1998
DOI: 10.1002/(sici)1097-0207(19980330)41:6<1105::aid-nme327>3.3.co;2-s
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Boundary infinite elements for the Helmholtz equation in exterior domains

Abstract: A novel approach to the development of inÿnite element formulations for exterior problems of time-harmonic acoustics is presented. This approach is based on a functional which provides a general framework for domainbased computation of exterior problems. Special cases include non-re ecting boundary conditions (such as the DtN method). A prominent feature of this formulation is the lack of integration over the unbounded domain, simplifying the task of discretization. The original formulation is generalized to a… Show more

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Cited by 10 publications
(10 citation statements)
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“…Helmholtz equation has many real-world applications related to wave propagation and vibrating phenomena [1], the radiation and scattering of wave [2,3]. We focus on the important application of Helmholtz equation that is the problem of heat conduction in fins [4][5][6].…”
Section: Introductionmentioning
confidence: 99%
“…Helmholtz equation has many real-world applications related to wave propagation and vibrating phenomena [1], the radiation and scattering of wave [2,3]. We focus on the important application of Helmholtz equation that is the problem of heat conduction in fins [4][5][6].…”
Section: Introductionmentioning
confidence: 99%
“…More specifically, these equations are used to describe the Debye-Hückel equation [15], the scattering of a wave [17], the linearization of the Boltzmann equation [35], the vibration of a structure [6], the acoustic cavity problem [12], the radiation wave [19] and the steady-state heat conduction in fins [33]. In general, we assume the knowledge of the geometry of the domain of interest, the boundary conditions on the entire boundary of the solution domain and the so-called wave parameter, κ, and this gives rise to direct/forward problems for Helmholtz-type equations, which have been extensively studied both mathematically and numerically, e.g.…”
Section: Introductionmentioning
confidence: 99%
“…Most of the results studying on the numerical methods of the Helmholtz equation are related with the boundary value problems, i.e., the Dirichlet, Neumann or mixed boundary value problems (see, e.g., [1,4,10,12,14]). The well-posedness of the boundary value problems of the Helmholtz equation via the removal of the eigenvalues of the Laplacian operator is well established.…”
Section: Introductionmentioning
confidence: 99%