Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants

We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how they deal with improper divergent integrals and how they estimate the integration error. The main focus of these improvements is to increase the reliability of the algorithms without significantly impacting their efficiency. Both algorithms are implemented in Matlab and tested using both the "families" suggested by Lyness and Kaganove and the battery test used by Gander and Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases less efficient, than other commonly-used adaptive integrators.Comment: 32 pages, submitted to ACM Transactions on Mathematical Softwar

Performance analysis of business process models with advanced constructs

The importance of actively managing and analysing business processes is acknowledged more than ever in organisations nowadays. Business processes form an essential part of an organisation and their application areas are manifold. Most organisations keep records of various activities that have been carried out for auditing purposes, but they are rarely used for analysis purposes. This paper describes the design and implementation of a process analysis tool that replays, analyses and visualises a variety of performance metrics using a process definition and its corresponding execution logs. The replayer uses a YAWL process model example to demonstrate its capacity to support advanced language constructs.</p

Loop integration results using numerical extrapolation for a non-scalar integral

Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar four-point diagram. Extensions to accommodate loop integration by existing integration packages are also discussed. These include: using previously generated partitions of the domain and roundoff error guards.Comment: 4 pages, 3 figures, revised, contribution to ACAT03 (Dec. 2003

Performance Analysis of Business Process Models with Advanced Constructs

The importance of actively managing and analysing business processes is acknowledged more than ever in or- ganisations nowadays. Business processes form an essential part of an organisation and their application areas are manifold. Most organisations keep records of various activities that have been carried out for auditing pur- poses, but they are rarely used for analysis purposes. This paper describes the design and implementation of a process analysis tool that replays, analyses and visualises a variety of performance metrics using a process definition and its corresponding execution logs. The replayer uses a YAWL process model example to demon- strate its capacity to support advanced language constructs

Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces

We carry out an exact analysis of the average frequency $\nu_{\alpha x_i}^+$ in the direction $x_i$ of positive-slope crossing of a given level $\alpha$ such that, $h({\bf x},t)-\bar{h}=\alpha$, of growing surfaces in spatial dimension $d$. Here, $h({\bf x},t)$ is the surface height at time $t$, and $\bar{h}$ is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number $N^+$ of such level-crossings with positive slope in all the directions is then shown to scale with time as $t^{d/2}$ for both the KPZ equation and the RD model.Comment: 22 pages, 3 figure

Hydromechanical modelling of shaft sealing for CO2 storage

The geological sequestration of CO2 in abandoned coal mines is a promising option to mitigate climate changes while providing sustainable use of the underground cavities. In order to certify the efficiency of the storage, it is essential to understand the behaviour of the shaft sealing system. The paper presents a numerical analysis of CO2 transfer mechanisms through a mine shaft and its sealing system. Different mechanisms for CO2 leakage are considered, namely multiphase flow through the different materials and flow along the interfaces between the lining and the host rock. The study focuses on the abandoned coal mine of Anderlues, Belgium, which was used for seasonal storage of natural gas. A two-dimensional hydromechanical modelling of the storage site is performed and CO2 injection into the coal mine is simulated. Model predictions for a period of 500 years are presented and discussed with attention. The role and influence of the interface between the host rock and the concrete lining are examined. In addition the impact of some uncertain model parameters on the overall performance of the sealing system is analysed through a sensitivity analysis

Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches

A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used to solve the Laplace-transformed diffusion equation, producing a time-domain solution after a numerical Laplace transform inversion. Motivated by the needs of numerical methods posed in Laplace-transformed space, we compare five inverse Laplace transform algorithms and discuss implementation techniques to minimize the number of Laplace-space function evaluations. We investigate the ability to calculate a sequence of time domain values using the fewest Laplace-space model evaluations. We find Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time