Direct Boundary Element Method with Discretization of All Integral Operators

Sayas, Francisco–Javier

doi:10.1007/978-0-8176-4671-4_25

Cited by 1 publication

(3 citation statements)

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“…This kind of projection of data into discrete spaces is the Galerkin version of what is usually done in the engineering literature of BEM: treating data as unknowns and then substituting their known values at the final step [34]. The non-trivial spaces can be discretized (only X u or both of them) corresponding to Galerkin discretization of the equation with or without discretization of data.…”

Section: Mixed Exterior Boundary Conditionsmentioning

confidence: 99%

“…Since all operators that depend on s have to be discretized in time, we will have to deal with this effect. An alternative formulation to (34) at the continuous level consists of solving…”

Section: Non-homogeneous Penetrable Obstacles (2)mentioning

confidence: 99%

“…34), henceforth denoted H bf (s). Gaussian elimination and scaling of the rows and columns of the operator produce a simpler form of H bf (s), where the hidden ellipticity is recovered.…”

mentioning

confidence: 99%

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Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves

2009

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In this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non-homogeneous obstacles using convolution quadrature (CQ) techniques for the time variable and coupled boundary element method/finite element method for the space variable. The applicability of CQ to waves requires polynomial type bounds for operators related to the operator − s 2 in the right half complex plane. We propose a new systematic way of dealing with this problem, both at the continuous and semidiscrete-in-space cases. We apply the technique to three different situations: scattering by a group of sound-soft and -hard obstacles, by homogeneous and non-homogeneous obstacles.

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Section: Mixed Exterior Boundary Conditionsmentioning

confidence: 99%

“…Since all operators that depend on s have to be discretized in time, we will have to deal with this effect. An alternative formulation to (34) at the continuous level consists of solving…”

Section: Non-homogeneous Penetrable Obstacles (2)mentioning

confidence: 99%