We use the duality between a singly bordered and a doubly bordered block diagonal form to produce an efficient method of obtaining the stable factorization of a bordered system. This is particularly important in the exploitation of coarse-grained parallelism. We show how our partitioning and factorization scheme relates to domain decomposition partitioning but has greater control over stability...

We present a parallel algorithm for solving the next element search problem on a set of line segments, using a BSP like model referred to as the Coarse Grained Multicomputer (CGM). The algorithm requires O(1) communication rounds (h-relations with h=O(n/p)), O((n/ p) log n) local computation, and O((n/p) log n) storage per processor. Our result implies solutions to the point location, trapezoid...

The Balancing Domain Decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent. The abstract theory introduced in 19] is used to develop condition number bounds for conforming linear elements in two and three dimen...

We study basic questions of wavelet decompositions associated with multiresolution analysis. A rather complete analysis of multiresolution associated with the solution of a refinement equation is presented. The notion of extensibility of a finite set of Laurent polynomials is shown to be central in the construction of wavelets by decomposition of spaces. Two examples of extensibility, first ove...

A two-level iterative substructuring algorithm with a wire basket based coarse space is proposed and analyzed. The three dimensional model problem is scalar, elliptic, with discontinuous coeecients, and is discretized by conforming spectral elements. The condition number of the resulting iteration operator is bounded by C (1 + log p) 2 , where the constant is independent of the number of elemen...

One of the least understood aspects of aquatic ecology is the role of riparian zones of lakes, and how these habitats and their functions are impacted by human development of lakeshores. We investigated the effects of residential lakeshore development on littoral coarse woody debris (CWD) distribution and on riparian forest characteristics by comparing 18 lakes in the U.S. Pacific Northwest wit...

The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators. We derive an error estimator whic...

Climate Change has emerged as one of the grand global challenges facing humanity. The dominant anthropogenic greenhouse gas that seems to be contributing to the climate change problem, carbon dioxide (CO2), has a complex cycle through the atmosphere, oceans and biosphere. The combustion of fossil fuels (power production, transportation, etc.) remains the largest source of anthropogenic CO2 to t...

In the last decade, multiscale methods have been developed and proposed to efficiently solve large reservoir models. These techniques allow reducing the computational cost by decreasing the size of the largest problem to be solved: the initial fine-scale problem is divided into a set of independent local problems coupled by a coarse problem which is smaller than the original problem. This appro...

This short research announcement briefly describes the simplicial method underlying the GAP package SCO for computing the socalled orbifold cohomology of topological resp. smooth orbifolds. SCO can be used to compute the lower dimensional group cohomology of some infinite groups. Instead of giving a complete formal definition of an orbifold, we start with a simple construction, general enough t...