High Order Methods for Linear and Nonlinear Waves

Brown University, Providence RI

Investigators

Abstract

Shu 0207451 The investigator and his colleague study high-order-accuracy computational methods for linear and nonlinear waves, with emphasis on shock wave calculations and simulation of electro-magnetics waves. The work includes the development and analysis of high-order finite difference, finite element, and spectral methods, as well as applications of these methods to computational fluid dynamics and computational electro-magnetics. In particular, the efforts include the following components: high-order methods for shock wave calculations, including finite difference WENO schemes, spectral methods for supersonic reactive flows, and finite element discontinuous Galerkin methods; high-order methods for Maxwell's equations; and perfectly matched absorbing layers. Computers are now used more extensively in engineering and other applied sciences. An important component to effectively use computers is the design and analysis of efficient numerical algorithms. Important applications such as computer-aided design of aircraft are to a large extent dependent on efficient and reliable algorithms designed by applied mathematicians. The high-order methods the investigators develop and analyze in this project should significantly increase the efficiency and reliability of algorithms used in crucial application areas such as aerospace industry, communications, and material science.