DOMAIN MAPPINGS: A TOOL FOR THE DEVELOPMENT OF VECTOR ALGORITHMS FOR NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS (ADAPTIVE GRIDS, ELLIPTIC PROBLEMS)
Abstract
In this work we study domain mappings which facilitate efficient numerical solutions of partial differential equations on a vector computer. Domain mappings are shown to be an effective way to implement adaptive grid techniques while preserving the kind of regular grid structure that enhances vectorization. Several tensor product adaptive schemes are proposed and studied. Several mappings which map nonrectangular two-dimensional regions onto rectangular ones are also examined. We show that in many cases such domain transformations, and the associated problem transformation, can be carried out efficiently. In this way, the potential for vectorization that exists in the rectangular region can be fully exploited. A major extension to the ELLPACK system is described. With it, scientists can take advantage of these domain mappings in a natural and straightforward way.
Degree
Ph.D.
Subject Area
Computer science
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.