Block-adaptive Cross Approximation of Discrete Integral Operators

In this article we extend the adaptive cross approximation (ACA) method known for the efficient approximation of discretisations of integral operators to a block-adaptive version. While ACA is usually employed to assemble hierarchical matrix approximations having the same prescribed accuracy on all blocks of the partition, for the solution of linear systems it may be more efficient to adapt the accuracy of each block to the actual error of the solution as some blocks may be more important for the solution error than others. To this end, error estimation techniques known from adaptive mesh refinement are applied to automatically improve the block-wise matrix approximation. This allows to interlace the assembling of the coefficient matrix with the iterative solution

Numerics of boundary-domain integral and integro-differential equations for BVP with variable coefficient in 3D

This is the post-print version of the article. The official published version can be accessed from the links below - Copyright @ 2013 Springer-VerlagA numerical implementation of the direct boundary-domain integral and integro-differential equations, BDIDEs, for treatment of the Dirichlet problem for a scalar elliptic PDE with variable coefficient in a three-dimensional domain is discussed. The mesh-based discretisation of the BDIEs with tetrahedron domain elements in conjunction with collocation method leads to a system of linear algebraic equations (discretised BDIE). The involved fully populated matrices are approximated by means of the H-Matrix/adaptive cross approximation technique. Convergence of the method is investigated.This study is partially supported by the EPSRC grant EP/H020497/1:"Mathematical Analysis of Localised-Boundary-Domain Integral Equations for Variable-Coefficients Boundary Value Problems"

Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category

Fra bil til cykel – hvordan virksomheder kan få deres medarbejdere i cykelsadlen

Fysisk inaktivitet er en selvstændig faktor for udviklingen af forskellige civilisationssygdomme, herunder flere kræftformer (WHO, 2010; WCRF, 2012). For at få danskerne til at bevæge sig mere i en travl hverdag, er aktiv transport til og fra arbejde en relevant løsning på den stigende inaktivitet i den voksne befolkning (De Geus et al., 2007; Hendriksen, 2000; Oja et al., 2011; Wen & Rissel, 2010). Arbejdspladsen er en rele- vant arena for organisatoriske forandringer i forbindelse med forebyggelsesarbejdet. FormålKræftens Bekæmpelse har i et samarbejde med fire virksomheder undersøgt, hvad arbejdspladsen kan gøre for at motivere medarbejderne til at cykle (mere) til arbejde. MetodeEt indledende litteraturstudie og sparring med danske cykeleksperter dannede et overblik over eksisteren- de, effektive og bæredygtige cykelaktiviteter på arbejdspladser. Undersøgelsen bestod af en spørgeskema- undersøgelse blandt medarbejderne, kombineret med fokusgruppeinterview med udvalgte medarbejdere og feltstudier på arbejdspladserne. ResultaterEn temainddelt analyse resulterede i et katalog til hver arbejdsplads, med 3-5 anbefalinger for cykelfrem- mende aktiviteter til implementering. Anbefalingerne er rangeret efter medarbejdernes ønsker og motiva- tion for at cykle til arbejde, arbejdspladsens reelle mulighed for indsatsen samt den eksisterende viden om effekten af indsatserne. Resultaterne anvendes på arbejdspladserne ved at implementere mindst én af anbefalingerne i efteråret 2013. KonklusionGenerelt er der stort potentiale i at fremme cykling på arbejdspladsen. Gennem simple og helhedsoriente- rede indsatser kan arbejdspladsen være med til at motivere medarbejderne til at vælge cyklen (mere) til. PerspektiveringDer er behov for flere samarbejdsprojekter, hvor flere aktører går sammen om at anvende den viden, der findes om cykelfremme på arbejdspladsen. Ved at udnytte synergien mellem lignende projekter er det mu- ligt at flytte flere bilister over i cykelsadlen

Annealing diffusions in a slowly growing potential

We consider a continuous analogue of the simulated annealing algorithm in $R^d$. We prove a convergence result, under hypotheses weaker than the usual ones. In particular, we cover cases where the gradient of the potential goes to zero at infinity. The proof follows an idea of L. Miclo, but we replace the Poincar\'e and log-Sobolev inequalities (which do not hold in our setting) by weak Poincar\'e inequalities. We estimate the latter with measure-capacity criteria. We show that, despite the absence of a spectral gap, the convergence still holds for the "classical" schedule t = c/ ln(t), if c is bigger than a constant related to the potential

Complexity Analysis of a Fast Directional Matrix-Vector Multiplication

We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered directional multi-level approximation of the Helmholtz kernel can be applied even on high-frequency levels efficiently. We provide a detailed analysis of the almost linear asymptotic complexity of the presented method. Our numerical experiments are in good agreement with the provided theory.Comment: 20 pages, 2 figures, 1 tabl