73 citations · 348 across the 17 of their papers we have counts for
19 papers
Optimal control under uncertainty with joint chance state constraints: almost-everywhere bounds, variance reduction, and application to (bi-)linear elliptic PDEs
Rene Henrion, Georg Stadler, Florian Wechsung
We study optimal control of PDEs under uncertainty with the state variable subject to joint chance constraints. The controls are deterministic, but the states are probabilistic due…
Meta variance reduction for Monte Carlo estimation of energetic particle confinement during stellarator optimization
Frederick Law, Antoine Cerfon, Benjamin Peherstorfer +1
This work introduces meta estimators that combine multiple multifidelity techniques based on control variates, importance sampling, and information reuse to yield a quasi-multiplic…
Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry
Andrew Giuliani, Florian Wechsung, Antoine Cerfon +2
We present a robust optimization algorithm for the design of electromagnetic coils that generate vacuum magnetic fields with nested flux surfaces and precise quasi-symmetry. The me…
Permanent magnet optimization for stellarators as sparse regression
Alan A. Kaptanoglu, Tony Qian, Florian Wechsung +1
A common scientific inverse problem is the placement of magnets that produce a desired magnetic field inside a prescribed volume. This is a key component of stellarator design, and…
Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry
Andrew Giuliani, Florian Wechsung, Matt Landreman +2
We propose a new method to compute magnetic surfaces that are parametrized in Boozer coordinates for vacuum magnetic fields. We also propose a measure for quasi-symmetry on the com…
Stochastic and a posteriori optimization to mitigate coil manufacturing errors in stellarator design
Florian Wechsung, Andrew Giuliani, Matt Landreman +2
It was recently shown in [Wechsung et. al., Proc. Natl. Acad. Sci. USA, 2022] that there exist electromagnetic coils that generate magnetic fields which are excellent approximation…
Robust multigrid techniques for augmented Lagrangian preconditioning of incompressible Stokes equations with extreme viscosity variations
Yu-hsuan Shih, Georg Stadler, Florian Wechsung
We present augmented Lagrangian Schur complement preconditioners and robust multigrid methods for incompressible Stokes problems with extreme viscosity variations. Such Stokes syst…
Single-stage gradient-based stellarator coil design: stochastic optimization
Florian Wechsung, Andrew Giuliani, Matt Landreman +2
We extend the single-stage stellarator coil design approach for quasi-symmetry on axis from [Giuliani et al, 2020] to additionally take into account coil manufacturing errors. By m…
Single-stage gradient-based stellarator coil design: Optimization for near-axis quasi-symmetry
Andrew Giuliani, Florian Wechsung, Antoine Cerfon +2
We present a new coil design paradigm for magnetic confinement in stellarators. Our approach directly optimizes coil shapes and coil currents to produce a vacuum quasi-symmetric ma…
Fireshape: a shape optimization toolbox for Firedrake
Alberto Paganini, Florian Wechsung
We introduce Fireshape, an open-source and automated shape optimization toolbox for the finite element software Firedrake. Fireshape is based on the moving mesh method and allows u…
A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations
Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scott +1
Augmented Lagrangian preconditioners have successfully yielded Reynolds-robust preconditioners for the stationary incompressible Navier-Stokes equations, but only for specific disc…
Augmented Lagrangian preconditioners for the Oseen-Frank model of nematic and cholesteric liquid crystals
Jingmin Xia, Patrick E. Farrell, Florian Wechsung
We propose a robust and efficient augmented Lagrangian-type preconditioner for solving linearizations of the Oseen-Frank model arising in cholesteric liquid crystals. By applying t…
Robust multigrid methods for nearly incompressible elasticity using macro elements
Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scott +1
We present a mesh-independent and parameter-robust multigrid solver for the Scott-Vogelius discretisation of the nearly incompressible linear elasticity equations on meshes with a…
PCPATCH: software for the topological construction of multigrid relaxation methods
Patrick E. Farrell, Matthew G. Knepley, Lawrence Mitchell +1
Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß-Seidel are inadequate, and more sophisticated space decompos…
An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at high Reynolds number
Patrick E. Farrell, Lawrence Mitchell, Florian Wechsung
In Benzi & Olshanskii (SIAM J.~Sci.~Comput., 28(6) (2006)) a preconditioner of augmented Lagrangian type was presented for the two-dimensional stationary incompressible Navier--Sto…
Automated shape differentiation in the Unified Form Language
David A. Ham, Lawrence Mitchell, Alberto Paganini +1
We discuss automating the calculation of weak shape derivatives in the Unified Form Language (Alnæs et al., ACM Trans. Math. Softw., 2014) by introducing an appropriate additional…
Shape optimisation with nearly conformal transformations
José A. Iglesias, Kevin Sturm, Florian Wechsung
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations…
Higher-order moving mesh methods for PDE-constrained shape optimization
A. Paganini, F. Wechsung, P. E. Farrell
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatib…
A robust parallel algorithm for combinatorial compressed sensing
Rodrigo Mendoza-Smith, Jared Tanner, Florian Wechsung
In previous work two of the authors have shown that a vector with at most nonzeros can be recovered from an expander sketch in $\mathcal{O}(\mathr…