A parallel computer implementation of fast low-rank QR approximation of the Biot-Savart law

In this paper we present a low-rank QR method for evaluating the discrete Biot-Savart law on parallel computers. It is assumed that the known current density and the unknown magnetic field are both expressed in a finite element expansion, and we wish to compute the degrees-of-freedom (DOF) in the basis function expansion of the magnetic field. The matrix that maps the current DOF to the field DOF is full, but if the spatial domain is properly partitioned the matrix can be written as a block matrix, with blocks representing distant interactions being low rank and having a compressed QR representation. The matrix partitioning is determined by the number of processors, the rank of each block (i.e. the compression) is determined by the specific geometry and is computed dynamically. In this paper we provide the algorithmic details and present computational results for large-scale computations

Investigation of Radar Propagation in Buildings: A 10 Billion Element Cartesian-Mesh FETD Simulation

In this paper large scale full-wave simulations are performed to investigate radar wave propagation inside buildings. In principle, a radar system combined with sophisticated numerical methods for inverse problems can be used to determine the internal structure of a building. The composition of the walls (cinder block, re-bar) may effect the propagation of the radar waves in a complicated manner. In order to provide a benchmark solution of radar propagation in buildings, including the effects of typical cinder block and re-bar, we performed large scale full wave simulations using a Finite Element Time Domain (FETD) method. This particular FETD implementation is tuned for the special case of an orthogonal Cartesian mesh and hence resembles FDTD in accuracy and efficiency. The method was implemented on a general-purpose massively parallel computer. In this paper we briefly describe the radar propagation problem, the FETD implementation, and we present results of simulations that used over 10 billion elements

An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition

An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach

Performance of low-rank QR approximation of the finite element Biot-Savart law

We are concerned with the computation of magnetic fields from known electric currents in the finite element setting. In finite element eddy current simulations it is necessary to prescribe the magnetic field (or potential, depending upon the formulation) on the conductor boundary. In situations where the magnetic field is due to a distributed current density, the Biot-Savart law can be used, eliminating the need to mesh the nonconducting regions. Computation of the Biot-Savart law can be significantly accelerated using a low-rank QR approximation. We review the low-rank QR method and report performance on selected problems

A Hybrid FEM-BEM Unified Boundary Condition with Sub-Cycling for Electromagnetic Radiation

Hybrid solutions to time-domain electromagnetic problems offer many advantages when solving open-region scattering or radiation problems. Hybrid formulations use a finite-element or finite-difference discretization for the features of interest, then bound this region with a layer of planar boundary elements. The use of volume discretization allows for intricate features and many changes in material within the structure, while the boundary-elements provide a highly accurate radiating boundary condition. This concept has been implemented previously, using the boundary elements to set the E-field, H-field, or both for an FDTD grid, for example in [1][2][3], or as a mixed boundary condition for the second order wave equation solved by finite elements [4]. Further study has focused on using fast methods, such as the Plane Wave Time Domain method [3][4] to accelerate the BEM calculations. This paper details a hybrid solver using the coupled first-order equations for the E and H fields in the finite-element region. This formulation is explicit, with a restriction on the time step for stability. When this time step is used in conjunction with the boundary elements forming either a inhomogeneous Dirichlet or Neuman boundary condition on the finite-element mesh, late time instabilities occur. To combat this, a Unified Boundary Condition (UBC), similar to the one in [4] for the second-order wave equation, is used. Even when this UBC is used, the late time instabilities are merely delayed if standard testing in time is used. However, the late time instabilities can be removed by replacing centroid based time interpolation with quadrature point based time interpolation for the boundary elements, or by sub-cycling the boundary element portion of the formulation. This sub-cycling, used in [3] for FDTD to reduce complexity, is shown here to improve stability and overall accuracy of the technique

Fiscal Year 2006

This is the final report for LDRD 01-ERD-005. The Principle Investigator was Robert Sharpe. Collaborators included Niel Madsen, Benjamin Fasenfest, John D. Rockway, of the Defense Sciences Engineering Division (DSED), Vikram Jandhyala and James Pingenot from the University of Washington, and Mark Stowell of the Center for Applications Development and Software Engineering (CADSE). It should be noted that Benjamin Fasenfest and Mark Stowell were partially supported under other funding. The purpose of this LDRD effort was to enhance LLNL's computational electromagnetics capability in the area of broadband radiation and scattering. For radiation and scattering problems our transient EM codes are limited by the approximate Radiation Boundary Conditions (RBC's) used to model the radiation into an infinite space. Improved RBC's were researched, developed, and incorporated into the existing EMSolve finite-element code to provide a 10-100x improvement in the accuracy of the boundary conditions. Section I provides an introduction to the project and the project goals. Section II provides a summary of the project's research and accomplishments as presented in the attached papers

VERTICAL PILLAR ARRAYS FOR PLASMON NANOCAVITIES

We investigate tunable plasmon resonant cavity arrays in paired parallel nanowire waveguides. Resonances are observed when the waveguide length is an odd multiple of quarter plasmon wavelengths, consistent with boundary conditions of node and antinode at the ends. Two nanowire waveguides satisfy the dispersion relation of a planar metal-dielectric-metal waveguide of equivalent width equal to the square field average weighted gap. Confinement factors over 10{sup 3} are possible due to plasmon focusing in the inter-wire space

Living multiculture: understanding the new spatial and social relations of ethnicity and multiculture in England

Since 2001, as the social and spatial compositions of multiculture and migration have become more complicated and diverse, geography has moved back to the centre of policy, political and academic arguments about cultural difference and ethnic diversity in England. This spatial turn is most obvious in preoccupations with notions of increasing ethnic segregation but it is also apparent in discussions of the possibility of everyday multicultural exchanges in relationally understood places. Responding to the work of others on these questions and in these places, and informed by data from research exploring Ghanaian and Somali migrant settlement in Milton Keynes this paper reviews some of the quantitative and qualitative evidence being drawn on in academic, policy and political debates about contemporary multiculture. The paper problematises the dominance of the concept of segregation in these debates and examines the value of the concept of conviviality for understanding the ‘in-development’ ways in which multiculture is lived