Complexity bounds on supermesh construction for quasi-uniform meshes

Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh $n$. Given any two quasi-uniform meshes of $n_A$ and $n_B$ cells respectively, we show under standard assumptions that n is proportional to $n_A + n_B$. This result substantially improves on the best currently available upper bound on $n$ and is fundamental for the analysis of algorithms that use supermeshes

Deflation for semismooth equations

Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea is the combination of a semismooth Newton method with a deflation operator that eliminates known solutions from consideration. Given one root of a semismooth residual, deflation constructs a new problem for which a semismooth Newton method will not converge to the known root, even from the same initial guess. This enables the discovery of other roots. We prove the effectiveness of the deflation technique under the same assumptions that guarantee locally superlinear convergence of a semismooth Newton method. We demonstrate its utility on various finite- and infinite-dimensional examples drawn from constrained optimization, game theory, economics and solid mechanics.Comment: 24 pages, 3 figure

Present and future atmospheric blocking and its impact on European mean and extreme climate

Atmospheric blocking plays an important role in the mid-latitude climate variability and can be responsible for anomalous mean and/or extreme climate. In this study, a potential vorticity based blocking indicator is used to investigate the representation of Euro-Atlantic atmospheric blocking events in the ECHAM5/MPI-OM climate model. The impact of blocking events on present and future mean and extreme climate is studied by means of composite maps and correlation analyses. In comparison to ERA-40 re-analysis, the model represents the blocking frequency and seasonal distribution well. We show that European blocking events have a sustained influence particularly on anomalous cold winter temperatures in Europe. In a future climate, the blocking frequency is slightly diminished but the influence on the European winter climate remains robust. Due to a northeastward shift of the blocking pattern and an increase in maximum blocking duration, cold winter temperature extremes can still be expected in a future climat

Exploiting Kronecker structure in exponential integrators: Fast approximation of the action of phi-functions of matrices via quadrature

In this article, we propose an algorithm for approximating the action of  $\varphi$-functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum structure, which arise from problems admitting a tensor product representation. The method is based on quadrature approximations of the integral form of the  $\varphi$-functions combined with a scaling and modified squaring method. Owing to the Kronecker sum representation, only actions of 1D matrix exponentials are needed at each quadrature node and assembly of the full matrix can be avoided. Additionally, we derive a priori bounds for the quadrature error, which show that, as expected by classical theory, the rate of convergence of our method is supergeometric. Guided by our analysis, we construct a fast and robust method for estimating the optimal scaling factor and number of quadrature nodes that minimizes the total cost for a prescribed error tolerance. We investigate the performance of our algorithm by solving several linear and semilinear time-dependent problems in 2D and 3D. The results show that our method is accurate and orders of magnitude faster than the current state-of-the-art

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. We demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.Comment: 22 pages, 5 figures, 3 table

APPLICATION OF A ONE-STEP REAL TIME RT-PCR PROTOCOL FOR NOROVIRUS DETECTION IN SHELLFISH HARVERSTED AND COMMERCIALIZED IN CAMPANIA REGION

Shellfish are recognized as a potential vehicle of viral diseases. However, according to European Regulations, only bacteriological parameters (Salmonella and E. coli) are used to establish their microbiological quality. Because of the lack of a standard reference method for the detection of viruses, data on the incidence of enteric viruses in European production areas are still limited. Aim of the present study was the evaluation of the Norovirus (NoV) contamination in shellfish from different harvesting areas (both class A and B) and from registered and not- registered retails of the Campania region (Tyrrhenian Sea, Italy). Seventy shellfish (Mytilus galloprovincialis) were collected from 15 harvesting areas, one authorized and two not authorized retails and were examined for virus presence (NoV genogroups I and II) by Real Time PCR. Ten harvesting areas (66%) showed presence of viral contamination, with three of them belonging to A areas and seven to B areas. The shellfish collected from the registered retail tested positive for Norovirus presence, whereas the shellfish collected from not-authorized retails didn't show viral contamination. Twenty-nine samples were positive for genogroup II, ten of which tested positive also for NoV genogroup I

a telescope proton recoil spectrometer for fast neutron beam lines

A telescope proton recoil spectrometer for fast neutron beam-lines C. Cazzaniga1,3,∗, M. Rebai2,3, M. Tardocchi3, G. Croci2,3, M. Nocente2,3, S. Ansell1, C. D. Frost1, and G. Gorini2,3 1ISIS Facility, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Didcot OX11 0QX, UK 2Universita degli Studi di Milano-Bicocca, Dipartimento di Fisica, Piazza della Scienza 3, Milano, Italy 3Istituto di Fisica del Plasma "P. Caldirola", Associazione EURATOM-ENEA/CNR, Via Cozzi 53, Milano, Italy ∗E-mail: [email protected]