Symbolic and Numerical Computation - Towards Integration An Interactive Symbolic{Numeric Interface to Parallel ELLPACK for Building General PDE Solvers

In this paper we describe an interactive symbolic-numericinterfaceframework (editor) to the ELLPACK partial diierential equation (PDE) system for building PDE solvers for a much broader range of applications. The domain of applicability of ELLPACK and its parallel version (//ELLPACK) is restricted to second order linear elliptic boundary value problems. This editor allows the speciication of nonlinear initial and boundary value PDE problems. The editor applies hybrid symbolic{numeric techniques at the PDE problem level to automatically reduce them to a sequence of linear elliptic PDEs. The result of this preprocessing is recorded in the form of an ELLPACK program. Several examples are presented to demonstrate the functionality and applicability of this interface framework, and the eeciency of the underlying solution methods.