Multigrid method for periodic heterogeneous media. II: Multiscale modeling and quality control in multidimensional case.
From MaRDI portal
Publication:1578676
DOI10.1016/0045-7825(95)00812-FzbMath1067.74573MaRDI QIDQ1578676
Publication date: 4 September 2000
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Finite element methods applied to problems in solid mechanics (74S05) Homogenization in equilibrium problems of solid mechanics (74Q05) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)
Related Items (45)
Multiscale Modeling and Simulation of Composite Materials and Structures ⋮ Nonlinear micromechanical formulation of the high fidelity generalized method of cells ⋮ A space-time multilevel method for molecular dynamics simulations ⋮ Hierarchical modeling of heterogeneous bodies ⋮ Automatic construction of 3-D models in multiple scale analysis ⋮ Homogenization in finite thermoelasticity ⋮ An improved multiscale FEM for the free vibrations of heterogeneous solids ⋮ A multiscale finite element method for optimal control problems governed by the elliptic homogenization equations ⋮ Computational plasticity for composite structures based on mathematical homogenization: Theory and practice ⋮ Numerical homogenization of heterogeneous and cellular materials utilizing the finite cell method ⋮ A two-way coupled multiscale model for predicting damage-associated performance of asphaltic roadways ⋮ Adaptive delamination analysis ⋮ Hierarchical modeling of heterogeneous structures driven by a modeling error estimator ⋮ Computational damage mechanics for composite materials based on mathematical homogenization ⋮ A simple way to introduce fibers into FEM models ⋮ Multiscale discontinuous Petrov–Galerkin method for the multiscale elliptic problems ⋮ Constrained inverse formulations in random material design. ⋮ Modeling and simulation of piezocomposites. ⋮ Hierarchical modeling of heterogeneous solids ⋮ Multiple scale computational model for damage in composite materials ⋮ Automated modeling for complex woven mesostructures ⋮ Concurrent multi-scale analysis of elastic composites by a multi-level computational model. ⋮ The image-based multiscale multigrid solver, preconditioner, and reduced order model ⋮ A short and versatile finite element multiscale code for homogenization problems ⋮ An adaptive multiscale resolution strategy for the finite deformation analysis of microheterogeneous structures ⋮ Hierarchical composite grid method for global-local analysis of laminated composite shells ⋮ A parallel and efficient multi-split XFEM for 3-D analysis of heterogeneous materials ⋮ Direct estimation of generalized stress intensity factors using a three-scale concurrent multigrid X-FEM ⋮ Numerical methods for multiscale elliptic problems ⋮ A residual-based stabilized finite element formulation for incompressible flow problems in the Arlequin framework ⋮ An inelastic homogenization framework for layered materials with planes of weakness ⋮ A scalable time-space multiscale domain decomposition method: adaptive time scale separation ⋮ UNSTRUCTURED MULTIGRID METHOD FOR SHELLS ⋮ The discontinuous Petrov-Galerkin methodology for the mixed multiscale finite element method ⋮ A Partition of Unity-Based Multiscale Method ⋮ A heterogeneous multiscale modeling framework for hierarchical systems of partial differential equations ⋮ A grain boundary damage model for delamination ⋮ Multiscale enrichment based on partition of unity for nonperiodic fields and nonlinear problems ⋮ Convergence analysis of the multiscale method for a class of convection-diffusion equations with highly oscillating coefficients ⋮ Stochastic analysis of polymer composites rupture at large deformations modeled by a phase field method ⋮ An energetically consistent concurrent multiscale method for heterogeneous heat transfer and phase transition applications ⋮ ANALYSIS OF A HETEROGENEOUS MULTISCALE FEM FOR PROBLEMS IN ELASTICITY ⋮ Adaptive Two-Scale Nonlinear Homogenization ⋮ A Combined Finite Element and Multiscale Finite Element Method for the Multiscale Elliptic Problems ⋮ An analytical coarse grid operator applied to a multiscale multigrid method
Cites Work
- Unnamed Item
- Unnamed Item
- Multiscale finite element method for a locally nonperiodic heterogeneous medium
- Homogenization techniques for composite media. Lectures delivered at the CISM, International Center for Mechanical Sciences, Udine, Italy, July 1- 5, 1985
- Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods
- Bounds for effective elastic moduli of disordered materials
- Multigrid method for periodic heterogeneous media. I: Convergence studies for one-dimensional case.
- Adaptive \(s\)-method for linear elastostatics
- Analysis of Composite Materials—A Survey
- The Fast Adaptive Composite Grid (FAC) Method for Elliptic Equations
- Adaptivity and mesh generation
- A comparison of FAC and PCG methods for solving composite grid problems
- Multi-Level Adaptive Solutions to Boundary-Value Problems
This page was built for publication: Multigrid method for periodic heterogeneous media. II: Multiscale modeling and quality control in multidimensional case.