6 papers · 1 filter
Constrained Local Approximate Ideal Restriction for Advection-Diffusion Problems
Ahsan Ali, James Brannick, Karsten Kahl +3
This paper focuses on developing a reduction-based algebraic multigrid method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure a…
Matrix functions via linear systems built from continued fractions
Andreas Frommer, Karsten Kahl, Manuel Tsolakis
A widely used approach to compute the action of a matrix function on a vector is to use a rational approximation for and compute instead. If …
Coarsening in Algebraic Multigrid using Gaussian Processes
Hanno Gottschalk, Karsten Kahl
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Alge…
On the equivalence of the Hermitian eigenvalue problem and hypergraph edge elimination
Karsten Kahl, Bruno Lang
It is customary to identify sparse matrices with the corresponding adjacency or incidence graph. For the solution of linear systems of equations using Gaussian elimination, the rep…
Krylov type methods exploiting the quadratic numerical range
Andreas Frommer, Birgit Jacob, Karsten Kahl +2
The quadratic numerical range is a subset of the standard numerical range of a linear operator which still contains its spectrum. It arises naturally in operators which ha…
Automated Local Fourier Analysis (aLFA)
Karsten Kahl, Nils Kintscher
Local Fourier analysis is a commonly used tool to assess the quality and aid in the construction of geometric multigrid methods for translationally invariant operators. In this pap…