Penalty-Free Nitsche Method for Interface Problems

2017 ◽  
pp. 183-210 ◽  
Author(s):  
Thomas Boiveau ◽  
Erik Burman ◽  
Susanne Claus
Keyword(s):  
Interface Problems ◽  
Nitsche Method

A uniformly well-conditioned, unfitted Nitsche method for interface problems

2013 ◽  
Vol 53 (3) ◽  
pp. 791-820 ◽  
Author(s):  
Eddie Wadbro ◽  
Sara Zahedi ◽  
Gunilla Kreiss ◽  
Martin Berggren
Keyword(s):  
Interface Problems ◽  
Nitsche Method

scholarly journals Robust flux error estimation of an unfitted Nitsche method for high-contrast interface problems

2017 ◽  
Vol 38 (2) ◽  
pp. 646-668 ◽  
Author(s):  
Erik Burman ◽  
Johnny Guzmán ◽  
Manuel A Sánchez ◽  
Marcus Sarkis
Keyword(s):  
Error Estimation ◽  
Interface Problems ◽  
High Contrast ◽  
Nitsche Method

scholarly journals ANALYSIS OF OPTICAL WAVEGUIDES WITH ARBITRARY INDEX PROFILE USING AN IMMERSED INTERFACE METHOD

2011 ◽  
Vol 22 (07) ◽  
pp. 687-710 ◽  
Author(s):  
THEODOROS P. HORIKIS
Keyword(s):  
Optical Waveguides ◽  
Eigenvalue Problems ◽  
Numerical Technique ◽  
Interface Problems ◽  
Index Profile ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Light Confinement ◽  
Bragg Fibers ◽  
Matrix Eigenvalue Problems

A numerical technique is described that can efficiently compute solutions of interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces. A prime example of these problems are optical waveguides, and as such the scheme is applied to Maxwell's equations as they are formulated to describe light confinement in Bragg fibers. It is based on standard finite differences appropriately modified to take into account all possible discontinuities across the waveguide's interfaces due to the change of the refractive index. Second- and fourth-order schemes are described with additional adaptations to handle matrix eigenvalue problems, demanding geometries and defects.

Meshless analysis of parabolic interface problems

2018 ◽  
Vol 94 ◽  
pp. 134-152 ◽  
Author(s):  
Masood Ahmad ◽  
Siraj-ul-Islam
Keyword(s):  
Interface Problems
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