Simple high-order Galerkin finite element scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides

2004 ◽  
Vol 36 (1-3) ◽  
pp. 239-257 ◽  
Author(s):  
H.P. Uranus ◽  
H.J.W.M. Hoekstra ◽  
E. Van Groesen
Keyword(s):  
Finite Element ◽  
High Order ◽  
Planar Waveguides ◽  
Finite Element Scheme ◽  
Galerkin Finite Element ◽  
Element Scheme ◽  
Leaky Modes

scholarly journals GALERKIN FINITE ELEMENT SCHEME WITH BAYLISS–GUNZBURGER–TURKEL-LIKE BOUNDARY CONDITIONS FOR VECTORIAL OPTICAL MODE SOLVER

2004 ◽  
Vol 13 (02) ◽  
pp. 175-194 ◽  
Author(s):  
H. P. URANUS ◽  
H. J. W. M. HOEKSTRA ◽  
E. VAN GROESEN
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Optical Fibers ◽  
Finite Element Scheme ◽  
Galerkin Finite Element ◽  
Element Scheme ◽  
Crystal Fiber ◽  
Leaky Modes ◽  
Rib Structure ◽  
Channel Waveguides

A Galerkin finite element scheme furnished with 1st-order Bayliss–Gunzburger–Turkel-like boundary conditions is formulated to compute both the guided and leaky modes of anisotropic channel waveguides of non-magnetic materials with diagonal permittivity tensor. The scheme is formulated using transverse components of magnetic fields for nodal-based quadratic triangular elements. Results for some structures will be presented. The effectiveness of the boundary conditions will be illustrated using a step-index optical fiber with computational boundaries positioned near to the core, and the leaky modes computation of a leaky rib structure. In addition, a leaky mode solving of a six-hole "photonic crystal fiber" will be demonstrated. The computed results agree with their exact values (for optical fibers) and published results (for other structures).

scholarly journals A weak Galerkin finite element scheme for the Cahn-Hilliard equation

2018 ◽  
Vol 88 (315) ◽  
pp. 211-235 ◽  
Author(s):  
Junping Wang ◽  
Qilong Zhai ◽  
Ran Zhang ◽  
Shangyou Zhang
Keyword(s):  
Finite Element ◽  
Weak Galerkin ◽  
Finite Element Scheme ◽  
Galerkin Finite Element ◽  
Element Scheme ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation
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