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   Articles with "helmholtz equation" as a keyword



Well‐Posedness Analysis and Numerics of Boundary‐Domain Integral Equation Systems Equivalent to the Robin Problem for the Helmholtz Equation With Variable Coefficients in Lipschitz Domains

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recommendations! Published in 2025 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.10965

Abstract: Given the interior Robin boundary value problem (BVP) for the Helmholtz equation with variable coefficients, we use an appropriate parametrix to derive two boundary‐domain integral equation systems (BDIES) equivalent to the original Robin BVP in… read more here.

Keywords: equation; equation variable; variable coefficients; boundary domain ... See more keywords

Helmholtz-x : Parallelized adjoint open source solver for the thermoacoustic Helmholtz equation

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recommendations! Published in 2025 at "Engineering with Computers"

DOI: 10.1007/s00366-025-02107-1

Abstract: We create and describe an inhomogeneous Helmholtz equation solver, helmholtz-x, written in an open-source framework. The mesh is generated with Gmsh and the solver uses DOLFINx and UFL from FEniCSx. The performance, validity, stability and… read more here.

Keywords: open source; solver; helmholtz; helmholtz equation ... See more keywords

The Riemann–Hilbert approach to the Helmholtz equation in a quarter-plane: Neumann, Robin and Dirichlet boundary conditions

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recommendations! 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
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An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition

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recommendations! 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

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recommendations! 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
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The mollification method based on a modified operator to the ill-posed problem for 3D Helmholtz equation with mixed boundary

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recommendations! 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
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The double absorbing boundary method for the Helmholtz equation

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recommendations! 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

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recommendations! 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.

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recommendations! 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

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recommendations! 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

Inverse random scattering for the one-dimensional Helmholtz equation

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recommendations! Published in 2025 at "Inverse Problems"

DOI: 10.1088/1361-6420/addde3

Abstract: This paper concerns the inverse random potential scattering problem for the Helmholtz equation in one dimension. The random potential is assumed to be a generalized microlocally isotropic Gaussian random field, whose covariance is a classical… read more here.

Keywords: inverse random; inverse; problem; helmholtz equation ... See more keywords