computing

Modern engineering designs require fast and high credible scientific computations which usually run in a parallel way. The proposed research focuses on the development of the parallel preconditioning technology used in large scale scientific computations. A multi-level recursive strategy is developed to improve the parallel computing performance when a large number of processors (up to at least 5000) are used. An existing Newton-Krylov flow solver will be improved by coupling with this multi-level preconditioner.

The theoretical and practical aspects of manipulating mathematical expressions on computers are usually referred to as computer algebra or symbolic computation. In this field, calculations are designed to yield exact and complete results, by opposition to numerical analysis which is meant to handle approximate values, potentially producing incomplete results. Exactness and completeness have some significant computational overhead. Computer algebra software is highly demanding in CPU time and memory.

Computer algebra systems such as Maple compute using mathematical formulae as well as numbers, mechanizing the mathematics used in education and research labs. This project focuses on the design and implementation of algorithms for these systems. Emphasis is placed on efficiency that allows large and complex problems of the type encountered in industrial settings to be solved. In the past year the team has made major advances in the core tools that are needed to solve these complex problems.

Due to the explosive growth in the technology for manufacturing integrated circuits, modern chips contain millions of transistors. Using sophisticated optimization algorithms, it is possible to achieve notable increases in the performance of the chips, reduce the manufacturing costs, and produce faster, cheaper computing for society. Thus, the objective of this project is to enhance the solution of large-scale optimization problems arising in these applications.

Bacterial biofilms are microbial depositions on immersed surfaces and are ubiquitous in natural and engineered environments. For example, they play a significant role in medical applications where they can grow on artificial implants and cause infections; they form dental plaques and contribute to tooth decay; they can be utilized to assist in clean-up of contaminated soils or groundwater aquifers; they accelerate corrosion of metal surfaces; and they are a main culprit behind contamination of drinking water systems and food processing equipment.