Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 304, Issue -, Pages 479-500Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2016.02.032
Keywords
Helmholtz equation; Finite element method; Nitsche's method; Acoustic impedance; Surface wave; Garding inequality
Funding
- Swedish Foundation for Strategic Research [AM13-0029]
- Swedish Research Council [621-2013-3706]
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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. (C) 2016 Elsevier B.V. All rights reserved.
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