Knowledge representations for the automatic generation of numerical simulators for PDEs

In this paper we describe an automatic programming (AP) system which generates numerical discretization schemes for partial differential equation (PDE) problems. This system is based on the observation that a wide variety of discretization schemes can be mechanically produced by computing surface in...

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Bibliographic Details
Published in:Mathematics and computers in simulation 1989-10, Vol.31 (4), p.383-393
Main Authors: Balaban, David, Garbarini, Joseph, Greiman, William, Durst, Mark
Format: Article
Language:English
Subjects:
990200 - Mathematics & Computers
COMPUTERIZED SIMULATION
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
EQUATIONS
Exact sciences and technology
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical simulation
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICS
PROGRAMMING
Sciences and techniques of general use
SIMULATION
SURFACES
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Summary:In this paper we describe an automatic programming (AP) system which generates numerical discretization schemes for partial differential equation (PDE) problems. This system is based on the observation that a wide variety of discretization schemes can be mechanically produced by computing surface integrals of spacetime currents. However, surface integration is difficult to carry out using conventional vector calculus. For this reason, the system is structured to include the differential geometry formalisms which make high dimensional surface integration simple. The differential geometry formalisms have also simplified the representation of continuous physics problems and increased the domain of applicability of the system.
ISSN:0378-4754
1872-7166
DOI:10.1016/0378-4754(89)90132-8