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Towards a quantitative theory for transmission X-ray microscopy. [PDF]
Beilstein J NanotechnolMcNally JG +8 more
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Applied Mathematical Sciences, 2019 Studying an inverse problem always requires a solid knowledge of the theory for the corresponding direct problem. Therefore, the following two chapters of our book are devoted to presenting the foundations of obstacle scattering problems for time-harmonic acoustic waves, that is, to exterior boundary value problems for the scalar Helmholtz equation ...
D. Colton, R. Kress
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Kernel Ridge Regression with Constraint of Helmholtz Equation for Sound Field Interpolation
International Workshop on Acoustic Signal Enhancement, 2018Kernel ridge regression with the constraint of the Helmholtz equation for three-dimensional sound field interpolation is proposed. Interpolation of a sound field is formulated as an optimization problem whose objective function to be minimized is a ...
Natsuki Ueno +2 more
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Learned Iterative Solvers for the Helmholtz Equation
81st EAGE Conference and Exhibition 2019, 2019Summary We propose a ‘learned’ iterative solver for the Helmholtz equation, by combining traditional Krylov-based solvers with machine learning. The method is, in principle, able to circumvent the shortcomings of classical iterative solvers, and has ...
G. Rizzuti, Ali Siahkoohi, F. Herrmann
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FEM and CIP-FEM for Helmholtz Equation with High Wave Number and Perfectly Matched Layer Truncation
SIAM Journal on Numerical Analysis, 2019The Helmholtz scattering problem with high wave number is truncated by the perfectly matched layer (PML) technique and then discretized by the linear continuous interior penalty--finite element met...
Yonglin Li, Haijun Wu
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New computational approaches to the fractional coupled nonlinear Helmholtz equation
Engineering computationsPurposeThe main aim of this paper is to investigate the fractional coupled nonlinear Helmholtz equation by two new analytical methods.Design/methodology/approachThis article takes an inaugural look at the fractional coupled nonlinear Helmholtz equation ...
Kang-Le Wang
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Deep Domain Decomposition Methods: Helmholtz Equation
Advances in Applied Mathematics and Mechanics, 2023Summary: This paper proposes a deep-learning-based Robin-Robin domain decomposition method (DeepDDM) for Helmholtz equations. We first present the plane wave activation-based neural network (PWNN), which is more efficient for solving Helmholtz equations with constant coefficients and wavenumber \(k\) than finite difference methods (FDM). On this basis,
Li, Wuyang +4 more
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PRECONDITIONING THE HELMHOLTZ EQUATION
Journal of Sound and Vibration, 1998An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme.
K.J. Baumeister, K.L. Kreider
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Helmholtz Equation and Visualization
2009 International Asia Symposium on Intelligent Interaction and Affective Computing, 2009The existence of electromagnetic waves is an important result of Maxwell's equations. For this reason, this paper, based on Maxwell's equations, after the introduction of potential functions, obtains Helmholtz equation of time-varying electromagnetic field, using the separation of variables, solves the equation on the basis of Spherical Symmetry, then ...
Wu Gang, Xiying Fan
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