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AI-DEQSOL. A knowledge-based environment for numerical simulation of engineering problems described by partial differential equations

Published online by Cambridge University Press:  27 February 2009

D. P. Finn ,
N. J. Hurley  and
N. Sagawa
D. P. Finn
Affiliation:
Hitachi Dublin Laboratory, Hitachi Europe Ltd, Trinity College, University of Dublin, Dublin 2, Ireland
N. J. Hurley
Affiliation:
Hitachi Dublin Laboratory, Hitachi Europe Ltd, Trinity College, University of Dublin, Dublin 2, Ireland
N. Sagawa
Affiliation:
Hitachi Dublin Laboratory, Hitachi Europe Ltd, Trinity College, University of Dublin, Dublin 2, Ireland
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Abstract

This paper presents a knowledge-based problem solving environment for numerical simulation of problems described by partial differential equations (PDEs). The system aims to facilitate the simulation requirements of different user groups that include engineers, mathematicians and numerical analysts. To attain this objective, a flexible multi-perspective modelling environment is proposed which incorporates three natural modelling platforms, namely; a physical model, a mathematical model and a numerical model. The modelling environment is integrated with a sophisticated numerical solver. We believe that combination of an open modelling system with a basic numerical simulator provides a powerful problem solving environment capable of meeting the needs of these different user groups. The overall system architecture is based on automatic transformation using mathematical and numerical knowledge bases between the three identified models. The knowledge bases are organized in a frame based manner to reflect the hierarchical nature of the knowledge in PDEs and numerical algorithms. The object oriented paradigm is used to bind local rule bases to each frame and for implementing a global inference mechanism which works over the hierarchical knowledge structures. Evaluation of the modelling environment has indicated that engineers can tackle PDE based engineering problems without the necessity for detailed knowledge of mathematics or numerical techniques and mathematicians can examine the mathematical properties of PDEs without the requirement of numerical expertise.

Type
Research Article
Information
AI EDAM , Volume 6 , Issue 3 , August 1992 , pp. 199 - 212
Copyright
Copyright © Cambridge University Press 1992

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References

Barras, P., Blum, J., Paumier, J. C., Witomski, P. and Rechenmann, F. 1990. EVE: An object-centred knowledge-based PDE solver. Proceedings of the Second International Conference on Expert Systems for Numerical Computing, Purdue University, USA.Google Scholar
Booch, G. 1991. Object Oriented Design. California: Benjamin/Cummins.Google Scholar
Buis, P. E. and Dyksen, W. R. 1991. XELLPACK: a distributed problem solving environment for elliptic partial differential equations. Proceedings of IMACS 13th World Congress on Computation and Applied Mathematics, 3, 1035–1036.Google Scholar
Clarke, J. A. 1991. Intelligent front-ends for engineering applications. Artificial Intelligence in Engineering, 6(1), 2–4.Google Scholar
Finn, D. P., Grimson, J. B. and Harty, N. M. 1992. An intelligent assistant for mathematical modelling of physical systems. Proceedings of the 2nd International Conference on Artificial Intelligence in Design, Carnegie Mellon University, Pittsburgh, 579–596.Google Scholar
Houstis, E. N. and Rice, J. R. 1991 a. The engineering of modern interfaces for PDE solvers. Proceedings of IMACS 13th World Congress on Computation and Applied Mathematics, 3, 1037–1038.Google Scholar
Houstis, E. N. and Rice, J. R. 1991 b. Parallel ELLPACK: a development and problem solving environment for high performance computing machines. Proceedings of IFIP Working Conference on Programming Environments for High-Level Scientific Problem Solving, pp. 229–242.Google Scholar
Jambunathan, K., Lai, E., Harte, S. and Button, B. L. 1991. Development of an intelligent front-end for a computational fluid dynamics package. Artificial Intelligence in Engineering, 6(1), 27–35.CrossRefGoogle Scholar
Konno, C. 1987. Automatic code generation method of DEQSOL (differential equation solver language). Journal of Information Processing, 11(7), 15–21.Google Scholar
Kowalski, A., Peskin, R. and Russo, M. 1988. Anatomy of AGNES: an automatic generator of numerical equation solutions. In: Intelligent Mathematical Software Systems, eds. Houstis, E. N., Rice, J. R., Vichnevetsky, R.North-Holland: Elsevier, pp. 33–42.Google Scholar
Schonauer, W. A., Schreiner, A. and Ecke-Schuth, J. 1988. A critical discussion of the user interface of a PDE solver in the Context of Numerical Expert Systems. In: Intelligent Mathematical Software Systems, eds. Houstis, E. N., Rice, J. R., Vichnevetsky, R., North-Holland: Elsevier, pp. 353–362.Google Scholar
Shephard, M. S. 1988. Approaches to the automatic generation and control of finite element meshes. Applied Mechanics Reviews, 41(4), 169–185.CrossRefGoogle Scholar
Tello, E. R. 1990. Object Oriented Programming in Artificial Intelligence. New York: Addison-Wesley.Google Scholar
Yip, K. M.-K. 1991. Computer-aided heuristic and qualitative reasoning in fluid mechanics. In: Proceedings of IMACS 13th World Congress on Computation and Applied Mathematics, pp. 1022–1027.Google Scholar