Experiences vectorizing software for elliptic partial differential equations

Abstract

ELLPACK is a FORTRAN-based package for solv­ ing elliptic partial differential equations; this package contains over 100 modules, each typically consisting of a number of subroutines. The enhancement of six ELLPACK modules to take advantage of the vector pro­ cessing capabilities of Cray supercomputers is discussed and variations in performance due to the use of three different compilers are also noted. Speedup factors arc computed which quantify improvements due to program optimization as well as the compiler effects. Graphic per­ formance profiles showing CPU time versus grid size arc presented. 1. Statement of the Problem One of the most important models of physical phenomena is the boundary-value problem. Examples of such phenomena include heat flow and diffusion, gravita­ tional and electrostatic potentials, fluid dynamics, and loading of beams, plates, and other objects. Because of this, much effort has been devoted to the development of reliable methods for numerically solving these equations. The underlying mathematical problem addressed by these methods is a second-order elliptic boundary-value prob­ lem consisting of a partial differential equation (PDE) Lu = auu + Ibiiry + ctiyy + duz + euy + fu = g (1) defined on a domain R and its accompanying boundary conditions