Generating Spectral Method Solvers for Partial Differential Equations
Berkooz, Gal; Chew, L. Paul; Cremer, James F.; Palmer, Richard S.; Zippel, Richard
A major cost in scientific computing is the creation of software that performs the numerical computations. This paper presents preliminary results on research to build a framework for automating the construction of numerical solvers for differential equations. Within this framework, the scientific computing problem is described using a very high level programming language that captures the original differential equations in a natural fashion. A sequence of code "transformers" are used to gradually refine the high level description of the problem into a concrete, executable form. Numerical techniques like the finite element method, the spectral method and the Crank-Nicolson discretization scheme are encoded in these transformers and once so encoded can be applied to a wide variety of different problems. This framework provides a natural environment for coarse scale parallelization based on relatively abstract properties of the specific equations and methods.
computer science; technical report
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