific Computing, edited by R. Vichnevetsky, P. Borne, J. Vignes, IMACS 1988, Vol. 4, pp. 227-229, and in W.F. Ames et al. (Eds.), Numerical and Applied Mathematics, J.C. Baltzer, Basel 1989, pp. 647-651.

W. Schönauer, R. Weiss

Efficient vectorizable PDE solvers

Journal of Computational and Applied Mathematics 27 (1989) (invited paper), pp. 279-297. W. Schönauer, M. Schlichte, R. Weiss

Wrong ways and promising ways towards robust and efficient iterative linear solvers

in Advances in Computer Methods for Partial Differential Equations - VI, edited by R. Vichnevetsky and R.S. Stepleman, IMACS 1987, pp. 7-14.

W. Schönauer, H. Müller, E. Schnepf

Pseudo-residual type methods for the iterative solution of large linear systems on vector computers

Parallel Computing 85, edited by M. Feilmeier, J. Joubert, U. Schendel, North-Holland 1986, pp. 193-198.

H. Müller, W. Schönauer, E. Schnepf

Vergleich verschiedener Lösungsverfahren für lineare Gleichungen mit Diagonalenspeicherung auf der CYBER 205

in Mitteilungen Nr. 3, Gesellschaft für Informatik, Parallelalgorithmen und -rechnerstrukturen (PARS), Univ. Erlangen, 1985, pp. 65-74. H. Müller, W. Schönauer, E. Schnepf

Design considerations for the linear solver LINSOL on the CYBER 205

in Supercomputer Applications, edited by A.H.L. Emmen, North-Holland 1985, pp. 39-49.

W. Schönauer, H. Müller, E. Schnepf

Numerical tests with biconjugate gradient type methods

ZAMM 65 (1985), pp. T400-T402.

Willi Schönauer, Karlheinz Raith

A Polyalgorithm with Diagonal Storing for the Solution of Very Large Indefinite Linear Banded Systems on a Vector Computer

in Parallel and Large-Scale Computers: Performance, Architecture, Applications, edited by M. Ruschitzka, IMACS Transactions on Scientific Computing, Vol. II, North-Holland (1983), pp. 213-220.

### A book on iterative linear solvers is addressed in

R. Weiss

Parameter-Free Iterative Linear Solvers

###

### Two papers on nonlinear systems are addressed in

R. Weiss

**On Solvers for Nonlinear Large Systems** (98 KB)

Internal Report 69-97, 1997.

R. Weiss, I. Podgajezkaya

**Overview on New Solvers for Nonlinear Systems** (135 KB)

Applied Numerical Mathematics, 1999.

### Papers on FDEM (Finite Difference Element Method) are addressed in

W. Schönauer, Torsten Adolph

**FDEM: The Evolution and Application of the Finite Difference Element Method (FDEM) Program Package for**

the Solution of Partial Differential Equations On Solvers for Nonlinear Large Systems (98 KB)

Abschlussbericht des Verbundprojekts FDEM: Weiterentwicklung und Anwendung des Finite Difference Element Method (FDEM) Programmpakets zur Lösung von partiellen Differentialgleichungen, BMBF, Förderkennzeichen 01 IR A16 A.

Torsten Adolph, Willi Schönauer

**Automatic Domain Decomposition for a Black-Box PDE Solver**

Institute for Scientific Computing, Forschungszentrum Karlsruhe, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

Torsten Adolph, Willi Schönauer

**The Application of a Black-Box Solver with Error Estimate to Different Systems of PDEs**

Institut für Wissenschaftliches Rechnen, Forschungszentrum Karlsruhe, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Deutschland

Hartwig Leser, Curt Wizemann, Mihai Vulcan

**ABSCHLUSSBERICHT: Weiterentwicklung und Anwendung des FDEM (Finite Difference Element Method) Programmpaketes zur Lösung von partiellen Differentialgleichungen**, Institut für Umformtechnik, Universität Stuttgart, 2004

Torsten Adolph, Willi Schönauer

**THE FINITE DIFFERENCE ELEMENT METHOD (FDEM) WITH EXAMPLES AND ERROR ESTIMATES**, February 2009

Matthias Messerschmidt, Werner Lehnert, Willi Schönauer, Torsten Adolph

**The Numerical Simulation of Fuel Cells of the PEMFC and SOFC type with the Finite Difference Element Method (FDEM)**

Torsten Adolph, Willi Schönauer

**Further Applications of the PDE Solver FDEM with Error Estimate to Different PDE Systems**, Forschungszentrum Karlsruhe, Institut für Wissenschaftliches Rechnen

Torsten Adolph

**The Parallelization of the Mesh Refinement Algorithm in the Finite Difference Element Method Program Package**, Dissertation, November 2005

Carlos J. Falconi, Jordan A. Denev, Jochen Fröhlich, Henning Bockhorn

**A test case for microreactor flows - a two-dimensional jet in crossflow with chemical reaction**, internal report, December 2006

York Christian Gerstenmaier, Torsten Adolph, Willi Schönauer

**The Snuffle Problem Gerstenmaier for the Heat Conduction in a Power Module with 6 Power Chips**, February 2007

Martin Petry, Torsten Adolph, Willi Schönauer

**The Snuffle Problem Petry for the Heat Conduction in a Thin Annulus**, December 2006