A Nitsche-type Method for Helmholtz Equation with an Embedded Acoustically Permeable Interface
2016 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 304, 479-500 p.Article in journal (Refereed) Published
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 ̊arding 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.
Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 304, 479-500 p.
Helmholtz equation, Finite Element method, Nitsche’s method, interface problem, surface wave, Gårding inequality
IdentifiersURN: urn:nbn:se:umu:diva-119977DOI: 10.1016/j.cma.2016.02.032ISI: 000374506600020OAI: oai:DiVA.org:umu-119977DiVA: diva2:925998