TY  - JOUR
A1  - Kaya, Adem
A1  - Freitag, Melina A.
T1  - Conditioning analysis for discrete Helmholtz problems
JF  - Computers and mathematics with applications : an international journal
N2  - In this paper, we examine conditioning of the discretization of the Helmholtz problem. Although the discrete Helmholtz problem has been studied from different perspectives, to the best of our knowledge, there is no conditioning analysis for it. We aim to fill this gap in the literature. We propose a novel method in 1D to observe the near-zero eigenvalues of a symmetric indefinite matrix. Standard classification of ill-conditioning based on the matrix condition number is not true for the discrete Helmholtz problem. We relate the ill-conditioning of the discretization of the Helmholtz problem with the condition number of the matrix. We carry out analytical conditioning analysis in 1D and extend our observations to 2D with numerical observations. We examine several discretizations. We find different regions in which the condition number of the problem shows different characteristics. We also explain the general behavior of the solutions in these regions.
KW  - Helmholtz problem
KW  - Condition number
KW  - Ill-conditioning
KW  - Indefinite
KW  - matrices
Y1  - 2022
U6  - https://doi.org/10.1016/j.camwa.2022.05.016
SN  - 0898-1221
SN  - 1873-7668
VL  - 118
SP  - 171
EP  - 182
PB  - Elsevier Science
CY  - Amsterdam
ER  -