Multilevel Monte Carlo methods for highly heterogeneous media

A.L. Teckentrup

doi:10.1109/WSC.2012.6465298

Multilevel Monte Carlo methods for highly heterogeneous media

A.L. Teckentrup

Department of Mathematical Sciences

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

7 Citations (SciVal)

Abstract

We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief review of recent advances in the numerical analysis of the multilevel algorithm under minimal assumptions on the random coefficient, and extend the analysis to cover also tensor-valued coefficients, as well as point evaluations. Our analysis includes as an example log-normal random coefficients, which are frequently used in applications.

Original language	English
Title of host publication	Proceedings of the 2012 Winter Simulation Conference (WSC)
Publisher	IEEE
ISBN (Print)	9781467347792
DOIs	https://doi.org/10.1109/WSC.2012.6465298
Publication status	Published - 2012
Event	2012 Winter Simulation Conference, WSC 2012 - Berlin, Germany Duration: 9 Dec 2012 → 12 Dec 2012

Conference

Conference	2012 Winter Simulation Conference, WSC 2012
Country/Territory	Germany
City	Berlin
Period	9/12/12 → 12/12/12

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10.1109/WSC.2012.6465298

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AB - We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief review of recent advances in the numerical analysis of the multilevel algorithm under minimal assumptions on the random coefficient, and extend the analysis to cover also tensor-valued coefficients, as well as point evaluations. Our analysis includes as an example log-normal random coefficients, which are frequently used in applications.

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M3 - Chapter in a published conference proceeding

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T2 - 2012 Winter Simulation Conference, WSC 2012

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ER -

Multilevel Monte Carlo methods for highly heterogeneous media

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