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Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations
| Content Provider | Scilit |
|---|---|
| Author | Borachok, Ihor Chapko, Roman |
| Editor | Johansson, B. Tomas |
| Copyright Year | 2016 |
| Description | We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert’s method [ |
| Related Links | https://publications.aston.ac.uk/id/eprint/29649/1/Elliptic_3_dimensional_Cauchy_problem_by_the_alternating_method_and_boundary_integral_equations.pdf |
| ISSN | 09280219 |
| e-ISSN | 15693945 |
| DOI | 10.1515/jiip-2015-0053 |
| Journal | Journal of Inverse and Ill-Posed Problems |
| Issue Number | 6 |
| Volume Number | 24 |
| Language | English |
| Publisher | Walter de Gruyter GmbH |
| Publisher Date | 2016-01-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Journal of Inverse and Ill-Posed Problems Journal of Inverse and Ill-posed Problems Alternating Method Cauchy Problem Integral Equation Laplace Equation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
