Since matrix compression has paved the way for discretizing the boundary integral
equation formulations of electromagnetics scattering on very fine meshes, preconditioners
for the resulting linear systems have become key to efficient simulations. Operator
preconditioning based on Calderón identities has proved to be a powerful device for
devising preconditioners. However, this is not possible for the usual first-kind boundary
formulations for electromagnetic...
Taking the cue from stabilized Galerkin methods for scalar advection problems, we adapt the technique to boundary value problems modeling the advection of magnetic fields. We provide rigorous error estimates for both fully discontinuous piecewise polynomial trial functions and -conforming finite elements.
Since matrix compression has paved the way for discretizing the boundary integral
equation formulations of electromagnetics scattering on very fine meshes, preconditioners
for the resulting linear systems have become key to efficient simulations. Operator
preconditioning based on Calderón identities has proved to be a powerful device for
devising preconditioners. However, this is not possible for the usual first-kind boundary
formulations for electromagnetic...
We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a -neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on . We apply the obtained estimates...
We consider ;Ω)-elliptic problems that have been discretized by
means of Nédélec's edge elements on tetrahedral meshes. Such
problems
occur in the numerical computation of eddy currents. From the defect
equation we derive localized expressions that can be used
as error estimators to control adaptive
refinement.
Under certain assumptions on material parameters and computational
domains, we derive local lower bounds and a global upper bound for the
total error measured in the energy norm. The...
We are concerned with a finite element approximation for time-harmonic wave
propagation governed by the Helmholtz equation. The usually oscillatory behavior of
solutions, along with numerical dispersion, render standard finite element methods
grossly inefficient already in medium-frequency regimes. As an alternative, methods
that incorporate information about the solution in the form of plane waves have
been proposed. We focus on a class of Trefftz-type discontinuous Galerkin methods that
...
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