Multiscale modeling using goal-oriented adaptivity and numerical homogenization. I: Mathematical formulation and numerical results

DOI10.1016/j.cma.2011.06.011zbMath1243.74168OpenAlexW2018914564MaRDI QIDQ438158

Chetan Jhurani, Leszek F. Demkowicz

Publication date: 20 July 2012

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2011.06.011

zbMATH Keywords

finite elementsheterogeneous mediaadaptive meshesnumerical homogenizationMoore-Penrose pseudoinversemolecular statics

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Homogenization applied to problems in fluid mechanics (76M50) Homogenization, determination of effective properties in solid mechanics (74Q99)

Related Items (15)

On the ill-conditioning in the new higher order multipoint method ⋮ Application of \(hp\)-adaptive finite element method to two-scale computation ⋮ A posteriori error estimation and adaptivity in non-intrusive couplings between concurrent models ⋮ An Introductory Review on A Posteriori Error Estimation in Finite Element Computations ⋮ Goal-oriented adaptivity for GMsFEM ⋮ Multiscale modeling using goal-oriented adaptivity and numerical homogenization. I: Mathematical formulation and numerical results ⋮ Multiscale modeling using goal-oriented adaptivity and numerical homogenization. II: Algorithms for the Moore-Penrose pseudoinverse ⋮ Online basis construction for goal-oriented adaptivity in the generalized multiscale finite element method ⋮ On two-scale adaptive FE analysis of micro-heterogeneous media with seamless scale-bridging ⋮ Goal-oriented error estimation and adaptivity in MsFEM computations ⋮ A framework for FFT-based homogenization on anisotropic lattices ⋮ Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation ⋮ On Moore-Penrose pseudoinverse computation for stiffness matrices resulting from higher order approximation ⋮ Goal-oriented adaptivity of mixed GMsFEM for flows in heterogeneous media ⋮ Numerical model reduction with error control in computational homogenization of transient heat flow

Uses Software

• PETSc
• TAO
• 2Dhp90
• VMD
• Algorithm 432

Cites Work

• Multiscale modeling using goal-oriented adaptivity and numerical homogenization. I: Mathematical formulation and numerical results
• Multiscale modeling using goal-oriented adaptivity and numerical homogenization. II: Algorithms for the Moore-Penrose pseudoinverse
• Adaptive multiscale modeling of polymeric materials with Arlequin coupling and goals algorithms
• Introduction to computational micromechanics
• The black box multigrid numerical homogenization algorithm
• A multiscale finite element method for elliptic problems in composite materials and porous media
• \(b=\int g\)
• \(FE^2\) multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials
• On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
• Homogenization and porous media
• Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
• Matrix-Dependent Multigrid Homogenization for Diffusion Problems
• Wavelet-Based Numerical Homogenization
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Computing with hp-ADAPTIVE FINITE ELEMENTS
• Approximation of Large-Scale Dynamical Systems
• Some geometric properties of Lyapunov equation and LTI system
• The generalized finite element method
• Shape optimization by the homogenization method
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