Interior numerical approximation of boundary value problems with a distributional data

We study the approximation properties of a harmonic function u ∈ H^1?k(Ω), k > 0, on a relatively compact subset A of Ω, using the generalized finite element method (GFEM). If Ω = ??, for a smooth, bounded domain ??, we obtain that the GFEM‐approximation u_S ∈ S of u satisfies ‖u ? u_S‖ ≤ Ch^γ‖u‖, where h is the typical size of the “elements” defining the GFEM‐space S and γ ≥ 0 is such that the local approximation spaces contain all polynomials of degree k + γ. The main technical ingredient is an extension of the classical super‐approximation results of Nitsche and Schatz (Applicable Analysis 2 (1972), 161–168; Math Comput 28 (1974), 937–958). In addition to the usual “energy” Sobolev spaces H¹(??), we need also the duals of the Sobolev spaces H^m(??), m ∈ ?₊. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

A product form solution to a system with multi-type jobs and multi-type servers

We consider a memoryless single station service system with servers \(\mathcal{S}=\{m_{1},\ldots,m_{K}\}\), and with job types \(\mathcal{C}=\{a,b,\ldots\}\). Service is skill-based, so that server m _i can serve a subset of job types \(\mathcal{C}(m_{i})\). Waiting jobs are served on a first-come-first-served basis, while arriving jobs that find several idle servers are assigned to a feasible server randomly. We show that there exist assignment probabilities under which the system has a product-form stationary distribution, and obtain explicit expressions for it. We also derive waiting time distributions in steady state.     

The G/M/1 queue revisited

The G/M/1 queue is one of the classical models of queueing theory. The goal of this paper is two-fold: (a) To introduce new derivations of some well-known results, and (b) to present some new results for the G/M/1 queue and its variants. In particular, we pay attention to the G/M/1 queue with a set-up time at the start of each busy period, and the G/M/1 queue with exceptional first service. Dedicated to Arie Hordijk on his 65th birthday, in friendship and admiration.     

On a generic class of two-node queueing systems

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on–off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in which it explicitly does. This dichotomy can be understood by using large-deviations heuristics. This work has been carried out partly in the Dutch BSIK/BRICKS project.     

Adaptive discretization of convex multistage stochastic programs

We propose a new scenario tree reduction algorithm for multistage stochastic programs, which integrates the reduction of a scenario tree into the solution process of the stochastic program. This allows to construct a scenario tree that is highly adapted on the optimization problem. The algorithm starts with a rough approximation of the original tree and locally refines this approximation as long as necessary. Promising numerical results for scenario tree reductions in the settings of portfolio management and power management with uncertain load are presented.     

Multi-objective Geometry Optimization of a Gas Cyclone Using Triple-Fidelity Co-Kriging Surrogate Models

Cyclone separators are widely used in a variety of industrial applications. A low-mass loading gas cyclone is characterized by two performance parameters, namely the Euler and Stokes numbers. These parameters are highly sensitive to the geometrical design parameters defining the cyclone. Optimizing the cyclone geometry therefore is a complex problem. Testing a large number of cyclone geometries is impractical due to time constraints. Experimental data and even computational fluid dynamics simulations are time-consuming to perform, with a single simulation or experiment taking several weeks. Simpler analytical models are therefore often used to expedite the design process. However, this comes at the cost of model accuracy. Existing techniques used for cyclone shape optimization in literature do not take multiple fidelities into account. This work combines cheap-to-evaluate well-known mathematical models of cyclones, available data from computational fluid dynamics simulations and experimental data to build a triple-fidelity recursive co-Kriging model. This model can be used as a surrogate with a multi-objective optimization algorithm to identify a Pareto set of a finite number of solutions. The proposed scheme is applied to optimize the cyclone geometry, parametrized by seven design variables.     

Algorithms for separable nonlinear least squares with application to modelling time-resolved spectra

The multiexponential analysis problem of fitting kinetic models to time-resolved spectra is often solved using gradient-based algorithms that treat the spectral parameters as conditionally linear. We make a comparison of the two most-applied such algorithms, alternating least squares and variable projection. A numerical study examines computational efficiency and linear approximation standard error estimates. A new derivation of the Fisher information matrix under the full Golub-Pereyra gradient allows a numerical comparison of parameter precision under variable projection variants. Under the criteria of efficiency, quality of standard error estimates and parameter precision, we conclude that the Kaufman variable projection technique performs well, while techniques based on alternating least squares have significant disadvantages for application in the problem domain.