An Open Structure for PDE Solving Systems
Elias N. Houstis, John R. Rice, Sanjiva Weerawarana · Purdue e-Pubs (Purdue University System) · 1994
Most PDE solving systems have a closed structure.That is, they use a certain set of problems, methods, data structures, etc., that they support and all the software must adhere to the resulting standards.Of course there are systems which allow usc of a general purpose programming language (e.g., Fortran) which means anything can be done.We exclude this form of open structure in this discussion even l.hough this feature is a useful one.Even the j jELLPACI{ ''foreign system" approach gives only limited openness, the new module must accept a complete PDE problem and return its solution.IIere we consider a structure of high level PDE solving modules which is as open ended as possible.The purpose of this open structure is to allow the problem solving software structure to directly reflect the problem solving process.We define the structure in terms of data objects and operators on them.There are five standard data objects which we call problem objects; the descriptions of them are at a high level and complete details are yet to be given.1. PDE PROBLEM.This is the abstract or mathematical problem expressed in continuous, symbolic terms.Its data is organized as follows:PDE: The partial differential equation (operator). Domain-Interior:Where the PDE is satisfied, -Boundary: The boundary of l.he interior.Be: The boundary conditions equations, including initial and global conditions.FRAME:-coordinates system and names -solution name -problem parameters -data: constants, fixed functions.2. NUMERICAL PDE PROBLEM.This is a finite problem, there arc a finite number of numerical variables and equations to be satisfied.Every function and operator involved can be evaluated exactly (to within round-off) in a finite computation.Its data is organized as follows:Coefficients: The unknowns to be determined.