Journal
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
Volume 28, Issue 1-2, Pages 313-332Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s12190-008-0107-7
Keywords
Free boundary problem; Optimal design; Inhomogeneous dam; Optimal control; Measure theory; Linear programming
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This paper is devoted to a new numerical technique for the approximation of the flow problem of incompressible liquid through an inhomogeneous porous medium (say dam). First the problem is expressed as an optimal control problem governed by variational forms on a fixed domain. Then by using an embedding method, the class of admissible shapes is replaced by a class of positive Radon measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this linear programming problem. Numerical example is also given.
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