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Problem We consider the Laplace problem on the open unit square Ω = (0, 1) 2. −∆u = f in Ω u = 0 on ∂Ω (1) Meshes We dene two meshes on Ω: a coarse mesh T H and a ne mesh T h. We use a N × N regular cartesian mesh of the unit square.
We propose a new class of approximate local DtN boundary conditions to be applied on prolate spheroid-shaped exterior boundaries when solving acoustic scattering problems by elongated obstacles. These conditions are : (a) exact for the first modes, (b) easy to implement and to parallelize, (c) compatible with the local structure of the computational finite… (More)
We develop a new PML formulation for the linearized shallow-water equations including the Coriolis force. The construction process is based on the uncoupling of the velocity components with the depth of water. Then the damping effect is only applied to the propagative modes just as was formerly done by Nataf  to the linearized Euler equations to enforce… (More)
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New approximate local DtN boundary conditions are proposed to be applied on elliptical-or prolate-spheroid exterior boundaries when solving respectively two-or three-dimensional acoustic scattering problems by elongated obstacles. These new absorbing conditions are designed to be exact for the first modes. They can be easily incorporated in any finite… (More)
The construction of accurate generalized impedance boundary conditions for the three-dimensional acoustic scattering problem by a homogeneous dissi-pative medium is analyzed. The technique relies on an explicit computation of the symbolic asymptotic expansion of the exact impedance operator in the interior domain. An efficient pseudolocalization of this… (More)
—We investigate analytically the asymptotic behavior of high-order spurious prolate spheroidal modes induced by a second-order local approximate DtN absorbing boundary condition (DtN2) when employed for solving high-frequency acoustic scattering problems. We prove that these reflected modes decay exponentially in the high frequency regime. This theoretical… (More)