Efficient High Order Numerical Methods for Convection Dominated Partial Differential

Brown University, Providence RI

Investigators

Abstract

In this project, research in the algorithm design and analysis of high order numerical methods, including the finite difference and finite volume weighted essentially non-oscillatory (WENO) schemes, discontinuous Galerkin finite element methods, and particle methods, for hyperbolic and other convection dominated partial differential equations, especially in adaptive, multiscale and uncertain environments, will be carried out. Parallel implementation and applications of these methods will also be addressed. The intellectual merit of the proposed activity lies in its comprehensive coverage of algorithm development, analysis, implementation and applications. Problems in applications motivate the design of new algorithms or new features in existing algorithms; mathematics tools are used to analyze these algorithms to give guidelines for their applicability and limitations; practical considerations including parallel implementation issues are addressed to make the algorithms competitive in large scale calculations; and collaborations with engineers and other applied scientists enable the efficient application of these new algorithms or new features in existing algorithms. The proposed research aims at the design of efficient algorithms, which, when used on today's powerful computers, will help to solve many problems from diversified applications such as aerodynamics and aeroacoustics for aircraft design, electromagnetism wave simulation for communications, and semiconductor device simulation for the computer industry. The thrust of this proposal is to use powerful mathematical tools to guide the design of algorithms, so that they are more efficient, more reliable, and more robust in applications.