Results 41 to 50 of about 3,669,023 (333)

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
semanticscholar   +1 more source

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, E. Spence, A. Gibbs, V. Smyshlyaev   +3 more
semanticscholar   +1 more source

Additive Sweeping Preconditioner for the Helmholtz Equation [PDF]

, 2016
We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfect matched layer (PML). This method divides the domain of interest into thin layers and proposes a new transmission condition between the subdomains where ...
Liu, Fei, Ying, Lexing
core   +1 more source

Multifrequency Analysis for the Helmholtz Equation [PDF]

PAMM, 2003
AbstractThis paper is a brief review of a new numerical method for the multifrequency analysis of the three‐dimensional Helmholtz equation. We describe the principles of this method which is based on the identity of the Fourier transform with respect to the wave number. Some numerical examples for the solution were presented at the oral session.
Köhl, M., Rjasanow, S.
openaire   +4 more sources

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
semanticscholar   +1 more source

Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator

, 2017
We introduce an efficient method for computing the Stekloff eigenvalues associated with the Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition repeatedly.
A Brandt, A.H. Sheikh, B Engquist, CC Stolk, D Colton, D Lahaye, D Osei-Kuffuor, F. Cakoni, Fioralba Cakoni, GH Golub, HC Elman, JW Cooley, L Zepeda-Núnez, M Eslaminia, M. J. Gander, OG Ernst, Z Chen   +16 more
core   +1 more source

Korteweg-de Vries description of Helmholtz-Kerr dark solitons [PDF]

, 2006
A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation.
Chamorro-Posada P, Chamorro-Posada P, Chi S, Christian J M, Christian J M, Dodd R K, Fedele R, Fedele R, G S McDonald, Infeld E, J M Christian, Kivshar Y S, Kivshar Y S, Kivshar Y S, Kivshar Y S, Kivshar Y S, Mandel P, P Chamorro-Posada, Remoissenet M, Satsuma J, Zakharov V E, Zakharov V E   +21 more
core   +3 more sources

Monopoles, instantons, and the Helmholtz equation [PDF]

Journal of Mathematical Physics, 2016
In this work we study the dimensional reduction of smooth circle invariant Yang-Mills instantons defined on 4-manifolds which asymptotically become circle fibrations over hyperbolic 3-space. A suitable choice of the 4-manifold metric within a specific conformal class gives rise to singular and smooth hyperbolic monopoles.
Franchetti, Guido, Maldonado, Rafael
openaire   +4 more sources

On controllability methods for the Helmholtz equation

Journal of Computational and Applied Mathematics, 2019
When the Helmholtz equation is discretized by standard finite difference or finite element methods, the resulting linear system is highly indefinite and thus notoriously difficult to solve, in fact increasingly so at higher frequency.
M. Grote, Jet Hoe Tang
semanticscholar   +1 more source

Exploring Solutions of Geometry Problems for Inverse Cauchy Problems in Helmholtz and Modified Helmholtz Equations

Academic Science Journal
In the present paper explores a reverse Cauchy problem for a heat transfer issue described by the Helmholtz and modified Helmholtz equation. Our goal is to identify an unknown defect  within a simply connected bounded domain , given the Dirichlet data ...
shurouq hasan, Zainab Ali Mansour, Fatima Mohammed Aboud   +2 more
doaj   +1 more source