Multi-Dimensional High Order Non-Oscillatory Numerical Methods for DiscontinuousProblems in Parallel Structure

摘要

In this project we have studied high order finite difference, finite element, andspectral methods for the numerical solution of discontinuous or high gradient solutions. Theoretical study of algorithm development, stability, accuracy and convergence analysis, as well as applications of the algorithms to computational fluid dynamics (both compressible and incompressible) and semiconductor device simulation are performed. Parallel implementation issues of these high order methods are also studied.