### Solution of a screened Poisson equation with Dirichlet boundary condition with the method of iterative extensions

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Astrakhantsev G.P. Method of Fictitious Domains for a Second-Order Elliptic Equation with Natural Boundary Conditions. USSR Computational Mathematics and Mathematical Physics, 1978, vol. 18, no. 1, pp. 114-121. DOI: 10.1016/0041555378900125

Dyakonov E.G. Minimizing Computational Work. Asymptotically Optimal Algorithms for Elliptic Problems. Moscow, Nauka, 1989, 272 p.

Bank R.E. Marching Algorithms for Elliptic Boundary Value Problems. SIAM J. on Numer. Anal., 1977, vol. 14, no. 5, pp. 792-829.

Kaporin I.E. Method of Fictitious Unknowns for Solving Difference Elliptic Boundary Value Problems in Irregular Domains. Differential Equations, 1980, vol. 16, no. 7, pp. 1211-1225.

Kaporin I.E. Method of Fictitious Unknowns for Solving Difference Equations of Elliptic Type in Domains of Complex Shape. USSR Reports of the Academy of Sciences, 1980, vol. 251, no. 3, pp. 544-548.

Matsokin А.М. The Method of Fictitious Components and a Modified Difference Analogue of the Schwartz Method. Computational methods of linear algebra: collection of scientific papers, 1980, pp. 66-77.

Matsokin A.M. The Fictitious-Domain Method and Explicit Continuation Operators. Computational Mathematics and Mathematical Physics, 1993, vol. 33, no. 1, pp.52-68.

Sorokin S.B. Preconditioning in the Numerical Solution to a Dirichlet Problem for the Biharmonic Equation. Numer. Analys. Appl., 2011, vol. 14, no. 2, pp. 205-213. DOI: 10.1134/S1995423911020078

Sorokin S.B. Analytical Solution to a Generalized Spectral Problem in a Method of Recalculating Boundary Conditions for the Biharmonic Equation. Numer. Analys. Appl., 2013, vol. 16, no. 3, pp. 267-274. DOI: 10.1134/S1995423913030063

Sorokin S.B. Sharp Constants of the Energy Equivalence Relation in the Method of Conversion of Boundary Conditions for Biharmonic Equation. Journal of Mathematical Sciences, 2015, vol. 205, no. 3, pp. 464-472. DOI: 10.1007/S1095801522605

Ushakov, A.L. A Review of Mathematical Models of Elasticity Theory Based on the Methods of Iterative Factorizations and Fictitious Components. Mathematics, 2023, vol. 11, no. 420, 17 p. DOI: 10.3390/math11020420

Eremchuk, M.P. Method of Iterative Extensions for Analysis of a Screened Harmonic Systems. Journal of Computational and Engineering Mathematics, 2023, vol. 10, no. 3, pp. 3-16. DOI: 10.14529/jcem230301

Ushakov, A.L. A Analysis of Shielded Harmonic and Biharmonic Systems by the Iterative Extension Method. Mathematics, 2023, vol. 12, no. 918, 15 p. DOI: 10.3390/math12060918

### Refbacks

- There are currently no refbacks.