Details
| Original language | English |
|---|---|
| Pages (from-to) | 937-949 |
| Number of pages | 13 |
| Journal | Computational mechanics |
| Volume | 64 |
| Issue number | 4 |
| Early online date | 25 Feb 2019 |
| Publication status | Published - 1 Oct 2019 |
Abstract
In this paper, we employ the multilevel Monte Carlo finite element method to solve the stochastic Cahn–Hilliard–Cook equation. The Ciarlet–Raviart mixed finite element method is applied to solve the fourth-order equation. In order to estimate the mild solution, we use finite elements for space discretization and the semi-implicit Euler–Maruyama method in time. For the stochastic scheme, we use the multilevel method to decrease the computational cost (compared to the Monte Carlo method). We implement the method to solve three specific numerical examples (both two- and three dimensional) and study the effect of different noise measures.
Keywords
- Cahn–Hilliard–Cook equation, Euler–Maruyama method, Finite element, Multilevel Monte Carlo, Time discretization
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 64, No. 4, 01.10.2019, p. 937-949.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation
AU - Khodadadian, Amirreza
AU - Parvizi, Maryam
AU - Abbaszadeh, Mostafa
AU - Dehghan, Mehdi
AU - Heitzinger, Clemens
N1 - Funding Information: Open access funding provided by Austrian Science Fund (FWF). The first and the last authors acknowledge support by FWF (Austrian Science Fund) START Project No. Y660 PDE Models for Nanotechnology. The second author also acknowledges support by FWF Project No. P28367-N35.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - In this paper, we employ the multilevel Monte Carlo finite element method to solve the stochastic Cahn–Hilliard–Cook equation. The Ciarlet–Raviart mixed finite element method is applied to solve the fourth-order equation. In order to estimate the mild solution, we use finite elements for space discretization and the semi-implicit Euler–Maruyama method in time. For the stochastic scheme, we use the multilevel method to decrease the computational cost (compared to the Monte Carlo method). We implement the method to solve three specific numerical examples (both two- and three dimensional) and study the effect of different noise measures.
AB - In this paper, we employ the multilevel Monte Carlo finite element method to solve the stochastic Cahn–Hilliard–Cook equation. The Ciarlet–Raviart mixed finite element method is applied to solve the fourth-order equation. In order to estimate the mild solution, we use finite elements for space discretization and the semi-implicit Euler–Maruyama method in time. For the stochastic scheme, we use the multilevel method to decrease the computational cost (compared to the Monte Carlo method). We implement the method to solve three specific numerical examples (both two- and three dimensional) and study the effect of different noise measures.
KW - Cahn–Hilliard–Cook equation
KW - Euler–Maruyama method
KW - Finite element
KW - Multilevel Monte Carlo
KW - Time discretization
UR - http://www.scopus.com/inward/record.url?scp=85062146029&partnerID=8YFLogxK
U2 - 10.1007/s00466-019-01688-1
DO - 10.1007/s00466-019-01688-1
M3 - Article
AN - SCOPUS:85062146029
VL - 64
SP - 937
EP - 949
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 4
ER -