Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries

We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty quantification results to tackle the efficient solution of such problem...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2018-07
Main Authors: Chaudhry, Jehanzeb H, Burch, Nathanial, Estep, Donald
Format: Article
Language:English
Subjects:
Boundaries
Boundary value problems
Domains
Error analysis
Partial differential equations
Transformations (mathematics)
Uncertainty
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Chaudhry, Jehanzeb H
Burch, Nathanial
Estep, Donald
description We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty quantification results to tackle the efficient solution of such problems. We introduce simple transformations that map a family of domains with stochastic boundaries to a fixed reference domain. We exploit the transformations to carry out a prior and a posteriori error analyses and to derive an efficient Monte Carlo sampling procedure.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2074054461</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2074054461</sourcerecordid><originalsourceid>FETCH-proquest_journals_20740544613</originalsourceid><addsrcrecordid>eNqNi8sKwjAQRYMgKOo_DLgWYvrQtVpxqajrEtsUR9pEMxNE8OOtjw9wdS-cczqir6JoOpnHSvXEiOgipVTpTCVJ1BfPrKqwQGMZVkjs8RQYnYWMGBv9udqWcLSF8azR8gN2QVvGtvriynnI6hqvjAVsvTvVpiFowco1bUBwRz7Dnl1x1vR2Fi7YUns0NBTdStdkRr8diPE6Oyw3k6t3t2CI84sL3rYoV3IWyySO02n0n_UCgfxQWw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2074054461</pqid></control><display><type>article</type><title>Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries</title><source>Publicly Available Content Database</source><creator>Chaudhry, Jehanzeb H ; Burch, Nathanial ; Estep, Donald</creator><creatorcontrib>Chaudhry, Jehanzeb H ; Burch, Nathanial ; Estep, Donald</creatorcontrib><description>We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty quantification results to tackle the efficient solution of such problems. We introduce simple transformations that map a family of domains with stochastic boundaries to a fixed reference domain. We exploit the transformations to carry out a prior and a posteriori error analyses and to derive an efficient Monte Carlo sampling procedure.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Boundaries ; Boundary value problems ; Domains ; Error analysis ; Partial differential equations ; Transformations (mathematics) ; Uncertainty</subject><ispartof>arXiv.org, 2018-07</ispartof><rights>2018. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2074054461?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>776,780,25731,36989,44566</link.rule.ids></links><search><creatorcontrib>Chaudhry, Jehanzeb H</creatorcontrib><creatorcontrib>Burch, Nathanial</creatorcontrib><creatorcontrib>Estep, Donald</creatorcontrib><title>Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries</title><title>arXiv.org</title><description>We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty quantification results to tackle the efficient solution of such problems. We introduce simple transformations that map a family of domains with stochastic boundaries to a fixed reference domain. We exploit the transformations to carry out a prior and a posteriori error analyses and to derive an efficient Monte Carlo sampling procedure.</description><subject>Boundaries</subject><subject>Boundary value problems</subject><subject>Domains</subject><subject>Error analysis</subject><subject>Partial differential equations</subject><subject>Transformations (mathematics)</subject><subject>Uncertainty</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNi8sKwjAQRYMgKOo_DLgWYvrQtVpxqajrEtsUR9pEMxNE8OOtjw9wdS-cczqir6JoOpnHSvXEiOgipVTpTCVJ1BfPrKqwQGMZVkjs8RQYnYWMGBv9udqWcLSF8azR8gN2QVvGtvriynnI6hqvjAVsvTvVpiFowco1bUBwRz7Dnl1x1vR2Fi7YUns0NBTdStdkRr8diPE6Oyw3k6t3t2CI84sL3rYoV3IWyySO02n0n_UCgfxQWw</recordid><startdate>20180713</startdate><enddate>20180713</enddate><creator>Chaudhry, Jehanzeb H</creator><creator>Burch, Nathanial</creator><creator>Estep, Donald</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20180713</creationdate><title>Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries</title><author>Chaudhry, Jehanzeb H ; Burch, Nathanial ; Estep, Donald</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20740544613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Boundaries</topic><topic>Boundary value problems</topic><topic>Domains</topic><topic>Error analysis</topic><topic>Partial differential equations</topic><topic>Transformations (mathematics)</topic><topic>Uncertainty</topic><toplevel>online_resources</toplevel><creatorcontrib>Chaudhry, Jehanzeb H</creatorcontrib><creatorcontrib>Burch, Nathanial</creatorcontrib><creatorcontrib>Estep, Donald</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chaudhry, Jehanzeb H</au><au>Burch, Nathanial</au><au>Estep, Donald</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries</atitle><jtitle>arXiv.org</jtitle><date>2018-07-13</date><risdate>2018</risdate><eissn>2331-8422</eissn><abstract>We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty quantification results to tackle the efficient solution of such problems. We introduce simple transformations that map a family of domains with stochastic boundaries to a fixed reference domain. We exploit the transformations to carry out a prior and a posteriori error analyses and to derive an efficient Monte Carlo sampling procedure.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2018-07
issn 2331-8422
language eng
recordid cdi_proquest_journals_2074054461
source Publicly Available Content Database
subjects Boundaries
Boundary value problems
Domains
Error analysis
Partial differential equations
Transformations (mathematics)
Uncertainty
title Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-12T19%3A31%3A19IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Efficient%20Distribution%20Estimation%20and%20Uncertainty%20Quantification%20for%20Elliptic%20Problems%20on%20Domains%20with%20Stochastic%20Boundaries&rft.jtitle=arXiv.org&rft.au=Chaudhry,%20Jehanzeb%20H&rft.date=2018-07-13&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2074054461%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_20740544613%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2074054461&rft_id=info:pmid/&rfr_iscdi=true