Nitsche's method for Helmholtz problems with embedded interfaces
| Autor: | Zilong Zou, Isaac Harari, Wilkins Aquino |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Numerical Analysis
Work (thermodynamics) Discretization Interface (Java) Computer science Applied Mathematics General Engineering 010103 numerical & computational mathematics Kinematics 01 natural sciences Finite element method Mathematics::Numerical Analysis 010101 applied mathematics symbols.namesake Helmholtz free energy Convergence (routing) symbols Applied mathematics 0101 mathematics Constant (mathematics) |
| Zdroj: | International Journal for Numerical Methods in Engineering. 110:618-636 |
| ISSN: | 0029-5981 |
| DOI: | 10.1002/nme.5369 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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