Introduction

LIBPARABOL is a software library that allows for quick solving of equation systems that arise when discretizing parabolic differential equations of the kind

$$u_t - L_{\epsilon} u = f\\\ u(0) = u_0\\\ u_{\Gamma} = \gamma$$

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.