A symbolic procedure for the diagonalization of linear PDEs in accelerated computational engineering

Abstract

In this contribution we conjecture that systems of linearized Partial Differential Equations, viewed as consistent models for physically realizable systems, are diagonalizable. While this property is interesting for its own sake, our discussion will focus on technicalities and implications for advanced accelerated computing. We will demonstrate that diagonalization with respect to a chosen spatial coordinate systematically "reshuffles" the original PDEs and creates equivalent differential forms. It turns out that diagonalization automatically distinguishes the variables in the interface- and boundary conditions defined on surfaces normal to the diagonalization direction. © Springer-Verlag Berlin Heidelberg 2003.