Adaptive Mesh Refinement for Characteristic Codes

The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference discretizations of wave-like equations using characteristic coordinates. We demonstrate the algorithm by constructing a code implementing the Einstein-Klein-Gordon system of equations in spherical symmetry. We discuss how the algorithm can trivially be generalized to higher dimensional systems, and suggest a method that can be used to parallelize a characteristic code.Comment: 36 pages, 17 figures; updated to coincide with journal versio

Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations

We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations.Comment: 24 pages, 1 figure. Corresponds to journal versio

State-of-the-art in Power Line Communications: from the Applications to the Medium

In recent decades, power line communication has attracted considerable attention from the research community and industry, as well as from regulatory and standardization bodies. In this article we provide an overview of both narrowband and broadband systems, covering potential applications, regulatory and standardization efforts and recent research advancements in channel characterization, physical layer performance, medium access and higher layer specifications and evaluations. We also identify areas of current and further study that will enable the continued success of power line communication technology.Comment: 19 pages, 12 figures. Accepted for publication, IEEE Journal on Selected Areas in Communications. Special Issue on Power Line Communications and its Integration with the Networking Ecosystem. 201

On convergence of higher order schemes for the projective integration method for stiff ordinary differential equations

We present a convergence proof for higher order implementations of the projective integration method (PI) for a class of deterministic multi-scale systems in which fast variables quickly settle on a slow manifold. The error is shown to contain contributions associated with the length of the microsolver, the numerical accuracy of the macrosolver and the distance from the slow manifold caused by the combined effect of micro- and macrosolvers, respectively. We also provide stability conditions for the PI methods under which the fast variables will not diverge from the slow manifold. We corroborate our results by numerical simulations.Comment: 43 pages, 7 figures; accepted for publication in the Journal of Computational and Applied Mathematic