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Domain decomposition in conjunction with sinc methods for Poisson’s equation. (English) Zbl 0857.65128
The authors essentially describe a weighted residual method with sinc functions as shape and trial functions. They couple this scheme with the domain decomposition method in both, patching and overlapping form. In this respect, they solve a two-point boundary value problem and the Poisson equation on an \(L\)-shaped domain. Some numerical results show that the proposed method works.

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65L10 Numerical solution of boundary value problems involving ordinary differential equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
34B05 Linear boundary value problems for ordinary differential equations
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References:
[1] Stenger, Math. Comp. 33 pp 85– (1979)
[2] Chan, RIACS Technical Report 86 (1988)
[3] and , Towards a unified theory of domain decomposition algorithms for elliptic problems, in Third International Symposium on Domain Decomposition Methods, , , and , Eds., SIAM, philadelphia, 1989, p. 3.
[4] Chan, Acta Numerica 61 (1994)
[5] Keyes, SIAM J. Sci. Stat. Comput. 8 pp s166– (1987) · Zbl 0619.65088 · doi:10.1137/0908020
[6] Bialecki, IMA J. Numer. Anal. 11 pp 357– (1991) · Zbl 0735.65052 · doi:10.1093/imanum/11.3.357
[7] and , Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, 1992. · Zbl 0753.65081 · doi:10.1137/1.9781611971637
[8] Stenger, SIAM Rev. 23 pp 165– (1981) · Zbl 0461.65007 · doi:10.1137/1023037
[9] Numerical Methods Based on Sinc and Analytic Functions, Spriner-Verlag, New York, 1993. · Zbl 0803.65141 · doi:10.1007/978-1-4612-2706-9
[10] Lybeck, Appl. Math. Comp. 75 pp 13– (1996) · Zbl 0846.65035 · doi:10.1016/0096-3003(95)00099-2
[11] , and , The convergence of sinc domain decomposition methods, submitted.
[12] , and , The Schwarz alternating sinc domain decomposition method, submitted. · Zbl 0887.65087
[13] Lund, Math. Comp. 47 pp 571– (1986) · doi:10.1090/S0025-5718-1986-0856703-9
[14] Funaro, SIAM J. Numer. Anal. 25 pp 1213– (1988) · Zbl 0678.65082 · doi:10.1137/0725069
[15] , , and , Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1988. · Zbl 0658.76001 · doi:10.1007/978-3-642-84108-8
[16] and , The Sinc-Galerkin Schwarz alternating method for Poisson’s equation, in Computation and Control IV, and , Eds., Brkhäuser, Boston, 1995, p. 165. · Zbl 0832.65121
[17] and , The Theory of Matrices, 2nd Ed., Academic Press, Orlando, 1985.
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