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RELAX: A Software Platform for PDE Interface Relaxation Methods

We describe the design of the RELAX system for programming interface relaxation techniques for partial differential equations (PDEs). The PDEs are solved over composite domains. Each domain is encapsulated with its own geometric modeling system and local PDE solvers. This encapsulation presents a challenging ~oftware problem, for it necessitates PDE algorithms which speak a language of "data interchange among objects", rather than the the usual language of grid points and linear systems. RELAX is geared towards rapid prototyping, allowing the user to sketch the composite domains on the screen and then to use this sketch to demonstrate the appropriate relaxation schedule visually. The editing of the relaxation program is closely intertwined with the editing of the domain sketch.