R
Robert Scheichl
Researcher at Heidelberg University
Publications - 154
Citations - 4324
Robert Scheichl is an academic researcher from Heidelberg University. The author has contributed to research in topics: Monte Carlo method & Multigrid method. The author has an hindex of 29, co-authored 142 publications receiving 3680 citations. Previous affiliations of Robert Scheichl include University of Tartu & University of Bath.
Papers
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Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
TL;DR: A novel variance reduction technique for the standard Monte Carlo method, called the multilevel Monte Carlo Method, is described, and numerically its superiority is demonstrated.
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Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
TL;DR: It is proved that convergence of the multilevel Monte Carlo algorithm for estimating any bounded, linear functional and any continuously Fréchet differentiable non-linear functional of the solution is convergence.
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Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods
TL;DR: A finite element approximation of elliptic partial differential equations with random coefficients is considered, which is used to perform a rigorous analysis of the multilevel Monte Carlo method for these elliptic problems that lack full regularity and uniform coercivity and boundedness.
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Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps
Nicole Spillane,Victorita Dolean,Patrice Hauret,Frédéric Nataf,Clemens Pechstein,Robert Scheichl +5 more
TL;DR: This work introduces in a variational setting a new coarse space that is robust even when there are such heterogeneities in the PDE coefficients, by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence.
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Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
TL;DR: Numerical experiments are reported, showing that the quasi-Monte Carlo method consistently outperforms the Monte Carlo method, with a smaller error and a noticeably better than O(N^-^1^/^2) convergence rate.