High-frequency Bounds for the Helmholtz Equation Under Parabolic Trapping and Applications in Numerical Analysis [PDF]
SIAM Journal on Mathematical Analysis, 2017 This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the obstacle is trapping.
S. Chandler-Wilde +3 more
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Nonlinear interfaces: intrinsically nonparaxial regimes and effects [PDF]
, 2009 The behaviour of optical solitons at planar nonlinear boundaries is a problem rich in intrinsically nonparaxial regimes that cannot be fully addressed by theories based on the nonlinear Schrödinger equation.
Boardman A D +10 more
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Stability estimate for the Helmholtz equation with rapidly jumping coefficients [PDF]
Zeitschrift für Angewandte Mathematik und Physik, 2017 The goal of this paper is to investigate the stability of the Helmholtz equation in the high-frequency regime with non-smooth and rapidly oscillating coefficients on bounded domains.
S. Sauter, C'eline Torres
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A computing method for bending problem of thin plate on Pasternak foundation
Advances in Mechanical Engineering, 2020 The governing equation of the bending problem of simply supported thin plate on Pasternak foundation is degraded into two coupled lower order differential equations using the intermediate variable, which are a Helmholtz equation and a Laplace equation. A
Jiarong Gan +4 more
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A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods [PDF]
SIAM Review, 2016 Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades, an important research effort has gone into developing preconditioners for the simplest representative of such wave propagation ...
M. Gander, Hui Zhang
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Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods [PDF]
, 2011 This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Taylor & Francis.This paper presents new formulations of the boundary–domain integral equation (BDIE) and the boundary–domain integro-
M. A. AL-Jawary +7 more
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Monotonicity and local uniqueness for the Helmholtz equation [PDF]
Analysis & PDE, 2017 This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schrodinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient
B. Harrach, V. Pohjola, M. Salo
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A boundary integral equation method for the fluid-solid interaction problem
Communications in Analysis and Mechanics, 2023 In this paper, a boundary integral equation method is proposed for the fluid-solid interaction scattering problem, and a high-precision numerical method is developed.
Yao Sun, Pan Wang, Xinru Lu , Bo Chen
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Boundary Element and Finite Element Coupling for Aeroacoustics Simulations [PDF]
, 2014 We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential.
Balin, Nolwenn +5 more
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The Helmholtz Equation in Random Media: Well-Posedness and A Priori Bounds [PDF]
SIAM/ASA J. Uncertain. Quantification, 2018 We prove well-posedness results and a priori bounds on the solution of the Helmholtz equation $\nabla\cdot(A\nabla u) + k^2 n u = -f$, posed either in $\mathbb{R}^d$ or in the exterior of a star-shaped Lipschitz obstacle, for a class of random $A$ and $n,
O. R. Pembery, E. Spence
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