%0 Conference Paper %1 citeulike:7177140 %A Saldamli, Levon %A Fritzson, Peter A. %A Bachmann, Bernhard %B Modelica 2002 %D 2002 %I The Modelica Association %K modelica 65n30-pdes-bvps-finite-elements 35j05-laplacian-operator-helmholtz-poisson-equation %P 307--314 %T Extending Modelica for Partial Differential Equations %X Currently, Modelica only supports models containing constants, time-dependent variables, and time-derivatives of variables, i.e. ordinary differential and algebraic equations. In this article, we present how the Modelica language can be extended to support object-oriented modeling with partial differential equations (PDEs), in order to solve initial and boundary value problems. The techniques we present have fairly general applicability to 1D, 2D or 3D domains, although we focus mostly on 2D domains in this paper. We also describe the architecture of a prototype implementation where the PDE problem is translated and passed to an external mesh generator and a PDE solver for solution using the finite element method. An example of a stationary heat conduction problem is included together with execution results.

@inproceedings{citeulike:7177140, abstract = {{Currently, Modelica only supports models containing constants, time-dependent variables, and time-derivatives of variables, i.e. ordinary differential and algebraic equations. In this article, we present how the Modelica language can be extended to support object-oriented modeling with partial differential equations (PDEs), in order to solve initial and boundary value problems. The techniques we present have fairly general applicability to 1D, 2D or 3D domains, although we focus mostly on 2D domains in this paper. We also describe the architecture of a prototype implementation where the PDE problem is translated and passed to an external mesh generator and a PDE solver for solution using the finite element method. An example of a stationary heat conduction problem is included together with execution results.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Saldamli, Levon and Fritzson, Peter A. and Bachmann, Bernhard}, biburl = {https://www.bibsonomy.org/bibtex/245a235be1c641e117f8dd72171bd353c/gdmcbain}, booktitle = {Modelica 2002}, citeulike-article-id = {7177140}, citeulike-attachment-1 = {saldamli_02_extending_491892.pdf; /pdf/user/gdmcbain/article/7177140/491892/saldamli_02_extending_491892.pdf; f035ed583e51128dcec0a470b57f0ef0b35c0ed5}, day = {18--19}, file = {saldamli_02_extending_491892.pdf}, interhash = {ae4c57a7709ac10ddd22db430753b5ce}, intrahash = {45a235be1c641e117f8dd72171bd353c}, keywords = {modelica 65n30-pdes-bvps-finite-elements 35j05-laplacian-operator-helmholtz-poisson-equation}, location = {Oberpfaffenhofen, Germany}, month = mar, organization = {The Modelica Association}, pages = {307--314}, posted-at = {2010-05-17 01:21:28}, priority = {2}, publisher = {The Modelica Association}, timestamp = {2019-04-01T02:01:18.000+0200}, title = {Extending {Modelica} for Partial Differential Equations}, year = 2002 }