Readily computable Green’s and Neumann functions for symmetry-preserving triangles

Autor:	D.K. Babu, Randy D. Hazlett
Rok vydání:	2009
Předmět:	Applied Mathematics Mathematical analysis MathematicsofComputing_GENERAL Line integral Function (mathematics) Equilateral triangle Domain (mathematical analysis) symbols.namesake Green's function Neumann boundary condition symbols Laplace operator Bessel function Mathematics
Zdroj:	Quarterly of Applied Mathematics. 67:579-592
ISSN:	1552-4485 0033-569X
DOI:	10.1090/s0033-569x-09-01157-x
Popis:	Neumann and Green’s functions of the Laplacian operator on 30 30 - 60 60 - 90 ∘ 90^{\circ } and 45 45 - 45 45 - 90 ∘ 90^{\circ } triangles can be generated with appropriately placed multiple sources/sinks in a rectangular domain. Highly accurate and easily computable Neumann and Green’s function formulas already exist for rectangles. The extension to equilateral triangles is illustrated. In applications, closed-form expressions can be constructed for the potential, the streamfunction, or the various spatial derivatives of these properties. The derivation of analytic line integrals of these functions allows the proper handling of singularities and facilitates extended applications to problems on domains with open boundaries. Using a boundary integral method, it is demonstrated how one can construct semi-analytical solutions to problems defined on domains that exhibit spatially-dependent properties (heterogeneous media) or possess irregular boundaries.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::54361579521eb1f2b1b334f5b8a016e3 https://doi.org/10.1090/s0033-569x-09-01157-x Zobrazit plný text záznamu