Cache optimization for structured and unstructured grid multigrid.
Comparing multilevel coarsening strategies.
Component mode synthesis and eigenvalues of second order operators : discretization and algorithm
Composite grid finite element method: Implementation and iterative solution with inexact subproblems
This paper concerns the composite grid finite element (FE) method for solving boundary value problems in the cases which require local grid refinement for enhancing the approximating properties of the corresponding FE space. A special interest is given to iterative methods based on natural decomposition of the space of unknowns and to the implementation of both the composite grid FEM and the iterative procedures for its solution. The implementation is important for gaining all benefits of the described...
Concept de zoom adaptatif en architecture multigrille locale ; étude comparative des méthodes L.D.C., F.A.C. et F.I.C.
Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law
In this paper, the convergence of a Neumann-Dirichlet algorithm to approximate Coulomb's contact problem between two elastic bodies is proved in a continuous setting. In this algorithm, the natural interface between the two bodies is retained as a decomposition zone.
Convergence of -cycle and -cycle multigrid methods for the biharmonic problem using the Morley element.
Convergence rate estimate for a domain decomposition method.
Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother
We extend the analysis of the recently proposed nonlinear EIS scheme applied to the partial eigenvalue problem. We address the case where the Rayleigh quotient iteration is used as the smoother on the fine-level. Unlike in our previous theoretical results, where the smoother given by the linear inverse power method is assumed, we prove nonlinear speed-up when the approximation becomes close to the exact solution. The speed-up is cubic. Unlike existent convergence estimates for the Rayleigh quotient...
Couplage entre éléments finis et calculs analytiques pour l'équation de Laplace dans un domaine à frontière angulaire
Coupling of transport and diffusion models in linear transport theory
This paper is concerned with the coupling of two models for the propagation of particles in scattering media. The first model is a linear transport equation of Boltzmann type posed in the phase space (position and velocity). It accurately describes the physics but is very expensive to solve. The second model is a diffusion equation posed in the physical space. It is only valid in areas of high scattering, weak absorption, and smooth physical coefficients, but its numerical solution is much cheaper...
Coupling of transport and diffusion models in linear transport theory
This paper is concerned with the coupling of two models for the propagation of particles in scattering media. The first model is a linear transport equation of Boltzmann type posed in the phase space (position and velocity). It accurately describes the physics but is very expensive to solve. The second model is a diffusion equation posed in the physical space. It is only valid in areas of high scattering, weak absorption, and smooth physical coefficients, but its numerical solution is...
Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements.
Different approaches to interface weights in the BDDC method in 3D
In this paper, we discuss the choice of weights in averaging of local (subdomain) solutions on the interface for the BDDC method (Balancing Domain Decomposition by Constraints). We try to find relations among different choices of the interface weights and compare them numerically on model problems of the Poisson equation and linear elasticity in 3D. Problems with jumps in coefficients of material properties are considered and both regular and irregular interfaces between subdomains are tested.
Dirichlet-Neumann alternating algorithm for an exterior anisotropic quasilinear elliptic problem
In this paper, by the Kirchhoff transformation, a Dirichlet-Neumann (D-N) alternating algorithm which is a non-overlapping domain decomposition method based on natural boundary reduction is discussed for solving exterior anisotropic quasilinear problems with circular artificial boundary. By the principle of the natural boundary reduction, we obtain natural integral equation for the anisotropic quasilinear problems on circular artificial boundaries and construct the algorithm and analyze its convergence....
Domain decomposition algorithms for first-order system least squares methods.
Domain decomposition algorithms for time-harmonic Maxwell equations with damping
Three non-overlapping domain decomposition methods are proposed for the numerical approximation of time-harmonic Maxwell equations with damping (i.e., in a conductor). For each method convergence is proved and, for the discrete problem, the rate of convergence of the iterative algorithm is shown to be independent of the number of degrees of freedom.
Domain Decomposition Algorithms for Time-Harmonic Maxwell Equations with Damping
Three non-overlapping domain decomposition methods are proposed for the numerical approximation of time-harmonic Maxwell equations with damping (i.e., in a conductor). For each method convergence is proved and, for the discrete problem, the rate of convergence of the iterative algorithm is shown to be independent of the number of degrees of freedom.
Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes.
Domain decomposition method and elastic multi-structures: the stiffened plate problem.