Ahstract We are developing an expen system environment for solving elliptic partial differential equations(pDEs) defined on two and three dimensional domains on MIMD type parallel machines. According to its design objectives, it will provide a uniform programming environment for implementing parallel MIMD PDE solution solvers, an automatic partitioning and allocation of the PDE computation, a very high level problem specification language, an interactive high level environment for grid

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... , a domain partitioning and mapping facility, a uniform environment for obtaining software engineering measurements and a graphical display of solution output. The IIELLPACK is implemented on a hardware facility consisting of a graphics workstation supporting Xl I window system and connected to an NCUBE and SEQUENT machines through a wide bandwidth local network. The software infrastructure includes i) a PDE problem oriented language processor, ii) a geometry processing tool which is capable of generating fixed meshes and domain decompositions automatically and interactively, iii) an algorithm mapper facility for partitioning and mapping the underlying PDE computation and iv) an expert front end that selects the discretization mesh, the parallel algorithm/machine pair and its configuration. In order to support the solution of elliptic PDEs on fixed meshes, we are building a library of finite difference and element discretization methods and direct/iterative solvers for the NCUBE and SEQUENT machines.