# Free Software

A number of software packages are stored on MGNet. Some are public domain, some are copyrighted, and some might be copyrighted someday (all rights reserved). When in doubt, contact the author(s) of the package(s) you are interested in.

Please remember that this is freely distributed software. Hence, the amount of support you receive will probably be extremely limited, if any is provided at all. Some of the authors will provide ample support on consulting or contractual basis, however.

If you have a multigrid, domain decomposition, or parallel code or package that you would like to contribute, please send e-mail to me.

## AMGLab

Derrick Cerwinsky's copyrighted Matlab algebraic multigrid package. The code was written as part of his Ph.D. dissertation under the direction of Craig Douglas. A number of smoothers and cycles are provided, a Matlab GUI, runtime analysis, graphics, and some built in examples. AMG algorithms provided include Ruge-Stueben, Beck, Smoother Aggregation, Roughed Aggregation, and the Austrian variant of AMGe. It relatively painless to add other AMG algorithms and to run your own examples.

## Barsky

Sandra Barsky's single processor code, written in C, which solves non-linear time-dependent 2-D equations. In particular, the equation should have the form (d/dt)u= (\nabla^2) u + g(x,y,u) + f(x,y) with periodic boundary conditions. The function g is easily tunable. The code is written as a primarily instructional code for a student who might have some familiarity with linear multigrid, and would want a slightly more general approach, or a student who can solve a linear boundary equation, but is now looking to include time. There are no detailed explanations of what restriction or prolongation do, but more details are provided in how the linearization occurs and what happens as a function of time.

## BDD

A single processor copyrighted Fortran-77 code by Jan Mandel for balancing domain decomposition. Jan and Solvers International own the copyright.

## Borzi

Alfio Borzi's public domain Fortran-77 codes. Controlla is for optimality systems and is a full multigrid method for the solution of an optimality system arising from optimal control of the solid fuel ignition model. Santafe is for open-loop optimal for open-loop optimal control of time-dependent reaction-diffusion systems. The code is designed to solve for tracking and terminal observation problems also in combination with receding horizon techniques.

## BOXMG

A single processor black box multigrid Fortran-77 code written by Victor Bandy and Joel Dendy. This might be public domain software, but it might be owned by the US Department of Energy (DOE). Check with Joel Dendy.

## Bunner

A public domain, parallel processor replacement Fortran-77 code for Mudpack written by Bernard Bunner. It requires both MPI and the C preprocessor. This code features staggered grids, rectangular domains, constant mesh spacing in 2 or 3 dimensions, V or W cycling, full weighting for the restriction and bilinear interpolation for the correction, either vertex-centered or cell-centered operations, and periodic, Neumann, or Dirichlet boundary conditions.

## DAGH

A one or more processor C++ copyrighted library written by M. Parashar and J. C. Browne. DAGH (Distributed Adaptive Grid Hierarchy) provides a program development infrastructure for implementation of solutions of partial differential equations using adaptive mesh refinement algorithms. The principles of hierarchical abstraction and separation of concerns were incorporated into the development of DAGH. The code solves problems in two and three dimensions. It includes multigrid as an option.

## Douglas

A one or more processor public domain Fortran-77 code written by Craig Douglas. This requires MPI and the preprocessor m4. Some simple example multigrid codes using MPI for message passing are provided.

## Featflow

A single processor Fortran-77 copyrighted code written by Stefan Turek et al. FEATFLOW is designed for the following MGNet Codesthree classes of applications:

- Education of students
- Scientific research
- Industrial applications

## Fortuna

A public domain, single processor code written by Armando de Oliveira Fortuna. This is a tutorial solver for the Laplace/Poisson equations which allows the user to select between multigrid, Line-SOR, or Point-SOR. It is a nice tool to introduce multigrid to new students. They can see for themselves how multigrid compares to SOR.

## GMD

The copyrighted Fortran-77 GMD multigrid solvers MG00. MG00 was written by Hartmut Foerster and Kristian Witsch.

## GRUMMP

This is a code written by Carl Ollivier-Gooch. The goal of the GRUMMP project is to develop automatic mesh generation software for unstructured meshes with mixed element types. The software will be able to produce high-quality meshes which meet user-defined mesh density requirements, using elements appropriate for the geometry and physics of a particular problem. We envision a system in which common types of physical problems have pre-defined mesh sizing and element aspect ratio functions, allowing easy generation of meshes for these applications areas. For flexibility and generality, the user will also be able to prescribe these functions (for totally different applications) or modify the pre-defined behaviors (to provide a quality mesh in the wake of an airplane wing, for example).

## Integra

A single processor public domain Fortran-77 program by Alfio Borzi to solve nonlinear integral equations using a multigrid method.

## Kaskade

A single processor copyrighted C program by Rainer Roitsch, Bodo Erdmann, and Jens Lang. The copyright owner is Konrad-Zuse Zentrum (ZIB). Kaskade is a finite element, adaptive mesh code for solving problems in two and three dimensions.

## LASPack

This is a copyrighted ANSI C program written by Tomas Skalicky. LASPack is a package for solving large sparse systems of linear equations like those which arise from discretization of partial differential equations. It contains classical as well as selected state of the art algorithms which are commonly used for large sparse systems such as conjugate gradient-like methods for non-symmetric systems (CGN, GMRES, BiCG, QMR, CGS, and BiCGStab) and multilevel methods such as multigrid and conjugate gradient method preconditioned by either a multigrid or BPX preconditioner. Two sets of documentation are included: PostScript and html formats.

