Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients
From MaRDI portal
Publication:1958923
DOI10.1016/j.jcp.2010.07.010zbMath1197.65191arXiv1004.1122OpenAlexW1991316006MaRDI QIDQ1958923
Ivo Marek, Jaroslav Vondřejc, Jan Novák, Zeman, J.
Publication date: 30 September 2010
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1004.1122
Related Items
A polarization-based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast ⋮ Mixed boundary conditions for FFT-based homogenization at finite strains ⋮ An FE-DMN method for the multiscale analysis of thermomechanical composites ⋮ A fast rapidly convergent method for approximation of convolutions with applications to wave scattering and some other problems ⋮ Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method ⋮ Use of composite voxels in FFT-based homogenization ⋮ Solving phase-field models in the tensor train format to generate microstructures of bicontinuous composites ⋮ Convergence of FFT‐based homogenization for strongly heterogeneous media ⋮ Filtering material properties to improve FFT-based methods for numerical homogenization ⋮ An FFT-based Galerkin method for homogenization of periodic media ⋮ Mixed strain/stress gradient loadings for FFT-based computational homogenization methods ⋮ Generating polycrystalline microstructures with prescribed tensorial texture coefficients ⋮ Combining FFT methods and standard variational principles to compute bounds and estimates for the properties of elastic composites ⋮ FFT-based homogenization of hypoelastic plasticity at finite strains ⋮ FFT phase-field model combined with cohesive composite voxels for fracture of composite materials with interfaces ⋮ Locally-synchronous, iterative solver for Fourier-based homogenization ⋮ An FFT-based approach for Bloch wave analysis: application to polycrystals ⋮ FFT-based homogenisation accelerated by low-rank tensor approximations ⋮ A fast method for solving microstructural problems defined by digital images: a space Lippmann-Schwinger scheme ⋮ Two-scale FE-FFT- and phase-field-based computational modeling of bulk microstructural evolution and macroscopic material behavior ⋮ Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials ⋮ Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields ⋮ The finite element square reduced (FE2R ) method with GPU acceleration: towards three-dimensional two-scale simulations ⋮ Improved guaranteed computable bounds on homogenized properties of periodic media by the Fourier-Galerkin method with exact integration ⋮ Superaccurate effective elastic moduli via postprocessing in computational homogenization ⋮ An FFT‐based Galerkin method for the effective permeability of porous material ⋮ An explicit dynamic FFT method for homogenizing heterogeneous solids under large deformations ⋮ Fourier transform approach to numerical homogenization of periodic media containing sharp insulating and superconductive cracks ⋮ On the effectiveness of the Moulinec–Suquet discretization for composite materials ⋮ A posteriori error estimations and convergence criteria in fast Fourier transform‐based computational homogenization ⋮ An algorithm for generating microstructures of fiber‐reinforced composites with long fibers ⋮ Voxel‐based finite elements with hourglass control in fast Fourier transform‐based computational homogenization ⋮ Boundary-volume Lippmann Schwinger formulation and fast iteration schemes for numerical homogenization of conductive composites. Cases of arbitrary contrasts and Kapitza interface ⋮ A wavelet-enhanced adaptive hierarchical FFT-based approach for the efficient solution of microscale boundary value problems ⋮ On the micromechanics of deep material networks ⋮ A FFT-based formulation for discrete dislocation dynamics in heterogeneous media ⋮ Maximum-entropy based estimates of stress and strain in thermoelastic random heterogeneous materials ⋮ Convergence of trigonometric and finite-difference discretization schemes for FFT-based computational micromechanics ⋮ An optimal preconditioned FFT-accelerated finite element solver for homogenization ⋮ Reconstructing material properties by deconvolution of full-field measurement images: The conductivity case ⋮ Efficient fixed point and Newton-Krylov solvers for FFT-based homogenization of elasticity at large deformations ⋮ A review of nonlinear FFT-based computational homogenization methods ⋮ Numerical modeling of aluminium foam on two scales ⋮ On the accuracy of spectral solvers for micromechanics based fatigue modeling ⋮ An FE-DMN method for the multiscale analysis of short fiber reinforced plastic components ⋮ A simple and flexible model order reduction method for FFT-based homogenization problems using a sparse sampling technique ⋮ An efficient solution scheme for small-strain crystal-elasto-viscoplasticity in a dual framework ⋮ Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts ⋮ Efficient and accurate two-scale FE-FFT-based prediction of the effective material behavior of elasto-viscoplastic polycrystals ⋮ Fourier-accelerated nodal solvers (FANS) for homogenization problems ⋮ A geometrically adapted reduced set of frequencies for a FFT-based microstructure simulation ⋮ A multiscale FE-FFT framework for electro-active materials at finite strains ⋮ A framework for FFT-based homogenization on anisotropic lattices ⋮ Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites ⋮ Geometric variational principles for computational homogenization ⋮ A computational multi-scale model for the stiffness degradation of short-fiber reinforced plastics subjected to fatigue loading ⋮ FFT based numerical homogenization method for porous conductive materials ⋮ Efficient two-scale FE-FFT-based mechanical process simulation of elasto-viscoplastic polycrystals at finite strains ⋮ Computation of macroscopic permeability of doubly porous media with FFT based numerical homogenization method ⋮ FFT-based homogenization on periodic anisotropic translation invariant spaces ⋮ Runtime optimization of a memory efficient CG solver for FFT-based homogenization: implementation details and scaling results for linear elasticity ⋮ Two-stage data-driven homogenization for nonlinear solids using a reduced order model ⋮ A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media ⋮ Numerical artifacts of fast Fourier transform solvers for elastic problems of multi-phase materials: their causes and reduction methods ⋮ FFTHomPy ⋮ Energy-based comparison between the Fourier-Galerkin method and the finite element method ⋮ A computational investigation of the effective viscosity of short-fiber reinforced thermoplastics by an FFT-based method ⋮ A model order reduction method for computational homogenization at finite strains on regular grids using hyperelastic laminates to approximate interfaces ⋮ Adaptation and validation of FFT methods for homogenization of lattice based materials ⋮ An FFT-based spectral solver for interface decohesion modelling using a gradient damage approach ⋮ An FFT-based fast gradient method for elastic and inelastic unit cell homogenization problems ⋮ Field dislocation mechanics for heterogeneous elastic materials: a numerical spectral approach ⋮ Fast implicit solvers for phase-field fracture problems on heterogeneous microstructures ⋮ The composite voxel technique for inelastic problems ⋮ FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials ⋮ On polarization-based schemes for the FFT-based computational homogenization of inelastic materials ⋮ A dynamical view of nonlinear conjugate gradient methods with applications to FFT-based computational micromechanics ⋮ A sequential addition and migration method for generating microstructures of short fibers with prescribed length distribution ⋮ DBFFT: a displacement based FFT approach for non-linear homogenization of the mechanical behavior ⋮ AutoMat: automatic differentiation for generalized standard materials on GPUs
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A numerical method for computing the overall response of nonlinear composites with complex microstructure
- Electrostatics and heat conduction in high contrast composite materials
- Living in a bubble? Toward a unified bubble theory
- An accelerated FFT algorithm for thermoelastic and non-linear composites
- Trigonometric Collocation Methods with Product Integration for Boundary Integral Equations on Closed Curves
- Methods of conjugate gradients for solving linear systems
