The immersed interface method for two-dimensional heat-diffusion equations with singular own sources

2007 ◽  
Vol 57 (5-7) ◽  
pp. 486-497 ◽  
Author(s):  
Juri D. Kandilarov ◽  
Lubin G. Vulkov
Keyword(s):  
Heat Diffusion ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Immersed Interface Method ◽  
Immersed Interface

scholarly journals Analysis of algebraic multigrid parameters for two-dimensional steady-state heat diffusion equations

2012 ◽  
Vol 36 (7) ◽  
pp. 2996-3006 ◽  
Author(s):  
R. Suero ◽  
M.A.V. Pinto ◽  
C.H. Marchi ◽  
L.K. Araki ◽  
A.C. Alves
Keyword(s):  
Steady State ◽  
Algebraic Multigrid ◽  
Heat Diffusion ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
State Heat ◽  
Steady State Heat

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.

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