Portland State University. Department of Applied Science
Term of Graduation
Date of Publication
Master of Science (M.S.) in Applied Science
Elliptic functions, Boundary value problems -- Numerical solutions, Computer science -- Mathematics
1 online resource (v, 36,  pages)
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.
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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.