The commutator method for form-relatively compact perturbations

1991 ◽  
Vol 22 (3) ◽  
pp. 211-223 ◽  
Author(s):  
Anne Boutet de Monvel-Berthier ◽  
Dragos Manda ◽  
Radu Purice
Keyword(s):  
Compact Perturbations ◽  
Commutator Method

scholarly journals On a question of Olsen concerning compact perturbations of operators.

1977 ◽  
Vol 24 (1) ◽  
pp. 119-127 ◽  
Author(s):  
C. K. Chui ◽  
D. A. Legg ◽  
P. W. Smith ◽  
J. D. Ward
Keyword(s):  
Compact Perturbations

Coburn Type Operators and Compact Perturbations

2021 ◽  
Vol 42 (5) ◽  
pp. 677-692
Author(s):  
Tingting Zhou ◽  
Bin Liang ◽  
Chaoyue Wang
Keyword(s):  
Compact Perturbations

Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media

2012 ◽  
Vol 11 (2) ◽  
pp. 303-318 ◽  
Author(s):  
J. Coatléven ◽  
P. Joly
Keyword(s):  
Multiple Scattering ◽  
Random Number ◽  
Good Method ◽  
Computational Domain ◽  
Periodic Media ◽  
Scattering Problems ◽  
Compact Perturbations ◽  
Time Harmonic ◽  
Operator Factorization ◽  
Interior Problem

AbstractThis work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.

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