Geodesic
Numerical solution of a problem of potential field continuation
Matematičeskoe modelirovanie, Tome 14 (2002) no. 6, pp. 91-104

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An ill-posed problem is considered for continuation of solutions of the Dirichlet problem for the Laplace equation into the domain adjoining a part of the boundary. This problem of potential field continuation is of great importance in gravy- and magneto-exploring. An iterative method is employed based on successive improvement of the boundary condition in an extended domain and solving the standard boundary value problem at each iteration. Issues of numerical implementation of this approach are discussed for the case of continuation of potential fields from a curvilinear surface. Predictions of model problems with perturbed input data are presented. 
@article{MM_2002_14_6_a7,
     author = {P. N. Vabishchevich and P. A. Pulatov},
     title = {Numerical solution of a problem of potential field continuation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {91--104},
     publisher = {mathdoc},
     volume = {14},
     number = {6},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2002_14_6_a7/}
}
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P. N. Vabishchevich; P. A. Pulatov. Numerical solution of a problem of potential field continuation. Matematičeskoe modelirovanie, Tome 14 (2002) no. 6, pp. 91-104. http://geodesic.mathdoc.fr/item/MM_2002_14_6_a7/