Abstract
We propose a justification of Ewald's method of obtaining rapidly convergent series for the Green's function of the 3-dimensional Helmholtz equation. Our point of view enables us to extend the method to Green's functions for the Helmholtz equation in certain domains of ℝd with quite general boundary conditions.
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REFERENCES
P. P. Ewald, Die berechnung optischer und electrostatischer gitterpotentiale, Ann. Phys. 64, 253-287 (1921); translated by A. Cornell, Atomics International Library, 1964.
K. E. Jordan, G. R. Richter, and P. Sheng, An efficient numerical evaluation of the Green's function for the Helmhotz operator on periodic structures, J. Comput. Phys. 63, 222-235 (1986).
Y. Katznelson, An Introduction to Harmonic Analysis, Dover, New York, 1976.
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Papanicolaou, V.G. Ewald's Method Revisited: Rapidly Convergent Series Representations of Certain Green's Functions. Journal of Computational Analysis and Applications 1, 105–114 (1999). https://doi.org/10.1023/A:1022622721152
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DOI: https://doi.org/10.1023/A:1022622721152