Finite element methods for Maxwell's equations

By Ronald H. W. Hoppe. Mathematics of Computation, 2005

1,563 citations recorded by the source corpus.

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Citations in the corpus

A Domain Decomposition Method With Nonconformal Meshes for Finite Periodic and Semi-Periodic Structures (2007, background): “Suppose that and , then the only way for (16) to be zero would be everywhere in . For the case and , we can conclude, from the assumption , that on . The desired result of in is then a direct consequence of analytic continuation from to . The details of the analytic continuation can be consulted wit”
Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media (2008, unknown): “The former can be classified into finite methods [1]–[9] and (pseudo-)spectral methods [10], [11].”
A review of unified a posteriori finite element error control (2012, background): “Eddy current problem We consider the semi-discrete eddy current equations [36] curlμ−1 curl u+σu = f in Ω, (2.”
Linear Algebra and its Applications (2010, unknown): “This 3D Maxwell problem is spatially discretized with ﬁrst-order, ﬁrst-type Nédélec edge ﬁnite elements on tetrahedral unstructured grids [34,36,37].”
Theory of adaptive finite element methods: An introduction (2009, unknown): “[15, 16, 18, 25, 51].”
Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system (2008, unknown): “that ([21], Thm.”
Isogeometric analysis in electromagnetics: B-splines approximation (2010, methodology): “This is made possible by the validity of the De Rham commuting diagram [1, 18].”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, methodology): “Using two dimensional curl-conforming vector basis functions (Ni) for the discretization of the transverse field (such as the basis functions from the Nédélec function space of the first kind (Nédélec, 1980; Webb, 1993; Monk, 2003)), and nodal scalar basis functions (Li) for the axial components (Ji”
The inverse electromagnetic scattering problem for anisotropic media (2010, unknown): “If we define Ẽ(ext,int) = 1√ E(ext,int), H̃ (ext,int) = 1√ μ0 H(ext,int), k2 = μ0ω2 and N(x) = (x)/ , the direct scattering problem for an anisotropic dielectric medium reads ∇ × Eext − ikH ext = 0 ∇ × H ext + ikEext = 0 } in R3\D (4) ∇ × Eint − ikH int = 0 ∇ × H int + ikN(x)Eint = 0 } in D…”
Choose a Transformer: Fourier or Galerkin (2021, background): “…the higher derivatives, DoFs for splines, etc.; another example is that a single entry in a column of Q, K, V may stand for an edge DoF vector representation in a graph, and the edge–edge interaction is extensively studied for the simulation of Maxwell’s equations [63, 15, 6] on manifolds [94].”
Deep learning enabled inverse design in nanophotonics (2020, methodology): “For arbitrarily complex nanophotonic structures, fully numerical simulations (such as the finite-element method or the finite difference time domain method [47, 48]) are employed to obtain the associated optical responses.”
A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics (2010, background): “This makes this approach feasible in situations of highly singular magnetic fields [34,40,42].”
High order edge elements on simplicial meshes (2007, background): “[17,18]), there is no analysis yet that provides error estimates including the influence of the polynomial degree k.”
High order Nédélec elements with local complete sequence properties (2005, unknown): “A recent monograph is [2].”