REDESIGN AND OPTIMIZATION OF THE PAVING ALGORITHM APPLIED TO ELECTROMAGNETIC TOOLS (Invited Paper)

Abstract

Abstract-To study any electromagnetic system, the geometry model must be discretized into elements with an appropriate size for the working frequency. The discretization of a system must be transparent to the user of electromagnetic computing tools. A mesher is presented based on the paving algorithm. The algorithm has been modified to allow triangular elements and has been accelerated by distributing the load on multiple processors simultaneously. Also, a multilevel mode has been implemented. With this tool, any geometry defined by NURBS (Non Uniform Rational B-Spline) surfaces can be decomposed into triangular and quadrangular curved elements.

Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures

“…of the MoM coefficient matrix of the system of linear equations given in (3). This convergence pattern is shown with respect to the number of MRW samples per region used in the integration of (7) and (8). Since the functions f j ind (j = 1, .…”

“…These results anticipate a CPU time savings when MRW quadrature rules are used instead of DE quadrature rules. In order to compare the CPU time consumption by MRW and DE quadrature rules, the phase curves shown at 29.75 GHz in [17] have been reproduced by MRW and DE quadrature rules in the numerical integration of (7) and (8). The geometrical variables ψ 1 and α used to reproduce results given in [17] are shown in Figure 5 (i.e., these values of the geometrical parameters ψ 1 and α ensure that the required condition of 180 deg of phase difference is satisfied at 29.75 GHz to apply VRT).…”

“…The singular behaviour of the periodic Green's functions is proportional to 1/(4πρ) where [21]. Since the periodic Green's functions provide singular behaviour when the Cartesian coordinates x and y of the observation point and the Cartesian coordinates x and y of the source point are close, the integrands of the bi-dimensional integrals shown in (7) and (8) show a similar singular behaviour. This singular behaviour of these integrands is produced in parametric domain of Bézier patch around values u obs and v obs , which satisfy the following system of equation:…”

“…Mature Computer Aided Geometric Design (CAGD) based on NURBS meshing is available. In this work, the NURBS meshing technique used is based on a redesigned and optimized Paving Algorithm [8]. Although a mesh of NURBS surfaces of an arbitrary layout is accurate for constructing and storing the surface of layout, more suitable surface meshing for numerical computation of parameters associated with the surface is preferred (curvature, derivatives, integrations, etc).…”

Simulation of hydrodynamic interaction forces acting on a ship sailing across a submerged bank or an approach channel

“…Although the paving algorithm has been improved by later contributions (White and Kinney, 1995;Kinney, 1997) and successfully applied in various engineering and scientific areas including, for instance, electromagnetics (Moreno et al, 2011), it still sometimes generates meshes containing poor quality elements, and even invalid elements that cannot be improved by its quality improving procedure. This issue is particular critical for online simulations that require dynamical meshing, and must be solved prudently as inferior or invalid elements can cause a meshing failure and thus halt the simulation.…”