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A Fourth-Order Modified Method for the Cauchy Problem of the Modified Helmholtz Equation
Numerical Mathematics: Theory, Methods and Applications, 2009This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain $0
Shi, R., Wei, T., Qin, H. H.
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A wavelet collocation method for boundary integral equations of the modified Helmholtz equation
Applied Mathematics and Computation, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiangling Chen, Ziqing Xie, Jianshu Luo
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Singular boundary method for modified Helmholtz equations
Engineering Analysis with Boundary Elements, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Wen, Zhang, Jin-Yang, Fu, Zhuo-Jia
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High Accuracy Solutions of the Modified Helmholtz Equation
2016We study the numerical solutions for modified Helmholz equation. Based on the potential theory, the problem can be converted into a boundary integral equation. Mechanical quadrature method (MQM) is presented for solving the equation, which possesses high accuracy order \(O(h_{max}^3)\) and low computing complexities.
Hu Li, Jin Huang 0011
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A modified Galerkin FEM for 1D Helmholtz equations
Applied Acoustics, 2013Abstract A method is presented that aims to eliminate the numerical errors inherent in the standard Galerkin finite element method (GFEM) for solving homogeneous Helmholtz equations. An error analysis of the standard GFEM with linear elements is first performed by using the concept of truncation error in finite difference methods, and then the ...
Hui Zheng, Richard C. Cai, L.S. Pan
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A Modified Helmholtz Equation With Impedance Boundary Conditions
Advances in Applied Mathematics and Mechanics, 2012AbstractHere considered is the problem of transient electromagnetic scattering from overfilled cavities embedded in an impedance ground plane. An artificial boundary condition is introduced on a semicircle enclosing the cavity that couples the fields from the infinite exterior domain to those fields inside.
Robert S. Callihan, Aihua W. Wood
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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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