Mar 13, 2018 Here, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assembly procedure and factorize each local mass matrix independently, hence avoiding the factorization of a large matrix.
Efficient White Noise Sampling and Coupling for Multilevel Monte Carlo with Nonnested Meshes | SIAM/ASA Journal on Uncertainty Quantification | Vol. 6, No. 4 | Society for Industrial and Applied Mathematics. solved using the FEM as it might be possible to reuse finite element bases and computations for both equations.
Here, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method (FEM) and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assembly procedure and factorize each local mass matrix independently, hence avoiding the factorization of a large ...
Here, we present a new sampling technique that can be used to effi-ciently compute white noise samples in a finite element method and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assem-bly procedure and factorize each local mass matrix independently, hence avoiding the factorization of a large matrix.
Mar 13, 2018 Here, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method and multilevel Monte Carlo (MLMC) setting. The key...
E cient white noise sampling and coupling for multilevel Monte Carlo M. Croci (Oxford), M. B. Giles (Oxford), P. E. Farrell (Oxford), M. E. Rognes (Simula) MCQMC2018 - July 4, 2018 EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling
ciently compute white noise samples in a nite element method and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the nite element matrix assem-
In this talk we present a novel sampling technique that can be used to efficiently compute white noise samples in a finite element and multilevel Monte Carlo (MLMC) setting. After discretization, the action of white noise on a test function yields a Gaussian vector with the FEM mass matrix as covariance.
Here, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method (FEM) and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assembly procedure and factorize each local mass matrix independently, hence avoiding the factorization of a large ...
Research. Efficient white noise sampling and coupling for multilevel Monte Carlo with non-nested meshes. Authors. M. Croci, M. B. Giles, M. E. Rognes and P. E. Farrell. Status. Published. Publication type. Journal Article. Year of publication. 2018. Journal. SIAM Journal on Uncertainty Quantification. Publisher. SIAM. Citation key. 14942.
'Multilevel quasi Monte Carlo methods for elliptic PDEs with random field coefficients via fast white noise sampling'. SIAM Journal on Scientific Computing, 43(4), A2840-A2868, 2021. link. This paper develops a wavelet representation of white noise to provide a consistent Multilevel Monte Carlo coupling for improved variance reduction.
Efficient white noise sampling and coupling for multilevel Monte Carlo with non-nested meshes CROCI, M GILES, M Rognes, M Farrell, P SIAM/ASA Journal on Uncertainty Quantification volume 6 issue 4 1630-1655 (20 Nov 2018)
Here, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method (FEM) and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assembly procedure and factorize each local mass matrix independently, hence avoiding the fa...
M. Croci, M.B. Giles, M.E. Rognes, P.E. Farrell. 'Efficient white noise sampling and coupling for multilevel Monte Carlo with non-nested meshes'. SIAM/ASA Journal on Uncertainty Quantification, 6(4):1454-1474, 2018. link; M. Croci, M.B. Giles, P.E. Farrell.
In the first, we develop two new strategies for spatial white noise and Gaussian-Mat\'ern field sampling that work within a non-nested multilevel (quasi) Monte Carlo (ML (Q)MC) hierarchy. In the second, we apply the techniques developed to quantify the level of uncertainty in a new stochastic model for tracer transport in the brain.
Aug 20, 2020 In this work, we propose a novel importance sampling (IS) algorithm that can be combined with the multilevel Monte Carlo (MLMC) estimator to numerically solve stochastic differential equations (SDEs) driven by Poisson random measures (Li 2007; nlar 2011 ).
Our new hierarchical multilevel method relies on a hierarchical decomposition of the white noise source function in L 2 which allows us to form Gaussian random field realizations across multiple levels of discretization in a way that fits into multilevel MCMC algorithmic frameworks.
Jan 1, 2021 Our method uses the stochastic PDE (SPDE) approach of Lindgren et al. combined with a new fast algorithm for white noise sampling which is tailored to (ML)QMC. We express white noise as a wavelet series expansion that we divide into two parts.
Sep 14, 2018 Here, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assembly procedure and factorize each local mass matrix independently, hence avoiding the factorization of a large matrix.
Aug 20, 2020 Our theoretical results, along with the conducted numerical experiments, demonstrate that our proposed method significantly reduces the kurtosis of the deep levels of MLMC, and also improves the strong convergence rate from =1 for the standard case (without IS), to =1+, where 0<<1 is a user-selected parameter in our IS algorithm.
Here, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method (FEM) and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assembly procedure and factorize each local mass matrix independently, hence avoiding the facto
Our method uses the stochastic PDE (SPDE) approach of Lindgren et al. combined with a new fast algorithm for white noise sampling which is tailored to (ML)QMC. We express white noise as a wavelet series expansion that we divide into two parts.
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