19 citations · 28 across the 7 of their papers we have counts for
7 papers
FIAT: improving performance and accuracy for high-order finite elements
Pablo D. Brubeck, Robert C. Kirby, Fabian Laakmann +1
FIAT (the FInite element Automatic Tabulator) provides a powerful Python library for the generation and evaluation of finite element basis functions on a reference element. This re…
Accuracy analysis for explicit-implicit finite volume schemes on cut cell meshes
Sandra May, Fabian Laakmann
The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem: standard schemes are not stable on the arbitrarily small cut cells if…
Discretisations and Preconditioners for Magnetohydrodynamics Models
Fabian Laakmann
The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve numerically, due to their highly nonlinear structure and the strong coupling between the elect…
Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem
Fabian Laakmann, Nicolas Boullé
We perform a bifurcation analysis of a two-dimensional magnetic Rayleigh--Bénard problem using a numerical technique called deflated continuation. Our aim is to study the influence…
Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations
Fabian Laakmann, Patrick E. Farrell, Kaibo Hu
We develop structure-preserving finite element methods for the incompressible, resistive Hall magnetohydrodynamics (MHD) equations. These equations incorporate the Hall current ter…
An augmented Lagrangian preconditioner for the magnetohydrodynamics equations at high Reynolds and coupling numbers
Fabian Laakmann, Patrick E. Farrell, Lawrence Mitchell
The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve numerically, due to their highly nonlinear structure and the strong coupling between the elect…
Efficient Approximation of Solutions of Parametric Linear Transport Equations by ReLU DNNs
Fabian Laakmann, Philipp Petersen
We demonstrate that deep neural networks with the ReLU activation function can efficiently approximate the solutions of various types of parametric linear transport equations. For…