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Simulation of partial differential equations models in Java

María José Cano (Mathematics Department, University of Murcia , Espinardo-Murcia, Spain and Department of Computer Science and Automatic Control, UNED, Juan del Rosal, Madrid, Spain)
Eliseo Chacon-Vera (Mathematics Department, University of Murcia , Espinardo-Murcia, Spain)
Francisco Esquembre (Mathematics Department, University of Murcia , Espinardo-Murcia, Spain)

Engineering Computations

ISSN: 0264-4401

Article publication date: 2 May 2017




Computer simulations improve the knowledge of physical models and are widely used in teaching and research. Key aspects are to understand their solutions and to make interactive changes to the models, observing their effects in real-time. The drawback of creating interactive simulations of physical models is the high level of programming expertise required. The purpose of this study is to facilitate this task.


Java is the perfect language for this task; it yields high-quality graphics and is widely spread in the scientific community. Because many important physical models are described by means of partial differential equations (PDEs), the combination of Java with FreeFem++, a C++ PDE solver based on the finite element method, is considered.


In this study, a Java library is introduced to numerically solve PDE equations via a run-time connection with FreeFem++. The solution is encapsulated into Java objects that are ready to be used in different programming tasks. The library also includes new Java visualization elements for solutions and meshes in the context of the Open Source Physics project library. Together, the connection features and the visualization elements facilitate the creation of Java simulations by programming researchers. For those with less programming capabilities, this work has been included into Easy Java Simulations, a tool to further ease the creation of interactive simulations.


The present study approach allows simulating models given PDEs. The equations are solved either in local or in remote mode (e.g. by a network accessible to a high-performance computer) and visualized locally, providing a high degree of interactivity to the end user.



The authors would like to thank Antoine Le Hyaric from the Jacques-Louis Lions Laboratory, Pierre and Marie Curie University in Paris, for introducing us to the ins and outs of FreeFem++. This work was partially funded by Fundación Séneca Murcia, the Regional Research Agency of the Region of Murcia (Spain) through grants 16007/BSCE/10 and 19294/PI/14, and by the Spanish Government projects MTM2012-36124-C02-01 and MTM2014-52920-P.


Cano, M.J., Chacon-Vera, E. and Esquembre, F. (2017), "Simulation of partial differential equations models in Java", Engineering Computations, Vol. 34 No. 3, pp. 800-813.



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