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04/18/2023
Diagonalization-based preconditioners and generalized convergence bounds for ParaOpt
The ParaOpt algorithm was recently introduced as a time-parallel solver ...
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03/25/2023
Pseudo-Marginal Approximation to the Free Energy in a Micro-Macro Markov Chain Monte Carlo Method
We introduce a generalised micro-macro Markov chain Monte Carlo (mM-MCMC...
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02/13/2023
On generalized preconditioners for time-parallel parabolic optimal control
The ParaDiag family of algorithms solves differential equations by using...
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02/11/2023
Hilbert expansion based fluid models for kinetic equations describing neutral particles in the plasma edge of a fusion device
Neutral particles in the plasma edge of fusion devices based on magnetic...
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02/06/2023
Reversible random number generation for adjoint Monte Carlo simulation of the heat equation
In PDE-constrained optimization, one aims to find design parameters that...
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10/15/2022
Projective Integration Methods in the Runge-Kutta Framework and the Extension to Adaptivity in Time
Projective Integration methods are explicit time integration schemes for...
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09/26/2022
Efficiency and Parameter Selection of a micro-macro Markov chain Monte Carlo method for molecular dynamics
We recently introduced a mM-MCMC scheme that is able to accelerate the s...
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05/24/2022
Accelerated simulation of Boltzmann-BGK equations near the diffusive limit with asymptotic-preserving multilevel Monte Carlo
Kinetic equations model the position-velocity distribution of particles ...
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08/29/2021
Spatially Adaptive Projective Integration Schemes For Stiff Hyperbolic Balance Laws With Spectral Gaps
Stiff hyperbolic balance laws exhibit large spectral gaps, especially if...
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12/16/2020
Kinetic-diffusion asymptotic-preserving Monte Carlo algorithm for Boltzmann-BGK in the diffusive scaling
We develop a novel Monte Carlo strategy for the simulation of the Boltzm...
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12/16/2020
A comparison of source term estimators in coupled finite-volume/Monte-Carlo methods with applications to plasma edge simulations in nuclear fusion
In many applications, such as plasma edge simulation of a nuclear fusion...
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08/24/2020
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
The data-driven discovery of partial differential equations (PDEs) consi...
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02/21/2020
A micro-macro Markov chain Monte Carlo method for molecular dynamics using reaction coordinate proposals I: direct reconstruction
We introduce a new micro-macro Markov chain Monte Carlo method (mM-MCMC)...
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12/19/2019
Parareal computation of stochastic differential equations with time-scale separation: a numerical study
The parareal algorithm is known to allow for a significant reduction in ...
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07/10/2019