ASYMPTOTIC EXPANSIONS FOR HIGH-CONTRAST ELLIPTIC EQUATIONS
From MaRDI portal
Publication:5411763
DOI10.1142/S0218202513500565zbMath1292.35100arXiv1204.3184OpenAlexW2071217080MaRDI QIDQ5411763
Juan Galvis, Victor Manuel Calo, Yalchin R. Efendiev
Publication date: 25 April 2014
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1204.3184
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Second-order elliptic equations (35J15)
Related Items
Nonoverlapping domain decomposition method with preconditioner from asymptotic analysis of steady flow in high contrast media, Gradient estimates for the insulated conductivity problem: The case of m-convex inclusions, Asymptotic analysis for the electric field concentration with geometry of the core-shell structure, Multiscale stabilization for convection-diffusion equations with heterogeneous velocity and diffusion coefficients, Gradient asymptotics of solutions to the Lamé systems in the presence of two nearly touching \(C^{1, \gamma }\)-inclusions, Multiscale stabilization for convection-dominated diffusion in heterogeneous media, Asymptotic expansions for high-contrast linear elasticity, A new boundary condition for homogenization of high-contrast random heterogeneous materials, Gradient estimates for the insulated conductivity problem with inclusions of the general m‐convex shapes, A Robust Preconditioner for High-Contrast Problems (Research), A convergence analysis of generalized multiscale finite element methods, Low-Rank Approximation to Heterogeneous Elliptic Problems, New homogenization method for diffusion equations, Heterogeneous domain decomposition method for high contrast dense composites, Asymptotics for the concentrated field between closely located hard inclusions in all dimensions, Asymptotic Expansions for High-Contrast Scalar and Vectorial PDEs, Localized harmonic characteristic basis functions for multiscale finite element methods, New asymptotic expansion for the diffusion problem with high-contrast inclusions: numerical results, Asymptotic Approximation of the Dirichlet to Neumann Map of High Contrast Conductive Media
Cites Work
- Unnamed Item
- Multiscale finite element methods for high-contrast problems using local spectral basis functions
- Flux norm approach to finite-dimensional homogenization approximations with non-separated scales and high contrast
- A large jump asymptotic framework for solving elliptic and parabolic equations with interfaces and strong coefficient discontinuities
- Analysis of FETI methods for multiscale PDEs
- Decomposition theorems and fine estimates for electrical fields in the presence of closely located circular inclusions
- Approximate method for solving an elliptic problem with discontinuous coefficients
- Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements
- Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients
- On an energy minimizing basis for algebraic multigrid methods
- Domain decomposition for multiscale PDEs
- Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms
- A Domain Decomposition Preconditioner for Multiscale High-Contrast Problems
- Spectral Element Agglomerate Algebraic Multigrid Methods for Elliptic Problems with High-Contrast Coefficients
- Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs
- Reduced-Contrast Approximations for High-Contrast Multiscale Flow Problems
- Domain Decomposition Preconditioners for Multiscale Flows in High-Contrast Media
- Domain Decomposition Preconditioners for Multiscale Flows in High Contrast Media: Reduced Dimension Coarse Spaces
- COARSE SPACES BY ALGEBRAIC MULTIGRID: MULTIGRID CONVERGENCE AND UPSCALING ERROR ESTIMATES
- A Coarse Space Construction Based on Local Dirichlet-to-Neumann Maps
- A new multiscale finite element method for high-contrast elliptic interface problems
- Multiscale Finite Element Methods
- A Simplified Method for Upscaling Composite Materials with High Contrast of the Conductivity
- Error of the Network Approximation for Densely Packed Composites with Irregular Geometry
- An Elliptic Regularity Result for a Composite Medium with "Touching" Fibers of Circular Cross-Section
- Multiscale Methods
- Discrete Network Approximation for Highly-Packed Composites with Irregular Geometry in Three Dimensions