Nitsche's method for Helmholtz problems with embedded interfaces

Zilong Zou, Wilkins Aquino, Isaac Harari

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, we use Nitsche's formulation to weakly enforce kinematic constraints at an embedded interface in Helmholtz problems. Allowing embedded interfaces in a mesh provides significant ease for discretization, especially when material interfaces have complex geometries. We provide analytical results that establish the well-posedness of Helmholtz variational problems and convergence of the corresponding finite element discretizations when Nitsche's method is used to enforce kinematic constraints. As in the analysis of conventional Helmholtz problems, we show that the inf-sup constant remains positive provided that the Nitsche's stabilization parameter is judiciously chosen. We then apply our formulation to several 2D plane-wave examples that confirm our analytical findings. Doing so, we demonstrate the asymptotic convergence of the proposed method and show that numerical results are in accordance with the theoretical analysis.

Original languageEnglish
Pages (from-to)618-636
Number of pages19
JournalInternational Journal for Numerical Methods in Engineering
Volume110
Issue number7
DOIs
StatePublished - 18 May 2017

Keywords

  • Helmholtz problem
  • Nitsche's method
  • embedded interface

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