PDE: Dymola/Modelica Library for 1D Parabolic and Hyperbolic Partial Differential Equations

Introduction

PDE offers modules that permit to model and simulate one-dimensional partial differential equations and systems of equations of the parabolic and hyperbolic types. To this end, the library implements various algorithms from the classes of the Method of Lines as well as the Finite Volume Method.

The library contains furthermore a series of application examples that demonstrate how these modules can be utilized.

Historical Development

In the seventies of the last century a number of programs were developed that were designed to support the simulation of general distributed parameter systems. Among them were programming packages such as Forsim-VI (Atomic Energy of Canada) and Leans-III (Lehigh University). Most of these programmes were based on Fortran. Some of these programmes required the user to write Fortran subroutines. Others offered a primitive preprocessor.
These programmes went out of fashion, in part because they weren't flexible enough to allow the formulation of practical applications, and in part because the overhead that was accepted in return for the sheer generality of these programs was so enormous that the resulting simulation code turned out to be extremely slow and sluggish.
For this reason, only special codes for specific subclasses of PDE systems were developed and described in the open literature during the past 20 years.
In the year 2006 we decided to embark on a new attempt at developing a generic PDE code. That code should at least reproduce the features offered earlier by the programs Forsim-VI and Leans-III [1]. The new code should be developed within the Dymola/Modelica framework, as this environment is flexible enough to support full modularity. Furthermore, the strong symbolic preprocessing capabilities of Dymola/Modelica enabled us to produce simulation code with a run-time efficiency that is at least as good as that of the best manually coded spaghetti program.
This research effort led to the new PDE library. ()

Most Important Publications

Dshabarow, F. (2007), Support for Dymola in the Modeling and Simulation of Physical Systems with Distributed Parameters, MS Thesis, Dept. für Computational Science, ETH Zürich, Zürich, Schweiz.

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