An ensemble scheme for the numerical solution of a random transient heat equation with uncertain inputs

An ensemble-based time stepping scheme is applied to solving a transient heat equation with random Robin boundary and diffusion coefficients. By introducing two ensemble means of Robin boundary and diffusion coefficients, we propose a new ensemble Monte Carlo (EMC) scheme for the transient heat equa...

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Vydáno v:Numerical algorithms Ročník 94; číslo 2; s. 643 - 668
Hlavní autoři: Yao, Tingfu, Ye, Changlun, Luo, Xianbing, Xiang, Shuwen
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.10.2023
Springer Nature B.V
Témata:
Algebra
Algorithms
Approximation
Computer Science
Error analysis
Expected values
Heat
Hypotheses
Numeric Computing
Numerical Analysis
Original Paper
Random variables
Stability analysis
Theory of Computation
Thermodynamics
65C20
Monte Carlo method
Transient heat equation
Robin boundary coefficient
Ensemble
65M60
65C05
Diffusion coefficient
ISSN:1017-1398, 1572-9265
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Popis
Shrnutí:An ensemble-based time stepping scheme is applied to solving a transient heat equation with random Robin boundary and diffusion coefficients. By introducing two ensemble means of Robin boundary and diffusion coefficients, we propose a new ensemble Monte Carlo (EMC) scheme for the transient heat equation. The EMC scheme solves a single linear system including several right-side vectors at each time step. Stability analysis and error estimates are derived. Two numerical examples verify the theoretical results and the validity of the EMC method.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-023-01514-z