Nitsche's Method For Helmholtz Problems with Embedded Interfaces.

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Zou, Z; Aquino, W; Harari, I

Published Date

  • May 2017

Published In

Volume / Issue

  • 110 / 7

Start / End Page

  • 618 - 636

PubMed ID

  • 28713177

Electronic International Standard Serial Number (EISSN)

  • 1097-0207

International Standard Serial Number (ISSN)

  • 0029-5981

Digital Object Identifier (DOI)

  • 10.1002/nme.5369

Language

  • eng