Irregular Regions and Constrained Optimization

by Edward Angel, Dept. of Electrical Engrg., Univ. of Southern California, Los Angeles, CA,

Serial Information: Journal of the Engineering Mechanics Division, 1973, Vol. 99, Issue 3, Pg. 581-594

Document Type: Journal Paper

Abstract: The study of equilibrium configurations in structural mechanics leads to the necessity of obtaining numerical solutions of high order elliptic boundary-value problems. A method is presented for the solution of these problems in realistic geometries. The method is based on considering a given irregular region as imbedded in a simple region such as a rectangle and working with the variational problem corresponding to the given partial differential equation. The original boundary conditions become linear constraints. A discretized version of the resulting problem is then solved using dynamic programming. Existence and stability are demonstrated in the case of the potential equation.

Subject Headings: Numerical analysis | Equilibrium | Structural mechanics | Numerical methods | Geometrics | Boundary conditions |

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