An object-oriented framework for the reliable automated solution of problems in mathematical physics.

摘要

An object-oriented framework, named Trellis, for general numerical simulations has been developed. Trellis is designed to overcome the limitations of current analysis tools and provided the basis for the development of the next generation of analysis tools. The specific driver of the development of this framework is the need for the next generation of analysis tools to effectively support adaptivity in all of its various forms. The types of adaptivity of interest include not only adaptivity of the discretization, but also of geometric idealizations, mathematical model selection and solution techniques. Trellis is unique in that it builds off a geometry-based problem description. The geometry-based environment consists of a geometric model, a general attribute system to describe the rest of the problem definition, a topology-based mesh description to house the discretization of the geometry and a field structure to store the solution.; The analysis framework itself decomposes the solution process in an object-oriented manner giving a strong separation between the mathematical description of the problem to be solved, the specifics of the numerical method used to solve the problem (e.g. the shape functions, mappings, integration rules, etc.) and the solution procedures used to solve the resulting linear and nonlinear systems.; Trellis is current being used to implement a number of finite element analysis codes in the areas of linear static and dynamic heat transfer, general advection-diffusion problems, solid mechanics including nonlinear material behavior, solution of Euler equations using discontinuous Galerkin methods, and biphasic analysis of soft tissues. In addition an implementation of a partition of unity analysis procedure for linear elasticity has been done using Trellis.