Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries
Year: 2018
Type: article
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 prior and a posteriori error analyses and to derive an efficient Monte Carlo sampling procedure.
DOI: 10.1137/17m112230x
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, National Institutes of Health, Defense Threat Reduction Agency, National Institute of General Medical Sciences, Division of Graduate Education, Division of Mathematical Sciences, Division of Electrical, Communications and Cyber Systems, Laboratory Directed Research and Development, Lawrence Livermore National Laboratory, Sandia National Laboratories, Idaho National Laboratory
Awards: A POSTERIORI ANALYSIS OF INTERFACE EFFECTS IN THE DISCRETIZATION OF MULTI-SCALED AND ..., G1749322094, G1773705062, G192452586, FRG: Collaborative Research: Error Quantification and Control for Gravitational Waveform Simulation, Data-Driven Inverse Sensitivity Analysis for Predictive Coastal Ocean Modeling, G2121601026, G2155057524, G222768804, DIAMOND: AN INTEGRATED MULTIFACETED APPROACH TO MATHEMATICS AT THE INTERFACES OF DATA, MODELS, AND DECISIONS, G2494830535, G2589658540, Collaborative Research: Finite Element Methods for Discretizing Geometric PDEs with Nonlinear Constraints and Gauge Freedom, G2824489399, Computational Error Estimation and Adaptive Error Control for Multiscaled Differential Equations, A MATHEMATICAL ANALYSIS OF ATOMISTIC-TO-CONTINUUM (ATC) MULTISCALE COUPLING METHODS, G3298822666, Statistical and Applied Mathematical Sciences Institute, G3746531689, G3779931483, Topics in Econometrics and Macroeconomics, G3857635189, TAS::89 0222::TAS NEW; ENABLING PREDICTIVE SIMULATION AND UQ OF COMPLEX MULTIPHYSICS PDE SYSTEMS BY THE DEVELOPMENT OF GOAL-ORIENTED VARIATIONAL SENS, G4141397756, NEW; TITLE: COLLABORATIVE PROPOSAL: TRANSFORMING HOW CLIMATE SYSTEM MODELS ARE USED: A GLOBAL, MULTI-RESOLUTION APPROACH; PI - DONALD ESTEP, G4919938975, Collaborative Research: A posteriori error analysis and adaptivity for discontinuous interface problems, G5856312243, G6029871236, A POSTERIORI ANALYSIS OF INTERFACE EFFECTS INT HE DISCRETIZATION OF MULTI SCALED AND MULTI PHYSICS PROBLEMS BY DECOMPOSITION TECHNIQUES, FRAMEWORK APPLICATION FOR CORE-EDGE TRANSPORT SIMULATION (FACETS), G6708587567, G6756071164, Inverse Problem for Estimating Structure of Biological Macromolecules from SAXS, Partial Differential Equation Models for Large Networks, MSPA-CSE: Novel A Posteriori Analysis of Ecological Models: The Carbon Cycle, G7577457485, G7824369045, FRAMEWORK APPLICATION FOR CORE-EDGE TRANSPORT SIMULATIONS (FACETS), G7912466688, G8175191356, G8206070842, G8231574683, A MATHEMATICAL ANALYSIS OF ATOMISTIC TO CONTINUUM (ATC) MULTISCALE COUPLING METHODS, G8579847962, G8591261798, G8813213588
OpenAlex ID: W2884888100