University of Western Ontario

Novel methods for the computationally efficient simulation of compressible fluid flow will be developed, with applications to aerospace and space physics. First, new formulations of multigrid techniques for the implicit solution of time-dependent flows will be studied, using parabolization to increase diagonal dominance and solution efficiency. Second, new direct solution methods for steady transonic flows will be developed, employing dynamical systems and characteristic analysis.

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.

Traders in both financial markets and commodity markets must make educated decisions about when to trade and at what price; this project develops tools to assist with this decision-making process. Working with energy companies, financial software companies as well as companies from the banking and insurance sectors, the research team develops optimal portfolio methods that produce both the best investment decisions and the best hedging strategies for claims in general markets.