72 citations · 124 across the 5 of their papers we have counts for
5 papers
Designing Illumination Lenses and Mirrors by the Numerical Solution of Monge-Ampère Equations
Kolja Brix, Yasemin Hafizogullari, Andreas Platen
We consider the inverse refractor and the inverse reflector problem. The task is to design a free-form lens or a free-form mirror that, when illuminated by a point light source, pr…
Solving the Monge-Ampère Equations for the Inverse Reflector Problem
Kolja Brix, Yasemin Hafizogullari, Andreas Platen
The inverse reflector problem arises in geometrical nonimaging optics: Given a light source and a target, the question is how to design a reflecting free-form surface such that a d…
Legendre-Gauss-Lobatto grids and associated nested dyadic grids
Kolja Brix, Claudio Canuto, Wolfgang Dahmen
Legendre-Gauss-Lobatto (LGL) grids play a pivotal role in nodal spectral methods for the numerical solution of partial differential equations. They not only provide efficient high-…
Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes
Kolja Brix, Martin Campos Pinto, Claudio Canuto +1
This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value prob…
Robust Preconditioners for DG-Discretizations with Arbitrary Polynomial Degrees
Kolja Brix, Claudio Canuto, Wolfgang Dahmen
Discontinuous Galerkin (DG) methods offer an enormous flexibility regarding local grid refinement and variation of polynomial degrees for a variety of different problem classes. Wi…