Analytical and computational methods for transmission eigenvalues

被引：132
作者：
Colton, David [1 ]
Monk, Peter [1 ]
Sun, Jiguang [2 ]
机构：
[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
[2] Delaware State Univ, Dept Math Sci, Dover, DE 19901 USA
来源：
INVERSE PROBLEMS | 2010年 / 26卷 / 04期
关键词：
EXISTENCE; SCATTERING;
D O I：
10.1088/0266-5611/26/4/045011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The interior transmission problem is a boundary value problem that arises in the scattering of time-harmonic waves by an inhomogeneous medium of compact support. The associated transmission eigenvalue problem has important applications in qualitative methods in inverse scattering theory. In this paper, we first establish optimal conditions for the existence of transmission eigenvalues for a spherically stratified medium and give numerical examples of the existence of both real and complex transmission eigenvalues in this case. We then propose three finite element methods for the computation of the transmission eigenvalues for the cases of a general non-stratified medium and use these methods to investigate the accuracy of recently established inequalities for transmission eigenvalues.
引用
收藏
页数：16
相关论文
共 20 条
[1]  
Bahriawati C., 2005, Comput. Meth. Appl. Math., V5, P333
[2]  
Brezzi F., 1991, Mixed and Hybrid Finite Element Methods, V15
[3]   On the determination of Dirichlet or transmission eigenvalues from far field data [J].
Cakoni, Fioralba ;
Colton, David ;
Haddar, Houssem .
COMPTES RENDUS MATHEMATIQUE, 2010, 348 (7-8) :379-383
[4]   THE EXISTENCE OF AN INFINITE DISCRETE SET OF TRANSMISSION EIGENVALUES [J].
Cakoni, Fioralba ;
Gintides, Drossos ;
Haddar, Houssem .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2010, 42 (01) :237-255
[5]   NEW RESULTS ON TRANSMISSION EIGENVALUES [J].
Cakoni, Fioralba ;
Gintides, Drossos .
INVERSE PROBLEMS AND IMAGING, 2010, 4 (01) :39-48
[6]   Transmission eigenvalues and the nondestructive testing of dielectrics [J].
Cakoni, Fioralba ;
Cayoeren, Mehmet ;
Colton, David .
INVERSE PROBLEMS, 2008, 24 (06)
[7]   THE COMPUTATION OF LOWER BOUNDS FOR THE NORM OF THE INDEX OF REFRACTION IN AN ANISOTROPIC MEDIA FROM FAR FIELD DATA [J].
Cakoni, Fioralba ;
Colton, David ;
Haddar, Houssem .
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2009, 21 (02) :203-227
[8]   On the existence of transmission eigenvalues in an inhomogeneous medium [J].
Cakoni, Fioralba ;
Haddar, Houssem .
APPLICABLE ANALYSIS, 2009, 88 (04) :475-493
[9]  
Ciarlet P.G., 2002, Classics in applied mathematics, DOI [10.1137/1.9780898719208, DOI 10.1137/1.9780898719208]
[10]   FAR-FIELD PATTERNS FOR ACOUSTIC-WAVES IN AN INHOMOGENEOUS-MEDIUM [J].
COLTON, D ;
KIRSCH, A ;
PAIVARINTA, L .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (06) :1472-1483
12