Automatic Programming System for PDEs (Partial Differential Equations) Based on a Relational Model of Continuous Physics Problems and a Functional Model of Mathematical Analysis.

摘要

The goal of this research is to improve the productivity of scientists and engineers who develop numerical simulations for physical systems describable by partial differential equations (PDEs). This is to be achieved by creating an automatic programming system. The system will accept as input a natural interactive mathematical specification of the problem, and its output will be an efficient program for computing an accurate numerical approximation to the solution of the problem. Such a system will reduce the tedium and human errors involved in the mathematical manipulations and programming normally involved in a solution. We are building a high-level simulation system for PDE problems based on conservation laws. This system will derive its schemes for many classes of problems. In addition, we are developing symbolic manipulation capabilities for dealing with mathematical analysis at a very sophisticated level. Initially the scope of the system will be limited to PDE problems with smooth solutions. The system will provide significant productivity gains for scientists and engineers working on these problems. Later the system will be extended to include PDE problems with discontinuous solutions. The mathematical techniques required to solve these two classes of problems are quite different. However, the symbolic manipulation capabilities for dealing with mathematical analysis will make the development of such a general system possible. 26 refs., 8 figs. (ERA citation 14:012380)