Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

GPU-accelerated discontinuous Galerkin methods on hybrid meshes

We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius of the DG operator using order-dependent constants in trace and Markov inequalities. Computational efficiency is achieved under a combination of element-specific kernels (including new quadrature-free operators for the pyramid), multi-rate timestepping, and acceleration using Graphics Processing Units.Comment: Submitted to CMAM

A multi-scale multi-frequency deconvolution algorithm for synthesis imaging in radio interferometry

Aims : We describe MS-MFS, a multi-scale multi-frequency deconvolution algorithm for wide-band synthesis-imaging, and present imaging results that illustrate the capabilities of the algorithm and the conditions under which it is feasible and gives accurate results. Methods : The MS-MFS algorithm models the wide-band sky-brightness distribution as a linear combination of spatial and spectral basis functions, and performs image-reconstruction by combining a linear-least-squares approach with iterative $\chi^2$ minimization. This method extends and combines the ideas used in the MS-CLEAN and MF-CLEAN algorithms for multi-scale and multi-frequency deconvolution respectively, and can be used in conjunction with existing wide-field imaging algorithms. We also discuss a simpler hybrid of spectral-line and continuum imaging methods and point out situations where it may suffice. Results : We show via simulations and application to multi-frequency VLA data and wideband EVLA data, that it is possible to reconstruct both spatial and spectral structure of compact and extended emission at the continuum sensitivity level and at the angular resolution allowed by the highest sampled frequency.Comment: 17 pages, 11 figure

Trying to break new ground in aerial archaeology

Aerial reconnaissance continues to be a vital tool for landscape-oriented archaeological research. Although a variety of remote sensing platforms operate within the earth’s atmosphere, the majority of aerial archaeological information is still derived from oblique photographs collected during observer-directed reconnaissance flights, a prospection approach which has dominated archaeological aerial survey for the past century. The resulting highly biased imagery is generally catalogued in sub-optimal (spatial) databases, if at all, after which a small selection of images is orthorectified and interpreted. For decades, this has been the standard approach. Although many innovations, including digital cameras, inertial units, photogrammetry and computer vision algorithms, geographic(al) information systems and computing power have emerged, their potential has not yet been fully exploited in order to re-invent and highly optimise this crucial branch of landscape archaeology. The authors argue that a fundamental change is needed to transform the way aerial archaeologists approach data acquisition and image processing. By addressing the very core concepts of geographically biased aerial archaeological photographs and proposing new imaging technologies, data handling methods and processing procedures, this paper gives a personal opinion on how the methodological components of aerial archaeology, and specifically aerial archaeological photography, should evolve during the next decade if developing a more reliable record of our past is to be our central aim. In this paper, a possible practical solution is illustrated by outlining a turnkey aerial prospection system for total coverage survey together with a semi-automated back-end pipeline that takes care of photograph correction and image enhancement as well as the management and interpretative mapping of the resulting data products. In this way, the proposed system addresses one of many bias issues in archaeological research: the bias we impart to the visual record as a result of selective coverage. While the total coverage approach outlined here may not altogether eliminate survey bias, it can vastly increase the amount of useful information captured during a single reconnaissance flight while mitigating the discriminating effects of observer-based, on-the-fly target selection. Furthermore, the information contained in this paper should make it clear that with current technology it is feasible to do so. This can radically alter the basis for aerial prospection and move landscape archaeology forward, beyond the inherently biased patterns that are currently created by airborne archaeological prospection

Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: explicit time-stepping and efficient mass matrix inversion

We present a class of spline finite element methods for time-domain wave propagation which are particularly amenable to explicit time-stepping. The proposed methods utilize a discontinuous Galerkin discretization to enforce continuity of the solution field across geometric patches in a multi-patch setting, which yields a mass matrix with convenient block diagonal structure. Over each patch, we show how to accurately and efficiently invert mass matrices in the presence of curved geometries by using a weight-adjusted approximation of the mass matrix inverse. This approximation restores a tensor product structure while retaining provable high order accuracy and semi-discrete energy stability. We also estimate the maximum stable timestep for spline-based finite elements and show that the use of spline spaces result in less stringent CFL restrictions than equivalent piecewise continuous or discontinuous finite element spaces. Finally, we explore the use of optimal knot vectors based on L2 n-widths. We show how the use of optimal knot vectors can improve both approximation properties and the maximum stable timestep, and present a simple heuristic method for approximating optimal knot positions. Numerical experiments confirm the accuracy and stability of the proposed methods

Parallel h-p spectral element method for elliptic problems on polygonal domains

It is well known that elliptic problems when posed on non-smooth domains, develop singularities. We examine such problems within the framework of spectral element methods and resolve the singularities with exponential accuracy