86 citations · 109 across the 10 of their papers we have counts for
9 papers · 1 filter
The multi-index Monte Carlo method for semilinear stochastic partial differential equations
Abdul-Lateef Haji-Ali, Håkon Hoel, Andreas Petersson
Stochastic partial differential equations (SPDEs) are often difficult to solve numerically due to their low regularity and high dimensionality. These challenges limit the practical…
Higher-order adaptive methods for exit times of Itô diffusions
Håkon Hoel, Sankarasubramanian Ragunathan
We construct a higher-order adaptive method for strong approximations of exit times of Itô stochastic differential equations (SDE). The method employs a strong Itô--Taylor scheme f…
Improved Efficiency of Multilevel Monte Carlo for Stochastic PDE through Strong Pairwise Coupling
Neil K. Chada, Håkon Hoel, Ajay Jasra +1
Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-k…
Multi-index ensemble Kalman filtering
Håkon Hoel, Gaukhar Shaimerdenova, Raúl Tempone
In this work we combine ideas from multi-index Monte Carlo and ensemble Kalman filtering (EnKF) to produce a highly efficient filtering method called multi-index EnKF (MIEnKF). MIE…
Multilevel ensemble Kalman filtering for spatio-temporal processes
Alexey Chernov, Håkon Hoel, Kody J. H. Law +2
We design and analyse the performance of a multilevel ensemble Kalman filter method (MLEnKF) for filtering settings where the underlying state-space model is an infinite-dimensiona…
Computable error estimates for finite element approximations of elliptic partial differential equations with rough stochastic data
Eric Joseph Hall, Håkon Hoel, Mattias Sandberg +2
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting,…
Multilevel ensemble Kalman filtering
Håkon Hoel, Kody J. H. Law, Raul Tempone
This work embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and…
Construction of a Mean Square Error Adaptive Euler--Maruyama Method with Applications in Multilevel Monte Carlo
Håkon Hoel, Juho Häppölä, Raúl Tempone
A formal mean square error expansion (MSE) is derived for Euler--Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a…
Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces
Christian Bayer, Hakon Hoel, Ashraful Kadir +3
The difference of the values of observables for the time-independent Schroedinger equation, with matrix valued potentials, and the values of observables for ab initio Born-Oppenhei…