Author(s) :
Matthias Ehrhardt
,
Houde Han
,
Chunxiong Zheng
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 48-2007
MSC 2000
- 35B27 Homogenization; partial differential equations in media with periodic structure
-
65M99 None of the above, but in this section
-
35Q60 Equations of electromagnetic theory and optics
-
35J05 Laplace equation, reduced wave equation , Poisson equation
PACS : 02.70.Bf, 31.15.-p, 42.82.Et, 85.35.-p, 85.35.Be
Abstract :
In this work we present a new numerical technique for solving
periodic structure problems.
This new approach possess several advantages.
First, it allows for a fast evaluation of the Dirichlet-to-Robin
operator for periodic array problems.
Secondly, this implementational method can also be used for
bi-periodic structure problems with local defects.
Our strategy is an improvement of the recently developed
recursive doubling process by Yuan and Lu.
In this paper we consider several problems,
such as the exterior elliptic problems with strong coercivity,
the time-dependent Schrödinger equation in one and two dimensions
and finally the Helmholtz equation.
Keywords :
periodic media, Helmholtz equation, Schrödinger equation, Dirichlet-to-Robin maps, Robin-to-Robin maps, band structure, Floquet-Bloch theory, high-order finite elements
Notes :
submitted to: Communications in Computational Physics