On the existence and the uniqueness of the solution of a fluid–structure interaction scattering problem

Journal of Mathematical Analysis and Applications

et al. 2018

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For a fluid-solid interaction problem with Lipschitz interface, we investigate the partial Fréchet differentiability of the solutions and the approximate far-fieldpattern with respect to solid material parameters. Differentiability is shown in standard Sobolev framework, and the derivatives are characterized as solutions to inhomogeneous fluid-solid transmission problems. To validate the accuracy of the characterization, we compare analytical values with numerical ones given by Interior Penalty Discontinuous Galerkin (IPDG) in a setting with circular obstacles. Our comparisons also show that IPDG gives results with high precision and incurs almost no effect of discretization error accumulation.

“…We now extend the result of [12,Thm 7] to arbitrary operator B satisfying (14), and obtain the well-posedness for OP B . The proof follows [12] with minor modification.…”

Section: Fluid-solid Transmission Problemsmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 91%

Section: Fluid-solid Transmission Problemsmentioning

confidence: 99%

Section: Fluid-solid Transmission Problemsmentioning

confidence: 99%

Section: Fluid-solid Transmission Problemsmentioning

confidence: 99%

See 3 more Smart Citations

Characterization of partial derivatives with respect to material parameters in a fluid–solid interaction problem

Azpiroz

Journal of Mathematical Analysis and Applications

et al. 2018

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Fréchet differentiability of the elasto‐acoustic scattered field with respect to Lipschitz domains

Math Methods in App Sciences

Estecahandy

2015

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a Communicated by S. NicaiseWe analyse the dependence with respect to a given domain of the solution of a fluid-structure interaction scattering problem. We establish that the scattered field is continuously Fréchet differentiable with respect to the shape of the elastic scatterer. Our proof assumes that the boundary of the scatterer as well as the admissible perturbations to be only Lipschitzian. Given the applied nature of this problem and its prevalence in engineering and numerical literature, this new result appears to be of practical interest.

Efficient DG‐like formulation equipped with curved boundary edges for solving elasto‐acoustic scattering problems

Numerical Meth Engineering

Estecahandy

2014

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SUMMARYA Discontinuous Galerkin (DG)‐based approach is proposed for computing the scattered field from an elastic bounded object immersed in an infinite homogeneous fluid medium. The proposed method possesses two distinctive features. First, it employs higher‐order polynomial‐shape functions needed to address the high‐frequency propagation regime. Second, it is equipped with curved boundary edges to provide an accurate representation of the fluid–structure interface. The most salient benefits resulting from the latter feature, as demonstrated by the numerical investigation, are the following: (i) an improvement by—at least—two orders of magnitude on the relative error and (ii) the disappearance of spurious resonance frequencies in the surrounding fluid medium. In addition, the reported numerical results reveal that when using cubic polynomials with less than three elements per wavelength, the proposed DG method computes the scattered field with a relative error below 1% for an elastic scatterer of about 30 wavelengths. This observation highlights the potential of the proposed solution methodology for efficiently solving mid‐frequency to high‐frequency elasto‐acoustic scattering problems. Copyright © 2014 John Wiley & Sons, Ltd.