An object-based problem-solving environment for collaborating PDE solvers and editors

This thesis describes RELAX, an object based problem solving environment for solving and editing composite partial differential equation (PDE) problems. Composite PDE problems are coupled, multi-domain, two-dimensional PDE problems with (possibly) distinct interior equations and boundary conditions assigned to each domain. Each domain and its local equations form a primitive PDE problem. Composite PDE problems are built from primitive PDE problems by assigning additional equations, called interface conditions, which couple local solutions of neighboring primitive PDE problems along geometric segments where their domains are joined. The global PDE problem is solved through a iterative process, called interface relaxation, in which primitive PDE problems are successively solved by local solvers and then solution and normal derivative values are smoothed among neighboring domains. RELAX has a component-based message-passing design, and incorporates two types of externally-supplied modules in the problem solving process. First, RELAX integrates local solution modules, called primitive objects, which handle individual primitive PDE problems. Primitive objects must handle the local geometry, equations, and solution process (e.g., meshing, discretization, etc.) of primitive PDE problems. Second, RELAX integrates user interface components, called editors, which are responsible for providing human interaction mechanisms for attaching to, displaying and manipulating various features of the problem solving environment. RELAX supports a dynamically configurable multiple-editor environment which allows editors to access all features of primitive and composite PDE problems, the global iterative process, and even operational parameters of the problem solving environment itself. RELAX supplies four system components for the problem solving environment. RELAX provides two software support components, the object support platform and the editor support platform which integrate and coordinate primitive objects and editors, respectively. RELAX provides a central message relay component, called the message dispatcher, which drives the message passing environment. RELAX also provides a composite problem platform, which builds and maintains data structures and services which define and solve composite PDE problems. This thesis describes the architecture and use of RELAX, and defines a message passing protocol for defining and solving composite PDE problems