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Modified equations of the first kind for the Helmholtz equation
Mathematical Methods in the Applied Sciences, 2014Integral 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.
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The modified jump problem for the Helmholtz equation
ANNALI DELL UNIVERSITA DI FERRARA, 2001Let \(\Gamma\) be a set of a finite number of simple open curves in the plane. (A non-closed smooth arc of finite length without self-intersections is called simple open curve). \(\Gamma\) is considered as a set of cuts. The author considers the Helmholtz equation \(\Delta u+k^2u=0\) \((k=\text{const}\neq 0\), \(0\leq\arg ...
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Adaptive Runge–Kutta regularization for a Cauchy problem of a modified Helmholtz equation
Journal of Inverse and Ill-posed Problems, 2023Abstract In this paper, we investigate the Cauchy problem for the modified Helmholtz equation. We consider the data completion problem in a bounded cylindrical domain on which the Neumann and the Dirichlet conditions are given in a part of the boundary. Since this problem is ill-posed, we reformulate it as an optimal control problem with
Jday, Fadhel, Omri, Haithem
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Meshless method with ridge basis functions for modified Helmholtz equations
2010 Sixth International Conference on Natural Computation, 2010A meshless method for modified Helmholtz equations has been developed by utilizing the collocation method and the ridge basis function interpolation. This method is a truly meshless technique without mesh discretization: it neither needs the computation of integrals, nor requires a partition of the region and its boundary.
Xinqiang Qin +3 more
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Reconstruction algorithms of an inverse geometric problem for the modified Helmholtz equation
Computational and Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Modified variational iteration method for solving Helmholtz equations
Computational Mathematics and Modeling, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Noor, M. A., Mohyud-Din, S. T.
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On modified Green functions in exterior problems for the Helmholtz equation
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1982Abstract The question of non-uniqueness in boundary integral equation formulations of exterior problems for the Helmholtz equation has recently been resolved with the use of additional radiating multipoles in the definition of the Green function. The present note shows how this modification may be included in a rigorous formalism and
Kleinman, R. E., Roach, G. F.
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A note on the CVBEM for the two‐dimensional Helmholtz equation or its modified form
Communications in Numerical Methods in Engineering, 2002AbstractA complex variable boundary element method is outlined for the numerical solution of the two‐dimensional Helmholtz equation or its modified form in a simply connected region subject to suitable boundary conditions. It is applied to solve a specific test problem. Copyright © 2002 John Wiley & Sons, Ltd.
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