CAREER: Wavelet Theory and Applications in 3D Physical Simulation

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

The objective of this research is to conduct a study of wavelet representations for complex surfaces and volumes with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Multiresolution techniques recently described in the computer graphics literature will be extended to develop high performance algorithms and implementations for simulating the partial differential equations of common physical processes on general three-dimensional domains, including potential problems, scattering problems and problems in elasticity. Emphasis is placed on unifying the mathematical analysis and signal-processing perspectives of wavelets, as this provides new insights for the large-scale simulation of a wide range of problems. The research consists of two interrelated thrusts. The first develops the mathematical foundations, including surface and volume wavelet constructions for PDEs, practical discretization strategies for linear and nonlinear PDEs, matrix compression, preconditioner design, adaptive refinement, accuracy estimates and error control strategies. The second thrust focuses on the practical issues of algorithm and data structure design, robust implementation for large-scale problems involving complex geometry, parallelization, and the interpretation and visualization of output aided by the multiresolution representation. This will result in a suite of multiresolution techniques and tools that provide (i) researchers with a context for conducting domain-specific studies (ii) engineers with application libraries for simulating large-scale real world problems and (iii) students and professionals with an environment for learning about wavelet theory and applications. The educational objectives of this project are closely linked to the research program. The continuing development of a course on wavelets and filter banks will enable the dissemination of fundamental knowledge on multiresolution techniques and it will serve as a conduit for the integration of research experience into the curriculum. Additional courses are oriented toward issues of computation and information technology more generally within the graduate and undergraduate engineering curriculum. The integration of educational and research activities will be facilitated by seminars, short courses, and new and continuing collaborations with industry and other institutions.