The Experts below are selected from a list of 41358 Experts worldwide ranked by ideXlab platform

Zhidong Zhang - One of the best experts on this subject based on the ideXlab platform.

  • application of the generalized multiscale finite element method in an inverse random source problem
    Journal of Computational Physics, 2021
    Co-Authors: Zhidong Zhang
    Abstract:

    Abstract In this work, an inverse random source problem in the fractional diffusion equation with Heterogeneous Medium is considered. The measurements used are the statistical moments of the realizations of the single point data u ( x 0 , t , ω ) . We build the representation of the solution u in integral sense, then prove that the unknowns can be bounded by the moments theoretically. For the numerical reconstruction, to handle the highly Heterogeneous Medium, the generalized multiscale finite element method (GMsFEM) will be employed in the forward problem solver. With the simulated data, we establish an iterative algorithm of regularized Levenberg-Marquardt type, and some numerical results generated from this algorithm are displayed.

  • recovery of the time dependent source term in the stochastic fractional diffusion equation with Heterogeneous Medium
    arXiv: Analysis of PDEs, 2020
    Co-Authors: Zhidong Zhang
    Abstract:

    In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data $u(x_0,t,\omega).$ We build the representation of the solution $u$ in integral sense, then prove that the unknowns can be bounded by the moments theoretically. For the numerical reconstruction, we establish an iterative algorithm with regularized Levenberg-Marquardt type and some numerical results generated from this algorithm are displayed. For the case of highly Heterogeneous media, the Generalized Multiscale finite element method (GMsFEM) will be employed.

Jacob Fish - One of the best experts on this subject based on the ideXlab platform.

  • hybrid impotent incompatible eigenstrain based homogenization
    International Journal for Numerical Methods in Engineering, 2013
    Co-Authors: Jacob Fish, Vasilina Filonova, Zheng Yuan
    Abstract:

    SUMMARY We present a constitutive framework for a periodic Heterogeneous Medium with minimal number of internal variables. The method is based on a variant of the transformation field analysis (TFA) where eigenstrains are discretized using C 0 continuous approximation in matrix dominated mode of deformation, hereafter referred to as impotent eigenstrain mode, whereas in multiphase mode of deformation, the eigenstrains are approximated using the usual C  − 1 approximation. The delay in the onset of inelastic response and the eigenstrain induced anisotropy in a microphase, both characteristic to averaging methods, are alleviated by introducing an eigenstrain upwinding scheme and by enhancing constitutive laws of microphases. The proposed formulation has been verified against a direct numerical simulation. The method has been found to be very accurate in predicting an overall material response at a computational cost comparable with the phenomenological modeling of a periodic Heterogeneous Medium. Copyright © 2013 John Wiley & Sons, Ltd.

  • a dispersive model for wave propagation in periodic Heterogeneous media based on homogenization with multiple spatial and temporal scales
    Journal of Applied Mechanics, 2001
    Co-Authors: Wen Chen, Jacob Fish
    Abstract:

    A dispersive model is developed for wave propagation in periodic Heterogeneous media. The model is based on the higher order mathematical homogenization theory with multiple spatial and temporal scales. A fast spatial scale and a slow temporal scale are introduced to account for the rapid spatial fluctuations as well as to capture the long-term behavior of the homogenized solution. By this approach the problem of secularity, which arises in the conventional multiple-scale higher order homogenization of wave equations with oscillatory coefficients, is successfully resolved. A model initial boundary value problem is analytically solved and the results have been found to be in good agreement with a numerical solution of the source problem in a Heterogeneous Medium.

  • multigrid method for periodic Heterogeneous media part 1 convergence studies for one dimensional case
    Computer Methods in Applied Mechanics and Engineering, 1995
    Co-Authors: Jacob Fish, V Belsky
    Abstract:

    Abstract A multi-grid method for a periodic Heterogeneous Medium in 1-D is presented. Based on the homogenization theory, special integrid transfer operators have been developed to simulate a low frequency response of the differential equations with oscillatory coefficients. The proposed multi-grid method has been proved to have a fast rate of convergence governed by the ratio q (4− q ) , where 0

Santanu Manna - One of the best experts on this subject based on the ideXlab platform.

  • propagation of love waves in a Heterogeneous Medium over an inhomogeneous half space under the effect of point source
    Journal of Vibration and Control, 2016
    Co-Authors: Santimoy Kundu, Shishir Gupta, Pramod Kumar Vaishnav, Santanu Manna
    Abstract:

    The present paper deals with the effect of point source on the propagation of Love wave in a Heterogeneous layer and inhomogeneous half-space. The upper Heterogeneous layer is caused by consideration of exponential variation in rigidity and density. Also in half-space inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of Love wave has been obtained by using Green’s function technique. As a special case when the upper layer and lower half-space are homogeneous, our computed equation coincides with the general equation of Love wave. The propagation of Love waves are influenced by inhomogeneity parameters. The dimensionless phase velocity has been plotted against the dimensionless wave number for different values of inhomogeneity parameters. We have observed that the velocity of wave increases with the increase of inhomogeneity parameters.

Maria Vasilyeva - One of the best experts on this subject based on the ideXlab platform.

  • generalized multiscale finite element method for unsaturated filtration problem in Heterogeneous Medium
    International Conference on Finite Difference Methods, 2018
    Co-Authors: Denis Spiridonov, Maria Vasilyeva
    Abstract:

    We consider a mathematical model for simulation of the unsaturated flow problems in Heterogeneous porous Medium that describes by the Richards equation. To resolve all heterogeneity, we construct fine grid and construct finite element approximation. For dimension reduction of the discrete system, we construct multiscale solver for coarse grid solution using Generalized Multiscale Finite Element Method (GMsFEM). We generate multiscale basis functions by solution of the local spectral problems. We present numerical result and compare relative error for different number of the multiscale basis functions for 2D and 3D model problems.

Santimoy Kundu - One of the best experts on this subject based on the ideXlab platform.

  • propagation of love waves in a Heterogeneous Medium over an inhomogeneous half space under the effect of point source
    Journal of Vibration and Control, 2016
    Co-Authors: Santimoy Kundu, Shishir Gupta, Pramod Kumar Vaishnav, Santanu Manna
    Abstract:

    The present paper deals with the effect of point source on the propagation of Love wave in a Heterogeneous layer and inhomogeneous half-space. The upper Heterogeneous layer is caused by consideration of exponential variation in rigidity and density. Also in half-space inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of Love wave has been obtained by using Green’s function technique. As a special case when the upper layer and lower half-space are homogeneous, our computed equation coincides with the general equation of Love wave. The propagation of Love waves are influenced by inhomogeneity parameters. The dimensionless phase velocity has been plotted against the dimensionless wave number for different values of inhomogeneity parameters. We have observed that the velocity of wave increases with the increase of inhomogeneity parameters.