Geodesic
Solution of a screened Poisson equation with Dirichlet boundary condition with the method of iterative extensions
Journal of computational and engineering mathematics, Tome 11 (2024) no. 2, pp. 22-33.

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In this paper, numerical solution of the screened Poisson equation with the Dirichlet boundary condition in two-dimensional and three-dimensional domains is proposed. The continuation of the boundary value problems is carried out, and then they are approximated by the finite element method. In the developed method of iterative extensions, solutions to extended problems after approximation are iteratively approximated by solutions of the proposed extended problems. This method has optimal asymptotics in terms of the number of operations.
Keywords: fictitious domain method, method of iterative extensions, screened harmonic systems, screened Poisson equation. 
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     author = {M. P. Eremchuk and A. L. Ushakov},
     title = {Solution of a screened {Poisson} equation with {Dirichlet} boundary condition with the method of iterative extensions},
     journal = {Journal of computational and engineering mathematics},
     pages = {22--33},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2024_11_2_a2/}
}
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M. P. Eremchuk; A. L. Ushakov. Solution of a screened Poisson equation with Dirichlet boundary condition with the method of iterative extensions. Journal of computational and engineering mathematics, Tome 11 (2024) no. 2, pp. 22-33. http://geodesic.mathdoc.fr/item/JCEM_2024_11_2_a2/