Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number [PDF]
Journal of Applied Mathematics, 2014 We construct modified forward, backward, and central finite difference schemes, specifically for the Helmholtz equation, by using the Bloch wave property.
Hafiz Abdul Wajid +3 more
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Fourier Truncation Regularization Method for a Three-Dimensional Cauchy Problem of the Modified Helmholtz Equation with Perturbed Wave Number [PDF]
Mathematics, 2019 In this paper, the Cauchy problem of the modified Helmholtz equation (CPMHE) with perturbed wave number is considered. In the sense of Hadamard, this problem is severely ill-posed. The Fourier truncation regularization method is used to solve this Cauchy
Fan Yang, Ping Fan, Xiao-Xiao Li
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Fast integral equation methods for the modified Helmholtz equation [PDF]
Journal of Computational Physics, 2011 Many problems in physics and engineering require the solution of the forced heat equation, $u_{t}-Delta u = F(xx,u,t)$, with Dirichlet boundary conditions. In this thesis, we solve such PDEs in two-dimensional, multiply-connected domains, with a twice continuously differentiable boundary.
Kropinski, Mary Catherine A. +1 more
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A quasi-reversibility regularization method for a Cauchy problem of the modified Helmholtz-type equation [PDF]
Boundary Value Problems, 2019 The Cauchy problem of the modified Helmholtz-type equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Thus the regularization methods are required to recover the numerical stability. In this paper, we
Hong Yang, Yanqi Yang
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The Modified Helmholtz Equation on a Regular Hexagon—The Symmetric Dirichlet Problem [PDF]
Axioms, 2020 Using the unified transform, also known as the Fokas method, we analyse the modified Helmholtz equation in the regular hexagon with symmetric Dirichlet boundary conditions; namely, the boundary value problem where the trace of the solution is given by ...
Konstantinos Kalimeris +1 more
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Generalized Tikhonov Method and Convergence Estimate for the Cauchy Problem of Modified Helmholtz Equation with Nonhomogeneous Dirichlet and Neumann Datum [PDF]
Mathematics, 2019 We investigate a Cauchy problem of the modified Helmholtz equation with nonhomogeneous Dirichlet and Neumann datum, this problem is ill-posed and some regularization techniques are required to stabilize numerical computation. We established the result of
Hongwu Zhang, Xiaoju Zhang
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On relations between harmonic functions and solutions of the modified Helmholtz equation [PDF]
, 2022 We consider the $m$-dimensional modified Helmholtz equation and establish two relations between its solutions in a bounded domain and harmonic functions. Both relations essentially rely on properties of the Newtonian potential. Some other characteristics of these solutions are also obtained.
Н. В. Кузнецов
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High-frequency asymptotics for the modified Helmholtz equation in a half-plane [PDF]
Boundary Value Problems, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang Min-hai
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On Solving Modified Helmholtz Equation in Layered Materials Using the Multiple Source Meshfree Approach [PDF]
Mathematics, 2019 This paper presents a study for solving the modified Helmholtz equation in layered materials using the multiple source meshfree approach (MSMA). The key idea of the MSMA starts with the method of fundamental solutions (MFS) as well as the collocation ...
Cheng-Yu Ku +3 more
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A Modified Natural BEM for Exterior Problems of the Helmholtz Equation [PDF]
Advances in Intelligent Systems Research, 2015 In this paper, a modified natural boundary element method (MNBEM) by using a modified DtN operator to improve the natural boundary element method (NBEM) is proposed for Neumann BVPs of the Helmholtz equation on unbounded domains. We prove the existence and the uniqueness of the solution of its variational problem in L 2 (Γ), and obtain L 2 error ...
Quan Zheng, Yue Gao
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