9 citations · 21 across the 9 of their papers we have counts for
12 papers
On the Selection of Random Field Evaluation Points in the p-MLQMC Method
Philippe Blondeel, Pieterjan Robbe, Stijn François +2
Engineering problems are often characterized by significant uncertainty in their material parameters. A typical example coming from geotechnical engineering is the slope stability…
MG/OPT and MLMC for Robust Optimization of PDEs
Andreas Van Barel, Stefan Vandewalle
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The le…
Enhanced Multi-Index Monte Carlo by means of Multiple Semi-Coarsened Multigrid for Anisotropic Diffusion Problems
Pieterjan Robbe, Dirk Nuyens, Stefan Vandewalle
In many models used in engineering and science, material properties are uncertain or spatially varying. For example, in geophysics, and porous media flow in particular, the uncerta…
A multilevel Monte Carlo method for asymptotic-preserving particle schemes in the diffusive limit
Emil Løvbak, Giovanni Samaey, Stefan Vandewalle
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional re…
h- and p-refined Multilevel Monte Carlo Methods for Uncertainty Quantification in Structural Engineering
Philippe Blondeel, Pieterjan Robbe, Cédric van hoorickx +2
Practical structural engineering problems are often characterized by significant uncertainties. Historically, one of the prevalent methods to account for this uncertainty has been…
Multilevel Monte Carlo for uncertainty quantification in structural engineering
Philippe Blondeel, Pieterjan Robbe, Cédric van hoorickx +2
Practical structural engineering problems often exhibit a significant degree of uncertainty in the material properties being used, the dimensions of the modeled structures, etc. In…
Recycling Samples in the Multigrid Multilevel (Quasi-)Monte Carlo Method
Pieterjan Robbe, Dirk Nuyens, Stefan Vandewalle
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantifi…
Robust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo Method
Andreas Van Barel, Stefan Vandewalle
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average cont…
A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger
Pieterjan Robbe, Dirk Nuyens, Stefan Vandewalle
We present an adaptive version of the Multi-Index Monte Carlo method, introduced by Haji-Ali, Nobile and Tempone (2016), for simulating PDEs with coefficients that are random field…
A Multi-Index Quasi-Monte Carlo Algorithm for Lognormal Diffusion Problems
Pieterjan Robbe, Dirk Nuyens, Stefan Vandewalle
We present a Multi-Index Quasi-Monte Carlo method for the solution of elliptic partial differential equations with random coefficients. By combining the multi-index sampling idea w…
Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials
Haiyong Wang, Daan Huybrechs, Stefan Vandewalle
Barycentric interpolation is arguably the method of choice for numerical polynomial interpolation. The polynomial interpolant is expressed in terms of function values using the so-…
Schwarz Methods: To Symmetrize or Not to Symmetrize
Michael Holst, Stefan Vandewalle
A preconditioning theory is presented which establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditio…