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An Interactive Computer Graphics System fur Boundary Value Problems: II

IP.com Disclosure Number: IPCOM000128537D
Original Publication Date: 1976-Dec-31
Included in the Prior Art Database: 2005-Sep-16
Document File: 6 page(s) / 25K

Publishing Venue

Software Patent Institute

Related People

Uri M. Ascher: AUTHOR [+5]

Abstract

The IBV system was originally developed for the interactive formulation and solution of linear elliptic boundary value problems on general two-dimensional domains. This report describe, the extension of the IBV system to the formulation and solution of both quasilinear parabolic and quasilinear elliptic problems in two space variables. This research was supported in part by the National Science Foundation Office of Computer Research (Grant No. GJ32552), and the University of Minnesota Computing Center.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

An Interactive Computer Graphics System fur Boundary Value Problems: II

by

Uri M. Ascher, Steve Savitt and J.B. Rosen

Computer Science Department

114 Lind Hall

University of Minnesota

Minneapolis, Minnesota 55455

Technical Report 76-2

March, 1976 Cover design courtesy of Ruth and Jay Leavitt An Interactive Computer Graphics System for Boundary Value Problems: II* by

Uri M. Ascher, Steve Savitt and J.B. Rosen Computer Science Department, University of Minnesota

Abstract

The IBV system was originally developed for the interactive formulation and solution of linear elliptic boundary value problems on general two-dimensional domains. This report describe, the extension of the IBV system to the formulation and solution of both quasilinear parabolic and quasilinear elliptic problems in two space variables. This research was supported in part by the National Science Foundation Office of Computer Research (Grant No. GJ32552), and the University of Minnesota Computing Center.

1. Introduction

In a recent report [3], a general purpose interactive computer graphics system was described which solved linear boundary value problems (biharmonic, elliptic and L1-approximation, problems) on general two-dimensional domains. The computer graphics capabilities were used both in order to formulate the problems and to examine the results, thus providing a flexible and useful system. The system has now been extended to handle quasilinear parabolic and quasilinear elliptic Dirichlet problems, based on the numerical methods described in [1]. In both cases an initial approximation is obtained using the original system [3], and then a call is made to one of the new modules of the system in order to iterate on the collocation points (in time for the parabolic case, or on the non-linear term of the equation in the elliptic case). In addition, the capability of plotting three-dimensional curves has been added to the system, so that plots of the approximate solution (or of an error, in the case of a known trial solution) as a function of its two independent space variables can be displayed on the graphics screen. In the case of a parabolic Dirichlet problem, the evolution of the solution in time can be displayed in animation

University of Minnesota Page 1 Dec 31, 1976

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An Interactive Computer Graphics System fur Boundary Value Problems: II

using a sequence of these three-dimensional plots. This report describes these new extensions to system IBV, and can be viewed as a extension of [3]. The description in [3] covers not only the graphics capabilities applicable here, but also the initial approximation methods for the parabolic and elliptic quas:ilinear problems. Familiarity with the report [3] will be assumed here. We now give a brief description of the methods used in obtaining the approximate solution for the parabolic and elliptic quasilinear problems. In the parabolic case, an approxi...