Integrated Symbolic-Numeric Computing in //ELLPACK: Experiences and Plans
Sanjiva Weerawarana, Ann C. Catlin, Elias N. Houstis, John R. Rice · Purdue e-Pubs (Purdue University System) · 1992
In this paper we describe the use of integrated symbolic-numeric computing techniques in the evolving / /ELLPACK1[HRC+90] Problem Solvillg Environment.I/ELLPACK is a problem solving environment (PSE) for solving partial differential equations (PDEs) using parallel architectures.It Wall originally developed to use the ELLPACK[RB85] system as the numerical computing engine.The domain of applicability of ELLPACK is restricted to second order linear elliptic bounda:ry value problems in two aud three dimensions.We apply hybrid symbolic-numeric techniques to extend the domaiD. of applicability of the IIELLPACK PSE using both BLLPACK and other numerical PDE solving systems as numerical engines.These techniques ha.ve been implemented as an interactive tool using the X Window System[SG86].Once the PDE problem is specified, it is symbolically manipulated using the MAXIMA'l computer algebra system to genera.tea. j jELLPACK program to solve the problem using either ELLPACK or FIDISOL[SSM85], a. finite-dif[erence method PDE solver.The GENCRAY[WW89] code generation system is used to genera.te the j jELLPACK program.Several examples of symbolic processing of PDE problems are presented to illustrate the approach.Finally, we consider the shortfalls of these techniques and discuss our plans for solving some of the problems.