Research Interests
Breaktrough in geometric multigrid/multilevel methods in
H (curl, Ω)
Publications
- chevron_right Multigrid method for H(div) in three dimensions
- external page call_made Multigrid method for Maxwell’s equations
- external page call_made Analysis of multilevel methods for eddy current problems
- external page call_made Stable multilevel splittings of boundary edge element spaces
- external page call_made Local multigrid in H(curl)
Auxiliary space methods (AMS), featured as breakthrough in computational science in the 2008 DOE “Report on recent significant advancements in computational science”.
Publications
Multilevel construction of discrete potentials
Publication
Seminal work for Finite Element Exterior Calculus (FEEC) on the construction of discrete differential forms
Publication
external pageCanonical construction of finite elementscall_made
Early contributions to the theory of discrete Hodge operators (“mimetic finite elements”) and higher order discrete differential forms, see also the widely cited survey.
Publications
Discrete Lie derivatives for transport problems, applications to magneto- hydrodynamics.
Publications
- chevron_right Extrusion contraction upwind schemes for convection - diffusion problems
- external page call_made Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms
- external page call_made Stabilized Galerkin methods for magnetic advection
- external page call_made Fully discrete semi-Lagrangian methods for advection of differential forms
- external page call_made Stabilized Galerkin for transient advection of differential forms
- chevron_right A semi-Lagrangian method for convection of differential forms
- chevron_right Splitting-based structure preserving discretizations for magnetohydrodynamics
(Coupled) boundary element methods for eddy current problems in frequency domain
Publications
- external page call_made Symmetric coupling for eddy current problems
- external page call_made Boundary element methods for eddy current computation
- external page call_made Generators of H1(Γh, Z) for triangulated surfaces: Construction and classification
- external page call_made Coupled boundary element scheme for eddy current computation
Discretization of electromagnetic integral equations set in natural trace spaces
Publications
- external page call_made Convergence of natural hp-BEM for the electric field integral equation on polyhedral surfaces
- external page call_made A coercive combined field integral equation for electromagnetic scattering
- external page call_made Coupling of finite elements and boundary elements in electromagnetic scattering
- external page call_made Natural boundary element methods for the electric field integral equation on polyhedra
Regularized combined field integral equations
Publications
Discovery of local and global multi-trace methods
Publications
- external page call_made Electromagnetic scattering at composite objects: A novel multi-trace boundary integral formulation
- external page call_made Multi-trace boundary integral formulation for acoustic scattering by composite structures
- chevron_right Multi-trace boundary integral equations
- chevron_right Novel multi- trace boundary integral equations for transmission boundary value problems
- external page call_made Multiple traces boundary integral formulation for Helmholtz transmission problems
- external page call_made Domain decomposition for boundary integral equations via local multi-trace formulations
Second-kind BEM for scattering at composite objects
Publications
- external page call_made Integral equations for acoustic scattering by partially impenetrable composite objects
- external page call_made A second-kind Galerkin boundary element method for scattering at composite objects
- external page call_made Second-kind boundary integral equations for electromagnetic scattering at composite objects
- chevron_right Second-kind boundary integral equations for scattering at composite partly impenetrable objects
Comprehensive theoretical treatment of h-, p-, and hp-versions of plane wave DG methods for both acoustics and electromagnetics
Publications
- external page call_made Plane wave discontinuous Galerkin methods: Analysis of the h-version
- external page call_made Plane wave discontinuous Galerkin methods for the 2d Helmholtz equation: Analysis of the p-version
- external page call_made Stability results for the time-harmonic Maxwell equations with impedance boundary conditions
- chevron_right Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
- external page call_made Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the hp-Version
- chevron_right A survey of trefftz methods for the helmholtz equation
- chevron_right Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-DGFEM
- external page call_made Plane wave approximation of homogeneous Helmholtz solutions
- external page call_made Vekua theory for the Helmholtz operator
Sparse tensor scheme for radiative transfer
Publication
external pageSparse adaptive finite elements for radiative transfercall_made
Deterministic spectral polynomial methods for the spatially inhomogeneous Boltzmann equation
Publications