Browsing by Subject "Helmholtz equation"
Now showing items 1-9 of 9
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Article
Compact optimal quadratic spline collocation methods for the Helmholtz equation
(2011)Quadratic spline collocation methods are formulated for the numerical solution of the Helmholtz equation in the unit square subject to non-homogeneous Dirichlet, Neumann and mixed boundary conditions, and also periodic ...
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Article
Efficient MFS algorithms for inhomogeneous polyharmonic problems
(2011)In this work we develop an efficient algorithm for the application of the method of fundamental solutions to inhomogeneous polyharmonic problems, that is problems governed by equations of the form Δ ℓ u=f, ℓ ε ℕ, in circular ...
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Article
Legendre Gauss spectral collocation for the Helmholtz equation on a rectangle
(2004)A spectral collocation method with collocation at the Legendre Gauss points is discussed for solving the Helmholtz equation -Δu+κ(x,y)u=f(x,y) on a rectangle with the solution u subject to inhomogeneous Robin boundary ...
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Matrix decomposition algorithms for modified spline collocation for Helmholtz problems
(2003)We consider the solution of various boundary value problems for the Helmholtz equation in the unit square using a nodal cubic spline collocation method and modifications of it which produce optimal (fourth-) order ...
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The method of fundamental solutions for axisymmetric acoustic scattering and radiation problems
(1998)The method of fundamental solutions (MFS) is applied to acoustic scattering and radiation for axisymmetric bodies and boundary conditions. The fundamental solution of the governing equation and its normal derivative, which ...
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The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation
(2001)We investigate the application of the method of fundamental solutions (MFS) for the calculation of the eigenvalues of the Helmholtz equation in the plane subject to homogeneous Dirichlet boundary conditions. We present ...
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The plane waves method for axisymmetric Helmholtz problems
(2016)The plane waves method is employed for the solution of Dirichlet and Neumann boundary value problems for the homogeneous Helmholtz equation in two- and three-dimensional domains possessing radial symmetry. The appropriate ...
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Article
Regularized MFS-Based boundary identification in two-dimensional Helmholtz-type equations
(2009)We study the stable numerical identification of an unknown portion of the boundary on which a given boundary condition is provided and additional Cauchy data are given on the remaining known portion of the boundary of a ...
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Spectral Chebyshev-Fourier collocation for the Helmholtz and variable coefficient equations in a disk
(2008)The paper is concerned with the spectral collocation solution of the Helmholtz equation in a disk in the polar coordinates r and θ. We use spectral Chebyshev collocation in r, spectral Fourier collocation in θ, and a simple ...