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A Boundary element method based on cauchy integrals for some linear quadratic boundary control problems on a circle
Author(s) -
Chen Goong,
Chen ChiangPu,
Aronov Irina
Publication year - 1988
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660090109
Subject(s) - mathematics , cauchy distribution , boundary (topology) , boundary knot method , boundary element method , mathematical analysis , finite element method , physics , thermodynamics
For certain types of elliptic boundary control problems, the boundary element method has considerable advantage over the traditional finite element or finite difference methods because of the reduction of dimensionality in computations. In this paper we examine a variant of such boundary integral methods based on Cauchy integrals. The cost functional here contains only finitely many quadratic terms related to sensory data at those finite interior points. We see that the numerical efficiency of this approach hinges largely on the complexity of the inverse of a certain boundary integral operator. In the case of a circle, such an inverse is readily obtainable and entire computations require only a small effort to yield useful numerical information about the optimal control. Other general situations are also discussed.