R. Hiptmair

Publications218
h-index39
Citations5,997
Highly Influential Citations426
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Finite elements in computational electromagnetism
This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching…
Multigrid Method for Maxwell's Equations
TLDR
A rigorous proof of the asymptotic optimality of the multigrid method can be given, which shows that convergence does not deteriorate on very fine grids.
Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
TLDR
This paper develops and analyzes a general approach to preconditioning linear systems of equations arising from conforming finite element discretizations of H(curl, )- and H(div,)-elliptic variational problems and proves mesh-independent effectivity of the precondITIONers by using the abstract theory of auxiliary space preconditionsing.
Galerkin Boundary Element Methods for Electromagnetic Scattering
Methods based on boundary integral equations are widely used in die numerical simulation of electromagnetic scattering in the frequency domain. This article examines a particular class of these…
Residual based a posteriori error estimators for eddy current computation
We consider H (curl ;Ω)-elliptic problems that have been discretized by means of Nedelec's edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From…
Canonical construction of finite elements
TLDR
This work takes a fresh look at the construction of the finite spaces, viewing them from the angle of differential forms, and arrives at a fairly canonical procedure to construct conforming finite element subspaces of function spaces related to differential forms.
Symmetric Coupling for Eddy Current Problems
TLDR
The properties of potentials and boundary integral operators arising from a Stratton--Chu-type representation formula for the electric field in the nonconducting region are thoroughly analyzed in a Hilbert-space setting, resulting in a variational problem with symmetric bilinear form that is coercive in the natural function spaces.
Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
TLDR
A priori convergence analysis of PWDG in the case of $p$-refinement is concerned, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased.
PLANE WAVE DISCONTINUOUS GALERKIN METHODS: ANALYSIS OF THE h-VERSION ∗, ∗∗
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…
Boundary Element Methods for Maxwell Transmission Problems in Lipschitz Domains
TLDR
The Maxwell equations in a domain with Lipschitz boundary and the boundary integral operator A occuring in the Calderón projector are considered and an inf-sup condition for A is proved using a Hodge decomposition to prove quasioptimal convergence of the resulting boundary element methods.
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