Improved error estimates of ensemble Monte Carlo methods for random transient heat equations with uncertain inputs

Jinjun Yong; Changlun Ye; Xianbing Luo; Shuyu Sun

doi:10.1007/s40314-024-03022-9

Improved error estimates of ensemble Monte Carlo methods for random transient heat equations with uncertain inputs

Jinjun Yong, Changlun Ye, Xianbing Luo^*, Shuyu Sun

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The ensemble Monte Carlo (MC) method reduces computational cost by transforming multiple linear equations into a system with multiple right-hand-side (RHS) vectors. The existing error estimates of ensemble MC Euler and BDF2 methods for random heat equation are not optimal. In this paper, we improve and obtain the optimal error estimates of the numerical approximations for the ensemble MC Euler and BDF2 methods. To verify the efficiency of the methods and theoretical analyses, two numerical examples are listed.

Original language	English (US)
Article number	58
Journal	Computational and Applied Mathematics
Volume	44
Issue number	1
DOIs	https://doi.org/10.1007/s40314-024-03022-9
State	Published - Feb 2025

Keywords

Diffusion coefficient
Ensemble
Monte Carlo method
Optimal convergence rate
Transient heat equation
Uncertainty

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s40314-024-03022-9

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title = "Improved error estimates of ensemble Monte Carlo methods for random transient heat equations with uncertain inputs",

abstract = "The ensemble Monte Carlo (MC) method reduces computational cost by transforming multiple linear equations into a system with multiple right-hand-side (RHS) vectors. The existing error estimates of ensemble MC Euler and BDF2 methods for random heat equation are not optimal. In this paper, we improve and obtain the optimal error estimates of the numerical approximations for the ensemble MC Euler and BDF2 methods. To verify the efficiency of the methods and theoretical analyses, two numerical examples are listed.",

keywords = "Diffusion coefficient, Ensemble, Monte Carlo method, Optimal convergence rate, Transient heat equation, Uncertainty",

author = "Jinjun Yong and Changlun Ye and Xianbing Luo and Shuyu Sun",

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T1 - Improved error estimates of ensemble Monte Carlo methods for random transient heat equations with uncertain inputs

AU - Yong, Jinjun

AU - Ye, Changlun

AU - Luo, Xianbing

AU - Sun, Shuyu

N1 - Publisher Copyright: © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024.

PY - 2025/2

Y1 - 2025/2

N2 - The ensemble Monte Carlo (MC) method reduces computational cost by transforming multiple linear equations into a system with multiple right-hand-side (RHS) vectors. The existing error estimates of ensemble MC Euler and BDF2 methods for random heat equation are not optimal. In this paper, we improve and obtain the optimal error estimates of the numerical approximations for the ensemble MC Euler and BDF2 methods. To verify the efficiency of the methods and theoretical analyses, two numerical examples are listed.

AB - The ensemble Monte Carlo (MC) method reduces computational cost by transforming multiple linear equations into a system with multiple right-hand-side (RHS) vectors. The existing error estimates of ensemble MC Euler and BDF2 methods for random heat equation are not optimal. In this paper, we improve and obtain the optimal error estimates of the numerical approximations for the ensemble MC Euler and BDF2 methods. To verify the efficiency of the methods and theoretical analyses, two numerical examples are listed.

KW - Diffusion coefficient

KW - Ensemble

KW - Monte Carlo method

KW - Optimal convergence rate

KW - Transient heat equation

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=85211249529&partnerID=8YFLogxK

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DO - 10.1007/s40314-024-03022-9

M3 - Article

AN - SCOPUS:85211249529

SN - 2238-3603

VL - 44

JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

IS - 1

M1 - 58

ER -

Improved error estimates of ensemble Monte Carlo methods for random transient heat equations with uncertain inputs

Abstract

Keywords

ASJC Scopus subject areas

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