Scattering from submerged objects by a hybrid asymptotic-boundary integral equation method

Barbone, Paul E.; Michael, Ofer

doi:10.1016/s0165-2125(98)00027-4

Cited by 3 publications

(1 citation statement)

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“…Combined asymptotic-numerical methods have the advantage of removing the hard core of the problem, namely, the dependence on the small parameter, by using analytical tools. See, for example, the work of Zrahia et al (1997) on a hybrid spectral element asymptotic method for analyzing boundary-layer problems (where ϵ is the thickness of the boundary layer), Giladi and Kellery (2001) and Barbone et al (Montgomery and Barbone 1998;Barbone and Michael, 1999) on hybrid numerical asymptotic methods for wave scattering problems (where ϵ is a typical wave-length), Panasenko (1998) on a hybrid asymptotic-FE method for rod structures (where ϵ is the size of the region where the structure behaves as a three-dimensional solid), and Marigo and Pideri (Marigo, 2011) on representing a sequence of micro cracks on a surface (where ϵ is the ratio of the micro scale to the macro scale). In our case, the small parameter ϵ is the thickness τ of the layer.…”

Section: Introductionmentioning

confidence: 99%

Hybrid asymptotic-numerical modeling of thin layers for dynamic thermal analysis of structures

Tuval

Givoli

Behar

2016

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a zero-thickness interface. The advantage of the new model is that it saves the need to construct and use a fine mesh inside the layer and in regions adjacent to it, and thus leads to a reduction in the computational effort associated with implicit or explicit finite element schemes. Design/methodology/approach -Special asymptotic models have been proposed for linear heat transfer and linear elasticity, to handle thin layers. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case. Findings -As shown here, and demonstrated by numerical examples, the new model offers a costeffective way of handling thin layers in linear time-dependent heat conduction problems. The hybrid asymptotic-FE scheme can be used with either implicit or explicit time stepping. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution. Originality/value -Most of the literature on asymptotic models for thin layers, replacing the layer by an interface, is analytic in nature. The proposed model is presented in a computational context, fitting naturally into a finite element framework, with both implicit and explicit time stepping, while saving the need for expensive mesh construction inside the layer and in its vicinity.

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