Jarle Berntsen

An adaptive algorithm for the approximate calculation of multiple integrals

An adaptive algorithm for numerical integration over hyperrectangular regions is described. The algorithm uses a globally adaptive subdivision strategy. Several precautions are introduced in the error estimation in order to improve the reliability. In each dimension more than one integration rule is made available to the user. The algorithm has been structured to allow ecient implementation on shared memory parallel computers.

Modelling the primary production in the North Sea using a coupled three-dimensional physical-chemical-biological ocean model

A coupled three-dimensional physical-chemical-biological model system has been implemented, and applied to study mass and volume transports and primary production throughout the North Sea. The model was run twice for the year 1985 with specified (for the North Sea Task Force) time series of riverine and atmospheric inputs of nutrients, and also with these nutrient inputs reduced by 40 and 50%, respectively. In particular, the evolution of the chemical and biological variables in the two situations was studied. The model output agreed quite well with the general quantitative and qualitative knowledge of the total yearly production. The intercomparison with some salinity profiles also indicated that the model handles the large-scale circulation and vertical mixing fairly well. Estimates for the transport of excess nutrients to Skagerrak and Kattegat in the highly pulsating Jutland coastal current are given. The estimates demonstrate the need for such models for calculating transport of matter from one area to another. Significant reductions in both primary production and transport of matter were seen from comparisons between the two runs.

Algorithm 698: DCUHRE: an adaptive multidemensional integration routine for a vector of integrals

J. Berntsen was supported by the Norwegian Research Council for Humanities and Sciences and STATOIL. T. O. Espelid was supported by the Norwegian Research Council for Humanities and Sciences. A Genz was supported by the Norwegian Marshall Fund. Authors’ addresses: J. Berntsen and T. 0. Espelid, Department of Informatics, University of Bergen, Thorm

Ecological modelling in coastal waters: Towards predictive physical-chemical-biological simulation models

hlensgate 55, N-5008 Bergen, Norway; A. Genz, Computer Science Department, Washington State University, Pullman, WA 99164-1210. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. @ 1991 ACM 0098-3500/91/1200-0452

Communication efficient matrix multiplication on hypercubes

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Error estimation in automatic quadrature routines

Abstract A simple, but general, simulation model is specified according to the state-of-the-art within phytoplankton modelling: Process representations are based upon prevailing theoretical and empirical representations given in the literature, and a set of earlier published values of model coefficients that have demonstrated good fit to reliable observations was selected. The emerging phytoplankton model was then validated against data obtained from enclosure experiments with light-, N-, P- and Si-limitations. We applied no tuning of the coefficients as the purpose of this test was to estimate the predictive power of the proposed model. The general standard deviations between model predictions and observations were on the range 0.04–0.36 and 0.13–0.42 for the nutrient and phytoplankton state variables respectively. Not surprisingly, these values are higher than those obtained in tuned simulations. Nevertheless, several characteristics, such as the balance between diatoms and flagellates, were predicted b...

Internal Pressure Errors in Sigma-Coordinate Ocean Models

Abstract In a recent paper Fox, Otto and Hey consider matrix algorithms for hypercubes. For hypercubes allowing pipelined broadcast of messages they present a communication efficient algorithm. We present in this paper a similar algorithm that uses only nearest neighbour communication. This algorithm will therefore by very communication efficient also on hypercubes not allowing pipelined broadcast. We introduce a new algorithm that reduces the asymptotic communication cost from 2(N 2 /P 1 2 )β to 3(N 2 /P 2 3 )β . This is achieved by regarding the hypercube as a set of subcubes and by using the cascade sum algorithm.

Ideal free distribution of copepods under predation risk

A new algorithm for estimating the error in quadrature approximations is presented. Based on the same integrand evaluations that we need for approximating the integral, one may, for many quadrature rules, compute a sequence of null rule approximations. These null rule approximations are then used to produce an estimate of the local error. The algorithm allows us to take advantage of the degree of precision of the basic quadrature rule. In the experiments we show that the algorithm works satisfactorily for a selection of different quadrature rules on all test families of integrals.

Algorithm 706: DCUTRI: an algorithm for adaptive cubature over a collection of triangles

Abstract Sigma-coordinate ocean models, or models based on more generalized topography following coordinate systems, are presently widely used in oceanographic studies. The controversy over internal pressure errors in sigma-coordinate ocean models is, however, still worrisome to at least some of the users. In the present study, experiments with the seamount case using both constant and large horizontal viscosities and a Smagorinsky-type viscosity are performed. For the constant viscosity (2000 m2 s−1) case, the errors do not grow prognostically. For the more realistic case with Smagorinsky viscosity and a value of the viscosity parameter in the range usually recommended, 0.2, the errors grow very strongly prognostically. Large vertical transports associated with the eight cyclones and anticyclones around the seamount create strong and real internal pressures that add on to the initial erroneous internal pressure. The growth may be balanced by multiplying the viscosity parameter by approximately a factor o...

Conservation of energy for schemes applied to the propagation of shallow-water inertia-gravity waves in regions with varying depth

Abstract Optimal vertical distribution of a copepod population of equal competitors under predation hazard is modelled by ideal free distribution (IFD). The foragers may be limited by both depletable (food) and non-depletable (temperature) resources. Individuals are assumed to maximize growth rate per mortality risk (g/M). Mortality risk is assumed density-dependent whenever the copepod concentration is high enough to satiate predators. The growth rate depends upon temperature or food concentration in absence of competition, and is density-dependent under competition. These relationships may yield peaked habitat profitability curves. For L depths with peaked profitability curves, the computational complexity scales to 3 L . Simplifying restrictions to allow numerical solutions when a large number of depths are available are presented and discussed. At moderate and high copepod stock size, the restrictions find the optimal distribution much faster, but at low stock sizes they may predict suboptimal distributions. The model predicts that individuals shall be more sensitive to predation risk at low and moderate competitor abundance and more sensitive to resource input rate at higher competitor abundances. Deviations from a food-based IFD are therefore most pronounced at low copepod population size. The IFDs are compared with predictions from a dynamic programming model with state- and time-resolved motivation of the copepods.