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HETEROGENEOUS SYSTEMS IN $d$ DIMENSIONS: LOWER SPECTRUM

Published online by Cambridge University Press:  03 November 2015

PAOLO AMORE
PAOLO AMORE*
Affiliation:
Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, Mexico email paolo.amore@gmail.com
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Abstract

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The lower part of the spectrum of the Helmholtz equation for a heterogeneous system in a finite region in $d$ dimensions, where the solutions to the corresponding homogeneous system are known, can be systematically approximated by means of iterative methods. These methods only require the specification of an arbitrary ansatz and converge to the desired solution, regardless of the strength of the inhomogeneities, provided the ansatz has a finite overlap with it. In this paper, different boundary conditions at the borders of the domain are assumed, and some applications are used to illustrate the methods.

Keywords

heterogeneous systemsHelmholtz equation
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 2 , October 2015 , pp. 150 - 165
Copyright
© 2015 Australian Mathematical Society 

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