ON AN INVERSE PROBLEMS FOR LAPLACE EQUATIONS WITH POTENTIAL TERMS ON ELECTRICAL NETWORKS
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In this paper, we deal with an inverse problem for electrical resistor networks to detect the location of nodes where an extraordinary currents flow into or out of the nodes proportional to the potentials on them. To achieve the goal, we solve a special type of mixed boundary value problem for Laplace equations with potential terms on rectangular networks which plays a role as a forward problem. Then we solve an inverse problem to develop an algorithm to locate the node where the extraordinary current flows on it at most four times of measurements of potential and current on its boundary.
Abstract
In this paper, we deal with an inverse problem for electrical resistor networks to detect the location of nodes where an extraordinary currents flow into or out of the nodes proportional to the potentials on them. To achieve the goal, we solve a special type of mixed boundary value problem for Laplace equations with potential terms on rectangular networks which plays a role as a forward problem. Then we solve an inverse problem to develop an algorithm to locate the node where the extraordinary current flows on it at most four times of measurements of potential and current on its boundary.
참고문헌 (5)
- E. Bendito, "Potential theory for Schrodinger operators on nite networks", Rev. Mat. Iberoamericana, 21(3), pp.771~818 (2005)
- L. Borcea, "Electrical impedance tomography with resistor networks", Inverse Problems, 24(3), pp.31~ (2008)
- S.-Y. Chung, "!-Harmonic functions and inverse conductivity prob- lems on networks", SIAM J. Appl. Math, 65(4), pp.1200~1226 (2005)
- E. B. Curtis, "The Dirichlet to Neumann map for a resistor network", SIAM J. Appl. Math, 51(4), pp.1011~1029 (1991)
- Younghun Mun, "The faulty resistor problems and the inverse source problems for rectangular electrical networks", 대한수학회논문집, 24(3), pp.467~479 (2009), 대한수학회