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Modified equations of the first kind for the Helmholtz equation
Author(s) -
Thomson G. R.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3349
Subject(s) - mathematics , helmholtz equation , integral equation , uniqueness , mathematical analysis , operator (biology) , electric field integral equation , helmholtz free energy , boundary value problem , dirichlet problem , dirichlet integral , dirichlet distribution , dirichlet's principle , transcription factor , gene , biochemistry , chemistry , physics , repressor , quantum mechanics
Integral equations of the first kind for exterior problems arising in the study of the three‐dimensional Helmholtz equation are considered. These equations are derived by seeking solutions in the form of layer potentials with modified fundamental solutions. For each first kind equation, existence and uniqueness of solution are proved with the aid of composition relations involving associated modified boundary integral operators. For the Dirichlet problem, an optimal choice of the modification coefficients is considered in order to minimize the condition number of the resulting integral operator. Copyright © 2014 John Wiley & Sons, Ltd.