Difference potentials for the Helmholtz equation in exterior domains

2000 ◽  
Vol 33 (1-4) ◽  
pp. 533-540 ◽  
Author(s):  
Victor S. Ryaben'kii ◽  
Ivan L. Sofronov
Keyword(s):  
Helmholtz Equation ◽  
Exterior Domains ◽  
Difference Potentials

A REVIEW OF INFINITE ELEMENT METHODS FOR EXTERIOR HELMHOLTZ PROBLEMS

2000 ◽  
Vol 08 (01) ◽  
pp. 43-62 ◽  
Author(s):  
KLAUS GERDES
Keyword(s):  
Helmholtz Equation ◽  
Mathematical Framework ◽  
Exterior Domains ◽  
Research Papers ◽  
Infinite Element ◽  
Element Discretizations ◽  
Variational Formulations

This work is devoted to review infinite element discretizations for the Helmholtz equation in exterior domains, which have become popular in recent years, as many research papers on this topic have appeared in the literature. The early contributions were mostly motivated by engineering considerations and the variational formulations have, in general, not been stated in a mathematically precise way. Only recently, theoretical aspects of the infinite element methodology have been analyzed and helped to put the different formulations into a mathematical framework. We build upon this, and present and compare the infinite element formulations within this context.

scholarly journals A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains

2013 ◽  
Vol 143 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Juan Antonio Barceló ◽  
Luca Fanelli ◽  
Alberto Ruiz ◽  
Maricruz Vilela
Keyword(s):  
Helmholtz Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Exterior Domains ◽  
Limiting Absorption Principle ◽  
Electromagnetic Potentials ◽  
Priori Estimates ◽  
Embedded Eigenvalues

We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension n ≥ 3. Using multiplier techniques in the style of Morawetz, we prove a family of a priori estimates from which the limiting absorption principle follows. Moreover, we give some standard applications to cases with an absence of embedded eigenvalues and zero resonances, under explicit conditions on the potentials.

On solutions of the Helmholtz equation in exterior domains

1961 ◽  
Vol 75 (1) ◽  
pp. 228-255 ◽  
Author(s):  
Philip Hartman ◽  
Calvin Wilcox
Keyword(s):  
Helmholtz Equation ◽  
Exterior Domains
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