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WaveHoltz: Iterative Solution of the Helmholtz Equation via the Wave Equation [PDF]
SIAM Journal on Scientific Computing, 2019 A new idea for iterative solution of the Helmholtz equation is presented. We show that the iteration which we denote WaveHoltz and which filters the solution to the wave equation with harmonic data evolved over one period, corresponds to a coercive ...
D. Appelö, Fortino Garcia, O. Runborg
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Solvability of discrete Helmholtz equations
IMA Journal of Numerical Analysis, 2022 Abstract We study the unique solvability of the discretized Helmholtz problem with Robin boundary conditions using a conforming Galerkin finite element method. Well-posedness of the discrete equations is typically investigated by applying a compact perturbation argument to the continuous Helmholtz problem so that a `sufficiently rich ...
Bernkopf, Maximilian +3 more
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Dimension Bounds in Monotonicity Methods for the Helmholtz Equation [PDF]
SIAM Journal on Mathematical Analysis, 2019 The article [HPS] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems.
B. Harrach, V. Pohjola, M. Salo
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Scalable Convergence Using Two-Level Deflation Preconditioning for the Helmholtz Equation
SIAM Journal on Scientific Computing, 2020 Recent research efforts aimed at iteratively solving the Helmholtz equation have focused on incorporating deflation techniques for accelerating the convergence of Krylov subpsace methods.
V. Dwarka, C. Vuik
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An efficient method for 3D Helmholtz equation with complex solution
AIMS Mathematics, 2023 The Helmholtz equation as an elliptic partial differential equation possesses many applications in the time-harmonic wave propagation phenomena, such as the acoustic cavity and radiation wave.
M. H. Heydari +2 more
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Applied Sciences, 2023 Recently, to simulate sound propagation inside architectural spaces at high frequencies, the application of computationally expensive wave-based numerical methods to room acoustics simulation is increasing gradually.
Takeshi Okuzono
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Abstract and Applied Analysis, 2022 The ill-posed Helmholtz equation with inhomogeneous boundary deflection in a Hilbert space is regularized using the divergence regularization method (DRM).
Benedict Barnes +2 more
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Transfer equation for the strain rate tensor and description of an incompressible dispersed mixture (incompressible fluid) by a system of equations of dynamic type [PDF]
E3S Web of Conferences, 2021 It is known that the application of the vector operation rot to the equations of hydrodynamics leads to the Helmholtz-Friedman equation for a vortex.
Yuldashov Askar +3 more
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Domain Decomposition preconditioning for high-frequency Helmholtz problems with absorption [PDF]
, 2016 In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation $-\Delta u - (k^2+ {\rm i} \varepsilon)u = f$, with absorption parameter ...
Graham, Ivan G. +2 more
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Helmholtz-Manakov solitons [PDF]
, 2005 A novel spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (H-M) equation, for describing the evolution of broad multi-component self-trapped beams in Kerr-type media. By omitting the slowly-varying envelope approximation, the H-M
Chamorro-Posada, P +2 more
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