The Riemann–Hilbert approach to the Helmholtz equation in a quarter-plane: Neumann, Robin and Dirichlet boundary conditions
Sign Up to like & getrecommendations! Published in 2017 at "Letters in Mathematical Physics"
DOI: 10.1007/s11005-017-1030-3
Abstract: We revisit the Helmholtz equation in a quarter-plane in the framework of the Riemann–Hilbert approach to linear boundary value problems suggested in late 1990s by A. Fokas. We show the role of the Sommerfeld radiation… read more here.
Keywords: riemann hilbert; equation quarter; helmholtz equation; quarter plane ... See more keywords
An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition
Sign Up to like & getrecommendations! Published in 2020 at "Numerical Algorithms"
DOI: 10.1007/s11075-020-00926-5
Abstract: Efficient and accurate numerical schemes for solving the Helmholtz equation are critical to the success of various wave propagation–related inverse problems, for instance, the full-waveform inversion problem. However, the numerical solution to a multi-dimensional Helmholtz… read more here.
Keywords: optimal point; helmholtz equation; point finite; difference scheme ... See more keywords
On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation
Sign Up to like & getrecommendations! Published in 2019 at "Analysis and Mathematical Physics"
DOI: 10.1007/s13324-018-0210-3
Abstract: The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro… read more here.
Keywords: dimensional helmholtz; riemann boundary; helmholtz equation; boundary value ... See more keywords
The mollification method based on a modified operator to the ill-posed problem for 3D Helmholtz equation with mixed boundary
Sign Up to like & getrecommendations! Published in 2021 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2020.10.012
Abstract: Abstract The paper is considered a Cauchy problem for Helmholtz equation with mixed boundary in three-dimensional case. The problem is severely ill-posed (small deviation in the data may produce large errors in the computed solution),… read more here.
Keywords: problem helmholtz; helmholtz equation; mixed boundary; equation mixed ... See more keywords
The double absorbing boundary method for the Helmholtz equation
Sign Up to like & getrecommendations! Published in 2021 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2021.05.029
Abstract: Abstract The Double Absorbing Boundary (DAB) is a recently proposed absorbing layer used to truncate an unbounded domain with high-order accuracy. While it was originally designed for time-dependent acoustics and elastodynamics, here the DAB construction… read more here.
Keywords: double absorbing; method helmholtz; helmholtz equation; boundary method ... See more keywords
A regularized approach evaluating origin intensity factor of singular boundary method for Helmholtz equation with high wavenumbers
Sign Up to like & getrecommendations! Published in 2019 at "Engineering Analysis with Boundary Elements"
DOI: 10.1016/j.enganabound.2019.01.008
Abstract: Abstract Evaluation of the origin intensity factor of the singular boundary method for Helmholtz equation with high wavenumbers has been a difficult task for a long time. In this study, a regularized approach is provided… read more here.
Keywords: regularized approach; method; helmholtz equation; boundary method ... See more keywords
A strict formulation of a nonlinear Helmholtz equation for the propagation of sound in bubbly liquids. Part I: Theory and validation at low acoustic pressure amplitudes.
Sign Up to like & getrecommendations! Published in 2018 at "Ultrasonics sonochemistry"
DOI: 10.1016/j.ultsonch.2018.04.014
Abstract: This paper strictly demonstrated a nonlinear Helmholtz equation, with its corresponding new expressions for the wave number of the mixture, for the propagation of sound trough a bubbly liquid. The demonstration was conducted under the… read more here.
Keywords: propagation; helmholtz equation; model; nonlinear helmholtz ... See more keywords
Reconstruction algorithms of an inverse conductive scattering problem for the Helmholtz equation
Sign Up to like & getrecommendations! Published in 2020 at "Applicable Analysis"
DOI: 10.1080/00036811.2020.1819533
Abstract: In this paper, we consider an inverse conductive scattering problem for the Helmholtz equation from measurements on the outer boundary. We want to seek reconstruction algorithms to detect the numbe... read more here.
Keywords: inverse conductive; helmholtz equation; reconstruction algorithms; scattering problem ... See more keywords
Oblique Derivative Problem for the Helmholtz Equation in a Disk
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DOI: 10.1134/s0012266118040067
Abstract: We show that the oblique derivative problem for the Helmholtz equation in a disk is uniquely solvable under certain restrictions on the parameter. read more here.
Keywords: helmholtz equation; oblique derivative; equation disk; derivative problem ... See more keywords
Mixed Oblique Derivative Problem for the Helmholtz Equation in a Half-Disk
Sign Up to like & getrecommendations! Published in 2018 at "Differential Equations"
DOI: 10.1134/s0012266118100087
Abstract: A mixed oblique derivative boundary value problem is considered for the Helmholtz equation in a half-disk. We prove the unique solvability of this problem for sufficiently large values of the parameter occurring in the equation,… read more here.
Keywords: mixed oblique; helmholtz equation; oblique derivative; equation half ... See more keywords
Analysis of Spatially Doped Fused Silica Fiber Optic by Means of a Hamiltonian Formulation of the Helmholtz Equation
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Materials Science and Engineering"
DOI: 10.1155/2018/5806947
Abstract: This paper discusses an alternative method for calculating modal parameters in optical fibers such as propagation constants, transverse distributions, and anisotropy, due to linear and nonlinear phenomena acting as perturbations caused by doped silica regions.… read more here.
Keywords: helmholtz equation; formulation helmholtz; hamiltonian formulation; silica ... See more keywords