Séminaires CMAP Ecole Polytechnique

Séminaire le 21 Septembre 2015, 16h15 à Salle de conférence du Centre de Mathématiques Appliquées (2e étage de l'aile 00 du bât. des laboratoires)

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29 septembre à 10h15, exceptionnellement en salle de conférence du CPHT (rdc Aile 0 des laboratoires).
10h15 - Nicole Spillane (CMAP) - Achieving robustness in domain decomposition
11h15 - Stanislav Molchanov (UNC Charlotte) - Anderson model on the fractal lattice

Résumé de N. Spillane : domain decomposition methods are a family of solvers tailored to very large linear systems that require parallel computers. They proceed by splitting the computational domain into subdomains and then approximating the inverse of the original problem with local inverses coming from the subdomains. I will present some classical domain decomposition methods and show that for realistic simulations (with heterogeneous materials for instance) convergence usually becomes very slow. Then I will explain how this can be fixed by injecting more information into the solver, either by adding a coarse space (this is also known as deflation) or by using multiple search directions within the conjugate gradient algorithm.

Résumé de S. Molchanov : the fractal lattice Γ is a skeleton, i.e. the discrete approximations of the nested fractal, say, the infinite Sierpinski gasket. The dimension d (Γ) of such lattice (Hausdorff’s dimension or spectral dimension) can be different but in all cases it has values on the interval (1,2).The Anderson Hamiltonian has the standard definition : Δ is the lattice Laplacian, (X_i) are i.i.d. random variables and σ is a coupling constant. We will discuss the following recent results :
a) The spectrum of H has no a.c. component P-a.s. for any non-degenerated potential.
b) If the random variables are heavy tailed, then the spectrum of H is p.p. P-a.s. This fact must be true for the arbitrary random variable, but it has not been proved.
Several results for the deterministic potential will be also presented.