A Fully Discrete Approximation Method for the Exterior Neumann Problem of the Helmholtz Equation | Zendy

Siegfried Prößdorf | Zendy; Jukka Saranen | Zendy

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A Fully Discrete Approximation Method for the Exterior Neumann Problem of the Helmholtz Equation

Author(s) -

Siegfried Prößdorf,

Jukka Saranen

Publication year - 1994

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/483

Subject(s) - mathematics , mathematical analysis , neumann boundary condition , discretization , helmholtz equation , boundary value problem , integral equation , collocation (remote sensing) , boundary (topology) , domain (mathematical analysis) , exponential function , mixed boundary condition , remote sensing , geology

Considering an exterior domain with smooth closed boundary curve we introduce a fully discrete scheme for the solution of the acoustic boundary value problem of the Neumann type. We use a boundary integral formulation of the problem which leads to a hypersingular boundary integral equation. Our discretization scheme for the latter equation can be considered as a discrete version of the trigonometric collocation method and has arbitrarily high convergence rate, even exponential if the solution and the curve are analytic.

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