Markus Bambach, Stephan Gerster, Michael Herty, Aleksey Sikstel
{"title":"用多项式混沌展开描述随机水平集","authors":"Markus Bambach, Stephan Gerster, Michael Herty, Aleksey Sikstel","doi":"10.4310/cms.2024.v22.n1.a4","DOIUrl":null,"url":null,"abstract":"We present a novel approach to determine the evolution of level sets under uncertainties in their velocity fields. This leads to a stochastic description of level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the equations for the propagation of level sets. A novel intrusive Galerkin formulation is presented and proven to be hyperbolic. It induces a corresponding finite-volume scheme that is specifically tailored to uncertain velocities.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"149 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Description of random level sets by polynomial chaos expansions\",\"authors\":\"Markus Bambach, Stephan Gerster, Michael Herty, Aleksey Sikstel\",\"doi\":\"10.4310/cms.2024.v22.n1.a4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a novel approach to determine the evolution of level sets under uncertainties in their velocity fields. This leads to a stochastic description of level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the equations for the propagation of level sets. A novel intrusive Galerkin formulation is presented and proven to be hyperbolic. It induces a corresponding finite-volume scheme that is specifically tailored to uncertain velocities.\",\"PeriodicalId\":50659,\"journal\":{\"name\":\"Communications in Mathematical Sciences\",\"volume\":\"149 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/cms.2024.v22.n1.a4\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cms.2024.v22.n1.a4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Description of random level sets by polynomial chaos expansions
We present a novel approach to determine the evolution of level sets under uncertainties in their velocity fields. This leads to a stochastic description of level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the equations for the propagation of level sets. A novel intrusive Galerkin formulation is presented and proven to be hyperbolic. It induces a corresponding finite-volume scheme that is specifically tailored to uncertain velocities.
期刊介绍:
Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.