## LPARX

This is a one or more processor copyrighted C++ library written by Scott R. Kohn and Scott B. Baden. The copyright owners are the two authors and The Regents of the University of California. LPARX provides efficient run-time support for dynamic, non-uniform scientific calculations running on MIMD distributed memory architectures. It extends HPF's data decomposition model to provide support for dynamic, block irregular data structures. LPARX represents data decompositions as first-class objects and expresses data dependencies in a manner which is logically independent of data decomposition and problem dimension.

## Madpack2

A public domain single processor family of solvers written by Craig Douglas. There are separate versions in C and Fortran-77. This is an abstract multilevel solver. It is PDE, domain, and discretization independent. Examples from two and three dimensions are provided.

## Madpack5

A public domain one or more processor object oriented code written primarily by Craig Douglas. There have been several other contributors (e.g., David Fyfe and Juan Santos). The parallel parts of the code is available upon request only. Madpack5 is an abstract multilevel solver. It is PDE, domain, and discretization independent. It only handles linear problems, however. A paper describing the code is available on MGNet. Madpack5 is an object oriented code. The user interface is written in C. Most of the solvers are written in Fortran-77+m4. The same calling sequence is used independent of the data's type (real and complex, single and double precision, user defined are supported). The user interface builds all of the truly nasty data structures used internally by the code.

## MGD9V

This is a copyrighted single processor Fortran-77 code written by Paul M. DeZeeuw. The copyright owner is probably CWI. MGD9V is a black box multigrid solver that assumes that a general second order elliptic problem in two dimensions has been discretized using a nine point operator.

## MGGHAT

This is a (mostly) public domain, single processor Fortran-77 code written by Bill Mitchell. MGGHAT (Multi Grid Galerkin Hierarchical Adaptive Triangles), version 1.1, is an adaptive grid refinement multigrid code for solving linear second order elliptic partial differential equations on polygonal domains with linear, quadratic, or cubic elements over triangles.

## MGLab

This is a public domain set of Matlab functions written by James Bordner and Faisal Saied. MGLab is an interactive environment for experimenting with multigrid algorithms. MGLab can solve two dimensional elliptic partial differential equations using finite differences and includes several built-in problems (Poisson, Helmholtz, discontinuous coefficient problems, and nonselfadjoint problems). A number of parameters controlling the V cycle can be set using a point and click mechanism. The menu based user interface also allows a choice of several Krylov subspace accelerators (PCG, GMRES(k), and BiCGSTAB). The package exploits Matlab's visualization and sparse matrix features. It has also been structured to be extensible.

## MUDPACK

This is copyrighted, licensed software in Fortran for one or more processors, written by John Adams. MUDPACK 4.0 replaces and is incompatible with earlier versions. The software includes a suite of portable Fortran programs which automatically discretize and use multigrid techniques to generate second- and fourth-order approximations to elliptic Partial Differential Equations (PDEs) on rectangular regions. The elliptic PDEs can be real or complex in two- and three-dimensions with any combination of mixed derivatives, specified, or periodic boundary conditions. Multigrid V or W cycles which use point, line(s), or planar relaxation and fully weighted residual restriction are available for algorithm tuning to obtain optimal multigrid performance. MUDPACK was written to avoid repeated "re-invention of the wheel" in human code development time which can be at least as important as saving machine cycles.

## ParMGridGen

This is copyrighted C code, written by Irene Moulitsas. ParMGridGen-1.0 is a highly optimized serial and parallel library for obtaining a sequence of successive coarse grids that are well suited for geometric multigrid methods. The quality of the elements of the coarse grids is optimized using a multilevel framework. The parallel library is based on MPI and is portable to a wide range of architectures.

## pARMS

Yousef Saad's parallel Algebraic Recursive Multilevel Solvers.

## PHAML

Parallel Hierarchical Adaptive MultiLevel (PHAML) is Bill Mitchell's Fortran 90 module for the solution of second order linear elliptic partial differential equations with Dirichlet, Neumann (natural) or Mixed boundary conditions.

## PLTMG

PLTMG (Piecewise Linear Triangle Multi-Grid), version 11.0, is an adaptive multigrid solver for elliptic partial differential equations in general regions of the plane. It is a copyrighted Fortran and C code by Randolf E. Bank.

## UG

This is a copyrighted single processor C code managed by Peter Bastian. UG is a flexible software library for the development of adaptive multigrid methods on unstructured meshes in two or three spatial dimensions. UG implements most parts in a problem independent way so that the software can be reused for many different applications. In order to use the software here, you must get a license which contains the missing header file.

## Vanek

This is a single processor public domain Fortran-77 code written by Petr Vanek. This is an algebraic multigrid solver based on smoothed aggregation. The code is reliable if the model consists of solids and plates. Some problems with convergence may occur in the case of very thin and curved shells.

## Wesseling

A single processor public domain Fortran-77 code written by Pieter Wesseling. The file mglab.for is a tutorial multigrid program. It solves elliptic boundary values in one dimension. The user may choose various multigrid cycles, transfer operators, smoothing methods, and nested iteration, and defect correction. Cell centered and vertex centered discretization and multigrid is included. Documentation is included in the program. The program is written in portable Fortran-77, and has run on MS-DOS PC's and Unix based computers. The methods used are fully described in the following book: P. Wesseling, An Introduction to Multigrid Methods, Wiley, Chichester, 1992.

## Wienands

LFA00_2D_scalar is a copyrighted Fourier analysis program written by Roman Wienands in Fortran-77. Both two and three grid analysis for 2D scalar partial differential equations is included. The code supports many variants of coarsening strategies, coarse grid discretization, prolongation, restriction, and relaxation methods.