Acoustic and electromagnetic equations

By J. Nédélec. 2001

1,368 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Ocean Engineering, Statistical and Nonlinear Physics

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Citations in the corpus

Understanding and mitigating gradient pathologies in physics-informed neural networks (2020, background): “This equation is closely related to many problems in natural and engineering sciences, such as wave propagation in acoustic, elastic and electromagnetic media [47].”
Finite elements in computational electromagnetism (2002, neutral): “A survey is given in Nédélec (2001).”
A FEM domain decomposition method for photonic and electromagnetic band gap structures (2006, background): “The electromagnetic scattering or radiation in unbounded domains is governed by Maxwell equations for the electric and magnetic fields ( , ), subject to the Silver–Müller radiation condition [34].”
Finite elements on degenerate meshes: inverse-type inequalities and applications (2005, positive): “…with the hypersingular operator can be written in the form (see Nédélec, 2001; Sauter & Schwab, 2004) a (u, v) = ∫ Γ×Γ 〈−→ curlΓ v (x) , −→ curlΓ u (y) 〉 + ω2 〈n(x), n(y)〉 v(x)u(y) 4π |x − y| dx dy, (6.13) where the tangential rotation −→ curlΓ is defined as follows (see Nédélec, 2001).”
A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain (2008, neutral): “acoustics [50], electromagnetics [ 35 , 39] or seismology [7, 22].”
Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels (2013, neutral): “Γ H (1) 0 ( ω|x − y|)q(y)ds(y), where q is the single-layer potential density function found from an integral equation of the first kind [3, 24], i 4 ∫”
A high-order algorithm for obstacle scattering in three dimensions (2004, neutral): “) Here, k > 0 is called the wavenumber and we use the standard notion of radiating solution [7, 8, 18], i.”
Hierarchical matrix techniques for low- and high-frequency Helmholtz problems (2007, neutral): “This problem describes the time-harmonic acoustic scattering problem, where a plane wave coming from infinity at an angleπ/4 is being scattered by a sound-soft obstacle Ω ⊂ R2 (seeColton & Kress, 1998; Néd́elec, 2001).”
Dirichlet-to-Neumann boundary conditions for multiple scattering problems (2004, neutral): “18”
OpenMEEG: opensource software for quasistatic bioelectromagnetics (2010, positive): “In OpenMEEG the approach is to consider an extended version of the Green representation theorem [6], involving more operators, and leading to a new BEM formulation, called the Symmetric Boundary Element Method [7].”
Multiscale Simulation of Complex Structures Using Equivalence Principle Algorithm With High-Order Field Point Sampling Scheme (2008, neutral): “This is known from the Calderon projectors [21]‐[ 23 ] that if the equivalent currents are the solutions of Maxwell’s equations on a closed surface, they will induce the same currents on this surface.”
A common formalism for the Integral formulations of the forward EEG problem (2005, positive): “Boundary Element Method The Boundary Element Method (BEM) [6, 7] is today a classical way of solving the forward problem.”
Inverse scattering problems with multi-frequencies (2015, background): “If the total field is viewed as the sum of an incident field and a scattered field, the direct scattering problems are to determine the scattered field from the incident field and the differential equations governing the wave motion; the inverse scattering problems are to determine the nature of the”