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Boundary Modulation with Mathematica

Gautam Dasgupta
Organization: Columbia University
Department: Department of Civil Engineering and Engineering Mechanics
Journal / Anthology

Software for Engineering Workstations
Year: 1990
Volume: 6
Issue: 1
Page range: 2-10

The boundary modulation technique combines the strengths of the boundary element method with the analytical Fourier series representation. The relevant lengthy algebra and calculus can be worked out symbolically without any error like the slip of the pen. Finally, any specific instantiation can be evaluated in the numerical form. The associated graphic plots can be displayed simultaneously. After the boundary modulation concept has been developed in the interactive mode with interpreting softwares, the computer program can be passed on to a mainframe, compiled to be executed from production runs. At a workstation--even with a personal computer--the computer mathematics program, called Mathematica, makes all necessary algebra and calculus tractable. Any geometrical domain can be tessellated conveniently, with an artificial intelligence based expert system, into generalized convex subcoverings and canonically modulated for the Poisson equation.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations