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Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization

Houman Owhadi;  Lei Zhang;  Leonid Berlyand — 2014

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ( ) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution ) minimizing the ...

A Sufficient Condition for Graphs to Be SuperK-Restricted Edge Connected

Shiying Wang;  Meiyu Wang;  Lei Zhang — 2017

Discussiones Mathematicae Graph Theory

For a subset S of edges in a connected graph G, S is a k-restricted edge cut if G − S is disconnected and every component of G − S has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. Let ξk(G) = min|[X, X̄]| : |X| = k, G[X] is connected, where X̄ = V (G). A graph G is super k-restricted edge connected if every minimum k-restricted edge cut of G isolates a component of order exactly k. Let k be a positive...

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