86 citations · 301 across the 37 of their papers we have counts for
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MDFEM: Multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM
Dong T. P. Nguyen, Dirk Nuyens
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used t…
Strang splitting in combination with rank- and rank- lattices for the time-dependent Schrödinger equation
Yuya Suzuki, Gowri Suryanarayana, Dirk Nuyens
We approximate the solution for the time dependent Schrödinger equation (TDSE) in two steps. We first use a pseudo-spectral collocation method that uses samples of functions on ran…
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…