Results 11 to 20 of about 3,669,023 (333)
Parallel controllability methods for the Helmholtz equation [PDF]
Computer Methods in Applied Mechanics and Engineering, 2020 The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform the problem back to the time-domain, where they seek the time-harmonic solution of the corresponding time-dependent wave equation.
Grote, Marcus +3 more
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Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations [PDF]
SIAM Journal on Mathematical Analysis, 2015 We consider three problems for the Helmholtz equation in interior and exterior domains in R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem.
Baskin, Dean +2 more
core +5 more sources
Solving Helmholtz Equation with Local Fractional Derivative Operators
Fractal and Fractional, 2019 The paper presents a new analytical method called the local fractional Laplace variational iteration method (LFLVIM), which is a combination of the local fractional Laplace transform (LFLT) and the local fractional variational iteration method (LFVIM ...
Dumitru Baleanu +2 more
doaj +2 more sources
Applied Mathematical Sciences, 1992 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 ...
Colton, David +3 more
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Wavefield solutions from machine learned functions constrained by the Helmholtz equation [PDF]
Artificial Intelligence in Geosciences, 2021 Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data.
T. Alkhalifah +3 more
semanticscholar +1 more source
Multigrid-augmented deep learning preconditioners for the Helmholtz equation [PDF]
SIAM Journal on Scientific Computing, 2022 In this paper, we present a data-driven approach to iteratively solve the discrete heterogeneous Helmholtz equation at high wavenumbers. In our approach, we combine classical iterative solvers with convolutional neural networks (CNNs) to form a ...
Yael Azulay, Eran Treister
semanticscholar +1 more source
A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound [PDF]
Journal of Computational Physics, 2020 Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict the acoustic ...
A. Stanziola +3 more
semanticscholar +1 more source
An analytical method for shallow spherical shell free vibration on two-parameter foundation
Heliyon, 2021 The free vibration control differential equation of shallow spherical shell on two-parameter foundation is a four order differential equation.
Jiarong Gan +4 more
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Solution to the Modified Helmholtz Equation for Arbitrary Periodic Charge Densities
Frontiers in Physics, 2021 We present a general method for solving the modified Helmholtz equation without shape approximation for an arbitrary periodic charge distribution, whose solution is known as the Yukawa potential or the screened Coulomb potential.
Miriam Winkelmann +13 more
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PENENTUAN JENIS FUNGSI BASIS RADIAL DALAM DUAL RECIPROCITY BOUNDARY ELEMENT METHOD
Majalah Ilmiah Matematika dan Statistika, 2021 Problems involving modified Helmholtz equation are considered in this paper. To solve the problem numerically, dual reciprocity boundary element method (DRBEM) is employed.
Millatuz Zahroh
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