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Abstract
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This paper is concerned with the numerical solutions of 3D Cauchy problems
of elliptic differential operators in the cylindrical domain. We assume
that the measurements are only available on the outer boundary while
the interior boundary is inaccessible and the solution should be obtained
from the measurements from the outer layer. The proposed discretization
approach uses the local weak equations and radial basis functions. Since
the Cauchy problem is known to be ill-posed, the Thikhonov regularization
strategy is employed to solve effectively the discrete ill-posed resultant
linear system of equations. Numerical results of a different kind of test
problems reveal that the method is very effective.
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