A fast numerical homogenization algorithm for finite element analysis

Cecchi, M. Morandi; Marcuzzi, Fabio

doi:10.1002/(sici)1097-0207(19991210)46:10<1639::aid-nme717>3.0.co;2-k

Int. J. Numer. Meth. Engng.

1999

DOI: 10.1002/(sici)1097-0207(19991210)46:10<1639::aid-nme717>3.0.co;2-k

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A fast numerical homogenization algorithm for finite element analysis

M. Morandi Cecchi

Fabio Marcuzzi

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Cited by 3 publications

References 12 publications

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Fast homogenization algorithm based on asymptotic theory and multiscale schemes

Cecchi

Fornasier

2005

Numer Algor

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A time-frequency interpretation of the classical asymptotic theory of homogenization for elliptic PDE with periodic coefficients is presented and the relations with known multilevel/multiscale numerical schemes are investigated. We formulate a new fast iterative algorithm for the approximation of homogenized solutions based on the combination of these two apparently different approaches. The asymptotic homogenization process is interpreted as a migration to infinity of the frequencies related to microscale contributions and the discovering of those related to the homogenized solution. At different scale/frequency of the periodic coefficients of the operator, band-pass filters select only the contributions of the homogenized solution which is then composed as the limit of an iterative procedure. This novel method can be interpreted in case of finite difference discretizations as a generalized nonstationary subdivision scheme and its convergence and stability are discussed. In particular, stable compositions of the homogenized solution are investigated in relation with the contracting behavior of specific operators generated by reduction processes and Schur's complements of suitable matrices produced by discretizations via wavelets and multiscale bases.

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Fast homogenization algorithm based on asymptotic theory and multiscale schemes

Cecchi

Fornasier

2005

Numer Algor

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A parallel solver for adaptive finite element discretizations

Marcuzzi

Cecchi

2005

Numer Algor

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A parallel solver for the adaptive finite element analysis is presented. The primary aim of this work has been to establish an efficient parallel computational procedure which requires only local computations to update the solution of the system of equations arising from the finite element discretization after a local mesh-adaptation step. For this reason a set of algorithms has been developed (two-level domain decomposition, recursive hierarchical mesh-refinement, selective solution-update of linear systems of equations) which operate upon general and easily available partitioning, meshing and linear systems solving algorithms.

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An anisotropic unstructured triangular adaptive mesh algorithm based on error and error gradient information

Marcuzzi

Cecchi

Venturin

2008

Mathematics and Computers in Simulation

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A fast numerical homogenization algorithm for finite element analysis

Cited by 3 publications

References 12 publications

Fast homogenization algorithm based on asymptotic theory and multiscale schemes

Fast homogenization algorithm based on asymptotic theory and multiscale schemes

A parallel solver for adaptive finite element discretizations

An anisotropic unstructured triangular adaptive mesh algorithm based on error and error gradient information

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