A Nitsche-type method for Helmholtz equation with an embedded acoustically permeable interface

作者：Yedeg Esubalewe Lakie^*; Wadbro Eddie; Han**o Peter; Larson Mats G; Berggren Martin^*

来源：Computer Methods in Applied Mechanics and Engineering, 2016, 304: 479-500.

DOI：10.1016/j.cma.2016.02.032

• Helmholtz equation
• Finite element method
• Nitsche's method
• Acoustic impedance
• Surface wave
• Garding inequality

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 Garding 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.

• 出版日期2016-6-1