Publications
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Random-prime–fixed-vector randomised lattice-based algorithm for high-dimensional integration KU Leuven
We show that a very simple randomised algorithm for numerical integration can produce a near optimal rate of convergence for integrals of functions in the d-dimensional weighted Korobov space. This algorithm uses a lattice rule with a fixed generating vector and the only random element is the choice of the number of function evaluations. For a given computational budget n of a maximum allowed number of function evaluations, we uniformly pick a ...
Convergence of the Micro-Macro Parareal Method for a Linear Scale-Separated Ornstein-Uhlenbeck SDE KU Leuven
Time-parallel methods can reduce the wall clock time required for the accurate numerical solution of differential equations by parallelizing across the time-dimension. In this paper, we present and test the convergence behavior of a multiscale, micro-macro version of a Parareal method for stochastic differential equations (SDEs). In our method, the fine propagator of the SDE is based on a high-dimensional slow-fast microscopic model; the coarse ...
An SQP-based multiple shooting algorithm for large-scale PDE-constrained optimal control problems KU Leuven
Multi-fidelity microstructure-induced uncertainty quantification by advanced Monte Carlo methods KU Leuven
A parallel-in-time multiple shooting algorithm for large-scale PDE-constrained optimal control problems KU Leuven
Multiple shooting methods for solving optimal control problems governed by ODEs have been extensively studied in past decades. However, their application for solving large-scale PDE-based optimal control problems still faces many challenges, including the difficulty of solving large scale equality constrained optimization problems in an efficient parallelizable way. The current work proposes and analyzes a new parallel-in-time multiple shooting ...