6 papers
Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory
Tobias Hartung, Karl Jansen, Frances Y. Kuo +3
High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class o…
Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness
Adrian Ebert, Peter Kritzer, Dirk Nuyens +1
Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-1 lattice rule to approximate an -dimensional integr…
Fast component-by-component construction of lattice algorithms for multivariate approximation with POD and SPOD weights
Ronald Cools, Frances Y. Kuo, Dirk Nuyens +1
In a recent paper by the same authors, we provided a theoretical foundation for the component-by-component (CBC) construction of lattice algorithms for multivariate approxima…
Function integration, reconstruction and approximation using rank-1 lattices
Frances Y. Kuo, Giovanni Migliorati, Fabio Nobile +1
We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fo…
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…
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…