Related papers: A sample-based stochastic finite element method fo…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…
The fracture simulation of random particle reinforced composite structures remains a challenge. Current techniques either assumed a homogeneous model, ignoring the microstructure characteristics of composite structures, or considered a…
The stochastic approximation EM algorithm (SAEM) is described for the estimation of item and person parameters given test data coded as dichotomous or ordinal variables. The method hinges upon the eigenanalysis of missing variables sampled…
In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomization idea is closely related to…
Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid…
Recently a likelihood-based methodology has been developed by the Collaboratory for the Study of Earthquake Predictability (CSEP) with a view to testing and ranking seismicity models. We analyze this approach from the standpoint of possible…
In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…
In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velocity and pressure of the fluid. Additionally, the points…
Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic…
We used numerical simulations based on the finite element method (FEM) to calculate both the amplitude and phase information of the scattered electric field from random rough surfaces, which can be directly compared to ellipsometric…
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
Structural equation models (SEMs) are widely used in sciences, ranging from economics to psychology, to uncover causal relationships underlying a complex system under consideration and estimate structural parameters of interest. We study…
This paper reviews standard oversampling strategies as performed in the Multiscale Finite Element Method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch but including coarse…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
New superconvergent structures are introduced by the finite volume element method (FVEM), which allow us to choose the superconvergent points freely. The general orthogonal condition and the modified M-decomposition (MMD) technique are…
I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and…
The article is devoted to the resampling approach application to the reliability problems. This approach to reliability problems was first proposed by Ivnitsky (1967). Resampling is intensive statistical computer method, which is…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…