Sponsor
Portland State University. Department of Applied Science
First Advisor
R.W. Rempfer
Term of Graduation
Fall 1971
Date of Publication
12-2-1971
Document Type
Thesis
Degree Name
Master of Science (M.S.) in Applied Science
Department
Applied Science
Language
English
Subjects
Elliptic functions, Boundary value problems -- Numerical solutions, Computer science -- Mathematics
DOI
10.15760/etd.1480
Physical Description
1 online resource (v, 36, [1] pages)
Abstract
One important aspect of our present age of monolithic high speed computers is the computer's capability to solve complex problems hitherto impossible to tackle due to their complexity. This paper explains how to use a. digital computer to solve a specific type of problem; specifically, to find the inverse solution of a in the elliptical equation V2U(x,y) = g(a,U,x,y), with appropriate boundary conditions. This equation is very useful in the electronics field. The knowns are the complete set of boundary values of U(x,y) and a set of observations taken on internal points of U(x,y). Given this information, plus the specific form of the governing equation, we can solve for the unknown a.
Once the computer program has been written using the technique of quasilinearization, Newton's convergence method, discrete invariant imbedding, and the use of sensitivity functions, then we take data from the computer results and analyse it for proper convergence. This data shows that there are definite limits to the usefulness and capability of the technique.
One of the results of this study is the observation that it is important to the proper functioning of this problem solving technique that the observations taken on U(x,y) are placed in the most efficient locations with the most efficient geometry in the region of largest effectiveness. Another result deals with the number of observation points used: too few gives insufficient information for proper program functioning, and too many tends to saturate the effectiveness of the observations.
Thus this paper has two objectives. first to develop the technique and secondly to analyse the results from the realization of the technique through the use of a computer.
Rights
In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
Persistent Identifier
https://archives.pdx.edu/ds/psu/10230
Recommended Citation
Jeter, Frederick Alvin, "Computer Solution to Inverse Problems of Elliptic Form: V²U(x,y) = g(a,U,x,y)" (1971). Dissertations and Theses. Paper 1481.
https://doi.org/10.15760/etd.1480
Included in
Computational Engineering Commons, Computer-Aided Engineering and Design Commons, Electrical and Computer Engineering Commons
Comments
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