Computing About Physical Objects
Chanderjit Bajaj, Christoph M. Hoffmann, Elias N. Houstis, John T. Korb, John R. Rice · Purdue e-Pubs (Purdue University System) · 1987
This report describes the technical aspects of the project Computing about Physical Objects.This project has received equipment and infrastructure support for five years from the National Science Foundation.The research is engaged in extending the geometric coverage of solid modelers to algebraic surfaces of arbitraIy degree.Here, questions such as effective parameterization, implicitization, and singularity resolution handling are addressed.Efficient computational procedures are being developed that will eliminate traditional bottlenecks that presently make modeling operations so expensive.The work also explores questions of representing surfaces succinctly, of approximately representing complicated surfaces by simpler ones, of approximating naturally occurring surfaces by mathematically defined ones, and of automatically generating standardized surface areas.It seeks to merge results from algebra, geometry, topology, and approximation theory into effective tools for a higher level of perfonnance in geomettic modeling. 1.2.C. Mathematical Software SystemsA high level mathematical software system targeted toward elliptic partial differential equations is already operational.Its principal components are an interactive, mathematically based, graphically oriented interface and a broad range of problem solving modules.This 100,000+ lines of code system is built using various software tools so that it can readily evolve and be enhanced.It is an ideal vehicle to test approaches to future systems for computations about physical objects.The new work will greatly enhance the quality and performance of the user interface.An expert system project is under way to provide users sophisticated guidance in using tools and problem solving modules.Significant expansion in the domain of applicability will be based on the following work on the algorithmic infrastructure: 1.The rectangular 3D geometry will be extended to general domains, 2. The single domain, single equation operation will be replaced by a multiple domain, multiple equation operation, 3. Time dependent and nonlinear problems will be allowed, 4.More extensive domain mapping and grid adaptation capabilities will be incorporated.These extensions involve a large number of specific projects, some very algorithmic in nature, e.g., interfacing algebraic geometry with numerical methods and 3D numerical methods.We will rely heavily on a high level software integration approach to gain many of the desired capabilities.For example, a structural engineering software package, an expert system, and MACSYMA will all be integrated, appearing to the user as though they were really pan of one system. 1.2.D. Parallel ProcessingComputing with physical models requires enormous computing power.This power will come mostly from massive parallelism.Our work concentrates on three of the many aspects of this problem area.First, we will be heavily involved in the algorithmic infrastructure both for numeric and geometric computation.Beyond parallelizing existing numerical methods, we will deeply explore new domain decomposition techniques as a means of effectively using hundreds or thousands of processors for realistic applications.A key ingredient of this work is to study how the numerical methods interact with the geometry of physical objects.Ultimately, this use of parallelism will result in reaching true interactive performance for complex geometric computations.Second, we will study how to create an intelligent system for resource allocation without significant user input or intervention.We will consider both tightly coupled