Accuracy Measures and Fourier Analysis for the Full Multigrid Algorithm

The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted ElFMG, which compares the total error of the l-level FMG solution against the inherent discretization error. This measure can be used for tuning algorithmic components so as to obtain discretization-level accuracy. A Fourier analysis is developed for estimating ElFMG, and the resulting estimates are confirmed by numerical tests.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

Fictitious domain formulations of unilateral problems: analysis and algorithms

The present article deals with fictitious domain methods for numerical realization of scalar variational inequalities with the Signorini type conditions on the boundary. Two variants are introduced and analyzed. A discretization is done by finite elements. It leads to a system of non-smooth, piecewise linear equations. This system is solved by the semismooth Newton method. Numerical experiments confirm the efficiency of this approach

A Spatial-Economic Multimodal Transportation Simulation Model For US Coastal Container Ports

Assessing the potential demand for container ports and related multimodal transportation is critical for several purposes, including financial feasibility analysis and the evaluation of net economic benefits and their distribution. When developed in conjunction with a geographical information system, port-related demand analysis also provides needed input for assessment of selected environmental issues, such as truck traffic on local roads and related potential external costs, such as air pollution and noise. However, container port demand analysis is very difficult due to the complexities of international trade in containerised goods, inter-port competition, and potential strategic behaviour by several parties. Difficulties also arise from the many factors to be considered, major data requirements, and the computationally intensive nature of the problem. This paper summarises the development and application of a spatial-economic, multimodal container transportation demand simulation model for major US container ports. The underlying economic framework assumes shippers minimise the total general cost of moving containers from sources to markets. The model is validated and then used to estimate (1) annual container transportation service demand for major container ports, (2) the market areas served by selected ports, and (3) the impact on port demand and interport competition due to hypothetical changes in port use fees at selected ports. This paper first describes the model and the underlying economic reasoning, followed by the assumptions, computational algorithms, and the software architecture. Then, the trade data, transportation networks, and economic variables are described. After that, model simulation results are presented with qualifications, needed refinements, and future directions. Maritime Economics & Logistics (2003) 5, 158–178. doi:10.1057/palgrave.mel.9100067

On Computable Numbers, Non-Universality, and the Genuine Power of Parallelism

We present a simple example that disproves the universality principle. Unlike previous counter-examples to computational universality, it does not rely on extraneous phenomena, such as the availability of input variables that are time varying, computational complexity that changes with time or order of execution, physical variables that interact with each other, uncertain deadlines, or mathematical conditions among the variables that must be obeyed throughout the computation. In the most basic case of the new example, all that is used is a single pre-existing global variable whose value is modified by the computation itself. In addition, our example offers a new dimension for separating the computable from the uncomputable, while illustrating the power of parallelism in computation