https://github.com/nschloe/sippp

Fortran library for the solution of singularly perturbed parabolic problems
https://github.com/nschloe/sippp

Last synced: 22 days ago
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Fortran library for the solution of singularly perturbed parabolic problems

• Host: GitHub
• URL: https://github.com/nschloe/sippp
• Owner: nschloe
• Created: 2015-08-24T16:51:33.000Z (about 9 years ago)
• Default Branch: master
• Last Pushed: 2021-07-20T18:01:51.000Z (over 3 years ago)
• Last Synced: 2024-10-10T09:12:51.774Z (about 1 month ago)
• Language: Fortran
• Homepage:
• Size: 4.92 MB
• Stars: 2
• Watchers: 3
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
## Introduction

LIBPARABOL is a software library that allows for quick solving of equation

systems that arise when discretizing parabolic differential equations of the

kind

```math

u_t - L_{\epsilon} u = f\\

u(0)        = u_0\\

u_{\Gamma}  = \gamma

```

with $`L_{\epsilon} = \sqrt{\epsilon} \Delta u - c(x) u`$ in one space dimension.

The library contains routines which handle the generation

of meshes (in particular layer adapted meshes) when treating singularly perturbed

problems as well as a wide range of A-stable Runge-Kutta methods. The

equation systems aring from the application of fully implicit Runge-Kutta

methods can be solved by a preconditioned GMRES method. Moreover, there

exist a number of user interfaces which neatly plot the approximated solution

in various formats or generate LaTeX style "convergence tables".

## Installation

In each of the subdirectories you will find Makefiles that will help you with

the compilation of the library. All you need to do is specify your favourite

Fortran95 compiler in "make.inc" which is to be found at the top level directory

Then type make, lean back, and watch the engine at work.

## Usage

The user needs to provide the parameters of the differential equation as well 

as everything that relates to the operator L_eps. Which routines are exactly

required can be seen from INTERMOD.f; the interfaces for the Fortran routines

are contained in this module.

The folder MAIN contains examples of provided operators and PDE parameters.

To see the library at work, go to the MAIN folder and link one of the files

in the folder "operators" to the file "operator.f" in the MAIN-directory. Do

the same for one of the parameter files. Then edit "main.f" to your liking

(a few usage examples are contained), type make, and then execute main.out.

The whole range of the routines which may be of interest to to are contained

in PUT.f.

Have fun!

This software was developed by Nico Schlömer as part of his diploma thesis in 2007.