We present the first efficient algorithm for a coarse grained multiprocessor that colors a graph G with a guarantee of at most ∆G +1 colors.

We describe a new implementation of a two-level overlapping Schwarz preconditioner with energy-minimizing coarse space (GDSW) and show numerical results for an additive and a hybrid additive-multiplicative version. Our parallel implementation makes use of the Trilinos software library and provides a framework for parallel two-level Schwarz methods. We show parallel scalability for two and three...

We propose a substructuring preconditioner for solving threedimensional elliptic equations with strongly discontinuous coefficients. The new preconditioner can be viewed as a variant of the classical substructuring preconditioner proposed by Bramble, Pasiack and Schatz (1989), but with much simpler coarse solvers. Though the condition number of the preconditioned system may not have a good boun...

In the theory of domain decomposition methods, it is often assumed that each subdomain is the union of a small set of coarse triangles or tetrahedra. In this study, extensions to the existing theory which accommodate subdomains with much less regular shapes are presented; the subdomains are required only to be John domains. Attention is focused on overlapping Schwarz preconditioners for problem...

In this paper we develop a new class of overlapping Schwarz type algorithms for solving scalar steady and unsteady convection di usion equations discretized by nite element or nite di erence methods The preconditioners consist of two components namely the usual additive Schwarz preconditioner and the sum of some second order terms constructed by using products of ordered neighboring subdomain p...

Polysaccharides (carbohydrates) are key regulators of a large number of cell biological processes. However, precise biochemical or genetic manipulation of these often complex structures is laborious and hampers experimental structure-function studies. Molecular Dynamics (MD) simulations provide a valuable alternative tool to generate and test hypotheses on saccharide function. Yet, currently us...

For a submanifold Σ ⊂ R Belkin and Niyogi showed that one can approximate the Laplacian operator using heat kernels. Using a definition of coarse Ricci curvature derived by iterating Laplacians, we approximate the coarse Ricci curvature of submanifolds Σ in the same way. More generally, on any metric measure we are able to approximate a 1-parameter family of coarse Ricci functions that include ...

A recent trial found that the presence of coarse soil in fine soil increased nutrient uptake by two plant species (Smaill et al., 2014). To determine if the additional nutrient uptake was derived directly from the coarse soil, the changes in coarse soil nutrient stocks were assessed. In most cases nutrient stocks increased, despite being associated with greater plant nutrient uptake. This sugge...