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arXiv · 1511.09363

A Nitsche-type Method for Helmholtz Equation with an Embedded Acoustically Permeable Interface

Esubalewe Lakie Yedeg·Eddie Wadbro·Peter Hansbo·Mats G. Larson·Martin Berggren
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Abstract

We propose a new finite element method for Helmholtz equation in the situation where an acoustically permeable interface is embedded in the computational domain. A variant of Nitsche's method, different from the standard one, weakly enforces the impedance conditions for transmission through the interface. As opposed to a standard finite-element discretization of the problem, our method seamlessly handles a complex-valued impedance function $Z$ that is allowed to vanish. In the case of a vanishing impedance, the proposed method reduces to the classic Nitsche method to weakly enforce continuity over the interface. We show stability of the method, in terms of a discrete G{\aa}rding inequality, for a quite general class of surface impedance functions, provided that possible surface waves are sufficiently resolved by the mesh. Moreover, we prove an a priori error estimate under the assumption that the absolute value of the impedance is bounded away from zero almost everywhere. Numerical experiments illustrate the performance of the method for a number of test cases in 2D and 3D with different interface conditions.

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Esubalewe Lakie Yedeg, Eddie Wadbro, Peter Hansbo, Mats G. Larson, Martin Berggren. 2015-11-30. A Nitsche-type Method for Helmholtz Equation with an Embedded Acoustically Permeable Interface. https://arxiv.org/abs/1511.09363

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