Problem-solving environments for partial differential equation based applications
Abstract
Problem solving environments represent the next generation of scientific computing software. This thesis deals with four aspects of building problem solving environments for partial differential equation based applications: software architecture of development frameworks, high level languages, computational intelligence, and integrating experimentation and computation. The software infrastructure available for building problem solving environments is low level and is designed for computer scientists rather than computational scientists. A software framework that allows computational scientists to develop their own problem solving environments for partial differential equation based applications is presented. The framework is a multi-layered architecture that provides infrastructure at all levels of the problem solving environment development process. High level, formal notations are a useful vehicle for expressing partial differential equation problems and their solution schemes. A high level symbolic language that supports the specification of arbitrary differential models and includes powerful solution scheme specification capabilities is presented. The language is based on decomposing the problem into its constituent parts and on decomposing the solution process into a sequence of transformations. Along with the increased complexity of scientific computing software, the choices and decisions users must make have also become increasingly complex. A technique for intelligently selecting optimal partial differential equation solvers is presented. The reasoning methodology uses the exemplar reasoning approach and is based on the observed performance of various solvers on a set of existing problems. Finally, the problem of integrating experimentation and computation is addressed. The idea of a "virtual science laboratory" that integrates experimentation and computation in one cohesive environment is developed. Methodologies for using the integrated environment in several scenarios are also presented. The environment is based on the problem solving environment infrastructure developed in this thesis and includes laboratory instrument control and data acquisition facilities.
Degree
Ph.D.
Advisors
Houstis, Purdue University.
Subject Area
Computer science
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