scholarly journals Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians

2017 ◽  
pp. 333-353 ◽  
Author(s):  
Anna Breger ◽  
Martin Ehler ◽  
Manuel Gräf
Keyword(s):  
Monte Carlo ◽  
Function Approximation ◽  
Monte Carlo Integration ◽  
Quasi Monte Carlo

Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion

2019 ◽  
Vol 77 (1) ◽  
pp. 144-172 ◽  
Author(s):  
Josef Dick ◽  
Robert N. Gantner ◽  
Quoc T. Le Gia ◽  
Christoph Schwab
Keyword(s):  
Monte Carlo ◽  
Higher Order ◽  
Monte Carlo Integration ◽  
Quasi Monte Carlo

Quasi-Monte Carlo Integration

1995 ◽  
Vol 122 (2) ◽  
pp. 218-230 ◽  
Author(s):  
William J. Morokoff ◽  
Russel E. Caflisch
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Integration ◽  
Quasi Monte Carlo

Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients

2019 ◽  
Vol 53 (5) ◽  
pp. 1507-1552 ◽  
Author(s):  
L. Herrmann ◽  
C. Schwab
Keyword(s):  
Monte Carlo ◽  
Random Field ◽  
Gaussian Random Field ◽  
Function Spaces ◽  
Monte Carlo Integration ◽  
Superior Performance ◽  
Elliptic Pdes ◽  
Weighted Function ◽  
Weighted Function Spaces ◽  
Quasi Monte Carlo

We analyze the convergence rate of a multilevel quasi-Monte Carlo (MLQMC) Finite Element Method (FEM) for a scalar diffusion equation with log-Gaussian, isotropic coefficients in a bounded, polytopal domain D ⊂ ℝd. The multilevel algorithm QL* which we analyze here was first proposed, in the case of parametric PDEs with sequences of independent, uniformly distributed parameters in Kuo et al. (Found. Comput. Math. 15 (2015) 411–449). The random coefficient is assumed to admit a representation with locally supported coefficient functions, as arise for example in spline- or multiresolution representations of the input random field. The present analysis builds on and generalizes our single-level analysis in Herrmann and Schwab (Numer. Math. 141 (2019) 63–102). It also extends the MLQMC error analysis in Kuo et al. (Math. Comput. 86 (2017) 2827–2860), to locally supported basis functions in the representation of the Gaussian random field (GRF) in D, and to product weights in QMC integration. In particular, in polytopal domains D ⊂ ℝd, d=2,3, our analysis is based on weighted function spaces to describe solution regularity with respect to the spatial coordinates. These spaces allow GRFs and PDE solutions whose realizations become singular at edges and vertices of D. This allows for non-stationary GRFs whose covariance operators and associated precision operator are fractional powers of elliptic differential operators in D with boundary conditions on ∂D. In the weighted function spaces in D, first order, Lagrangian Finite Elements on regular, locally refined, simplicial triangulations of D yield optimal asymptotic convergence rates. Comparison of the ε-complexity for a class of Matérn-like GRF inputs indicates, for input GRFs with low sample regularity, superior performance of the present MLQMC-FEM with locally supported representation functions over alternative representations, e.g. of Karhunen–Loève type. Our analysis yields general bounds for the ε-complexity of the MLQMC algorithm, uniformly with respect to the dimension of the parameter space.

An Analysis of Quasi-Monte Carlo Integration Applied to the Transillumination Radiosity Method

1997 ◽  
Vol 16 (3) ◽  
pp. C271-C281 ◽  
Author(s):  
Laszlo Szirmay-Kalos ◽  
Tibor Foris ◽  
Laszlo Neumann ◽  
Balazs Csebfalvi
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Integration ◽  
Quasi Monte Carlo

Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique

2003 ◽  
Vol 18 (1-2) ◽  
pp. 13-26 ◽  
Author(s):  
Karl Entacher ◽  
Thomas Schell ◽  
Wolfgang Ch. Schmid ◽  
Andreas Uhl
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Integration ◽  
Quasi Monte Carlo

scholarly journals Good parameters for a class of node sets in quasi-Monte Carlo integration

1993 ◽  
Vol 61 (203) ◽  
pp. 225-225 ◽  
Author(s):  
Tom Hansen ◽  
Gary L. Mullen ◽  
Harald Niederreiter
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Integration ◽  
Quasi Monte Carlo
Sign in / Sign up

Export Citation Format

Share Document