scholarly journals General Transmission Problems in the Theory of Elastic Oscillations of Anisotropic Bodies (Basic Interface Problems)

1998 ◽  
Vol 220 (2) ◽  
pp. 397-433 ◽  
Author(s):  
Lothar Jentsch ◽  
David Natroshvili ◽  
Wolfgang L Wendland
Keyword(s):  
Interface Problems ◽  
Transmission Problems ◽  
Anisotropic Bodies

scholarly journals A mathematical model and numerical solution of interface problems for steady state heat conduction

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
Z. Muradoglu Seyidmamedov ◽  
Ebru Ozbilge
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Layered Medium ◽  
Discontinuous Coefficient ◽  
Interface Problems ◽  
Interface Problem ◽  
State Heat ◽  
Transmission Problems ◽  
Fast Direct Solver ◽  
Steady State Heat

We study interface (or transmission) problems arising in the steady state heat conduction for layered medium. These problems are related to the elliptic equation of the formAu:=−∇(k(x)∇u(x))=F(x),x∈Ω⊂ℝ2, with discontinuous coefficientk=k(x). We analyse two types of jump (or contact) conditions across the interfacesΓδ−=Ω1∩ΩδandΓδ+=Ωδ∩Ω2of the layered mediumΩ:=Ω1∪Ωδ∪Ω2. An asymptotic analysis of the interface problem is derived for the case when the thickness (2δ>0) of the layer (isolation)Ωδtends to zero. For each case, the local truncation errors of the used conservative finite difference schemeareestimated on the nonuniform grid. A fast direct solver has been applied for the interface problems with piecewise constant but discontinuous coefficientk=k(x). The presented numerical results illustrate high accuracy and show applicability of the given approach.

Non - Classical Mixed Interface Problems for Anisotropic Bodies

1996 ◽  
Vol 179 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Lothar Jentsch ◽  
David Natroshvili
Keyword(s):  
Interface Problems ◽  
Anisotropic Bodies

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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