An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem

[EN] Problems in civil engineering are often characterized by significant uncertainty in their material parameters. Sampling methods are a straightforward manner to account for this uncertainty, which is typically modeled as a random field. A popular sampling method consists of the classic Multileve...

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Detalles Bibliográficos
Autores: Blondeel, Philippe, Robbe, Pieterjan, François, Stijn, Lombaert, Geert, Vandewalle, Stefan
Tipo de recurso: capítulo de libro
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/186593
Acceso en línea:https://riunet.upv.es/handle/10251/186593
Access Level:acceso abierto
Palabra clave:Multilevel Quasi-Monte Carlo
P-refinement
Uncertainty Quantification
Higher Order Finite Elements
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spelling An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability ProblemBlondeel, PhilippeRobbe, PieterjanFrançois, StijnLombaert, GeertVandewalle, StefanMultilevel Quasi-Monte CarloP-refinementUncertainty QuantificationHigher Order Finite Elements[EN] Problems in civil engineering are often characterized by significant uncertainty in their material parameters. Sampling methods are a straightforward manner to account for this uncertainty, which is typically modeled as a random field. A popular sampling method consists of the classic Multilevel Monte Carlo method (h-MLMC). Its most distinctive feature consists of a hierarchy of h-refined meshes, where most of the samples are taken on coarse and computationally inexpensive meshes, and few are taken on finer but computationally expensive meshes. We present an improvement upon the classic Multilevel Monte Carlo, called the prefined Multilevel quasi-Monte Carlo method (p-MLQMC). Its key features consist of a mesh hierarchy constructed from a p-refinement scheme combined with a deterministic set of samples points (quasi-Monte Carlo points). In this work we show how the uncertainty needs to be accounted for and present results comparing the total computational cost of the h-ML(Q)MC and p-MLQMC method. Specifically, we present two novel approaches in order to account for the uncertainty in case of p-MLQMC. We benchmarking the different multilevel methods on a slope stability problem, and find that p-MLQMC outperforms h-MLMC up to several orders of magnitude.The authors gratefully acknowledge the support from the Research Council of KU Leuven through project C16/17/008 “Efficient methods for large-scale PDE-constrained optimization in the presence of uncertainty and complex technological constraints”. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government – department EWI.Editorial Universitat Politècnica de ValènciaResearch Foundation FlandersKU LeuvenRepositorio Institucional de la Universitat Politècnica de València Riunet20222022-05-11book parthttp://purl.org/coar/resource_type/c_3248VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/bookPartapplication/pdfhttps://riunet.upv.es/handle/10251/186593reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengKU Leuven KU Leuven C16%2F17%2F008open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Compartir igual (by-nc-sa) http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1865932026-06-13T07:49:27Z
dc.title.none.fl_str_mv An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem
title An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem
spellingShingle An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem
Blondeel, Philippe
Multilevel Quasi-Monte Carlo
P-refinement
Uncertainty Quantification
Higher Order Finite Elements
title_short An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem
title_full An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem
title_fullStr An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem
title_full_unstemmed An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem
title_sort An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem
dc.creator.none.fl_str_mv Blondeel, Philippe
Robbe, Pieterjan
François, Stijn
Lombaert, Geert
Vandewalle, Stefan
author Blondeel, Philippe
author_facet Blondeel, Philippe
Robbe, Pieterjan
François, Stijn
Lombaert, Geert
Vandewalle, Stefan
author_role author
author2 Robbe, Pieterjan
François, Stijn
Lombaert, Geert
Vandewalle, Stefan
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Research Foundation Flanders
KU Leuven
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Multilevel Quasi-Monte Carlo
P-refinement
Uncertainty Quantification
Higher Order Finite Elements
topic Multilevel Quasi-Monte Carlo
P-refinement
Uncertainty Quantification
Higher Order Finite Elements
description [EN] Problems in civil engineering are often characterized by significant uncertainty in their material parameters. Sampling methods are a straightforward manner to account for this uncertainty, which is typically modeled as a random field. A popular sampling method consists of the classic Multilevel Monte Carlo method (h-MLMC). Its most distinctive feature consists of a hierarchy of h-refined meshes, where most of the samples are taken on coarse and computationally inexpensive meshes, and few are taken on finer but computationally expensive meshes. We present an improvement upon the classic Multilevel Monte Carlo, called the prefined Multilevel quasi-Monte Carlo method (p-MLQMC). Its key features consist of a mesh hierarchy constructed from a p-refinement scheme combined with a deterministic set of samples points (quasi-Monte Carlo points). In this work we show how the uncertainty needs to be accounted for and present results comparing the total computational cost of the h-ML(Q)MC and p-MLQMC method. Specifically, we present two novel approaches in order to account for the uncertainty in case of p-MLQMC. We benchmarking the different multilevel methods on a slope stability problem, and find that p-MLQMC outperforms h-MLMC up to several orders of magnitude.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-05-11
dc.type.none.fl_str_mv book part
http://purl.org/coar/resource_type/c_3248
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/186593
url https://riunet.upv.es/handle/10251/186593
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv KU Leuven KU Leuven C16%2F17%2F008
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Editorial Universitat Politècnica de València
publisher.none.fl_str_mv Editorial Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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