Modeling of cross-talk phenomena in thin film ferroelectric nanocapacitor arrays by finite element method combined with Monte Carlo calculations

2017 ◽  
Vol 122 (14) ◽  
pp. 144106
Author(s):  
Leontin Padurariu ◽  
Liliana Mitoseriu
Keyword(s):  
Thin Film ◽  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Cross Talk ◽  
Monte Carlo Calculations ◽  
Element Method

scholarly journals MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM

2021 ◽  
Author(s):  
Dong T.P. Nguyen ◽  
Dirk Nuyens
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Convergence Rates ◽  
Higher Order ◽  
Elliptic Pdes ◽  
Infinite Dimensional ◽  
Quasi Monte Carlo ◽  
Higher Order Convergence ◽  
Element Method

We introduce the \emph{multivariate decomposition finite element method} (MDFEM) for elliptic PDEs with lognormal diffusion coefficients, that is, when the diffusion coefficient has the form $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\bsy) = \sum_{j \ge 1} y_j \, \phi_j$ with $y_j \sim \calN(0,1)$ and a given sequence of functions $\{\phi_j\}_{j \ge 1}$. We use the MDFEM to approximate the expected value of a linear functional of the solution of the PDE which is an infinite-dimensional integral over the parameter space. The proposed algorithm uses the \emph{multivariate decomposition method} (MDM) to compute the infinite-dimensional integral by a decomposition into finite-dimensional integrals, which we resolve using \emph{quasi-Monte Carlo} (QMC) methods, and for which we use the \emph{finite element method} (FEM) to solve different instances of the PDE.   We develop higher-order quasi-Monte Carlo rules for integration over the finite-di\-men\-si\-onal Euclidean space with respect to the Gaussian distribution by use of a truncation strategy. By linear transformations of interlaced polynomial lattice rules from the unit cube to a multivariate box of the Euclidean space we achieve higher-order convergence rates for functions belonging to a class of \emph{anchored Gaussian Sobolev spaces} while taking into account the truncation error. These cubature rules are then used in the MDFEM algorithm.   Under appropriate conditions, the MDFEM achieves higher-order convergence rates in term of error versus cost, i.e., to achieve an accuracy of $O(\epsilon)$ the computational cost is $O(\epsilon^{-1/\lambda-\dd/\lambda}) = O(\epsilon^{-(p^* + \dd/\tau)/(1-p^*)})$ where $\epsilon^{-1/\lambda}$ and $\epsilon^{-\dd/\lambda}$ are respectively the cost of the quasi-Monte Carlo cubature and the finite element approximations, with $\dd = d \, (1+\ddelta)$ for some $\ddelta \ge 0$ and $d$ the physical dimension, and $0 < p^* \le (2 + \dd/\tau)^{-1}$ is a parameter representing the sparsity of $\{\phi_j\}_{j \ge 1}$.

scholarly journals Monte Carlo Simulation for Exploring Mechanical Properties of Porous Materials Based on Scaled Boundary Finite Element Method

2022 ◽  
Vol 12 (2) ◽  
pp. 575
Author(s):  
Guangying Liu ◽  
Ran Guo ◽  
Kuiyu Zhao ◽  
Runjie Wang
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
Porous Materials ◽  
Influencing Factors ◽  
Random Models ◽  
Scaled Boundary Finite Element ◽  
Element Method

The existence of pores is a very common feature of nature and of human life, but the existence of pores will alter the mechanical properties of the material. Therefore, it is very important to study the impact of different influencing factors on the mechanical properties of porous materials and to use the law of change in mechanical properties of porous materials for our daily lives. The SBFEM (scaled boundary finite element method) method is used in this paper to calculate a large number of random models of porous materials derived from Matlab code. Multiple influencing factors can be present in these random models. Based on the Monte Carlo simulation, after a large number of model calculations were carried out, the results of the calculations were analyzed statistically in order to determine the variation law of the mechanical properties of porous materials. Moreover, this paper gives fitting formulas for the mechanical properties of different materials. This is very useful for researchers estimating the mechanical properties of porous materials in advance.

scholarly journals Monte Carlo-Based Finite Element Method for the Study of Randomly Distributed Vacancy Defects in Graphene Sheets

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Liu Chu ◽  
Jiajia Shi ◽  
Eduardo Souza de Cursi ◽  
Xunqian Xu ◽  
Yazhou Qin ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Natural Frequencies ◽  
Vacancy Defect ◽  
Honeycomb Lattice ◽  
Graphene Sheets ◽  
Pristine Graphene ◽  
Vacancy Defects ◽  
Element Method

This paper proposed an effective stochastic finite element method for the study of randomly distributed vacancy defects in graphene sheets. The honeycomb lattice of graphene is represented by beam finite elements. The simulation results of the pristine graphene are in accordance with literatures. The randomly dispersed vacancies are propagated and performed in graphene by integrating Monte Carlo simulation (MCS) with the beam finite element model (FEM). The results present that the natural frequencies of different vibration modes decrease with the augment of the vacancy defect amount. When the vacancy defect reaches 5%, the regularity and geometrical symmetry of displacement and rotation in vibration behavior are obviously damaged. In addition, with the raise of vacancy defects, the random dispersion position of vacancy defects increases the variance in natural frequencies. The probability density distributions of natural frequencies are close to the Gaussian and Weibull distributions.

Sensitivity Analysis on Solder Joint Fatigue Life of Solid State Drives by Finite Element Method and Monte Carlo Simulation

2017 ◽  
Author(s):  
Y. J. Cho ◽  
J. W. Jang ◽  
G. H. Jang
Keyword(s):  
Finite Element Method ◽  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
Fatigue Life ◽  
Solid State ◽  
Thermal Cycling ◽  
Solder Ball ◽  
Solid State Drives ◽  
Element Method

We proposed a method to estimate a distribution of fatigue life of solid state drives (SSDs) due to thermal cycling excitation by using finite element method and Monte Carlo simulation. In the developed finite element model, we utilized the Anand model to represent the viscoplastic behavior of the solder balls, and we also utilized the Prony series to represent the viscoelastic behavior of the polymer material in underfill. We determined a fatigue life of the SSD by using the Morrow’s energy-based fatigue model. Finally, we determined a distribution of fatigue life considering the manufacturing tolerance of the design variables and the variation of material properties in the Monte Carlo simulation. Finite element analysis shows that the outermost solder ball at the corner of dynamic random access memory was the most vulnerable component under the thermal cycling excitation. We also show that temperature profile and diameter of solder ball affect dominantly the fatigue life of the SSD.

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