Parameterization adaption for 3D shape optimization in aerodynamics

When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an explicit geometrical representation, it is natural to seek for an analogous concept of parameterization adaptivity. We propose here an adaptive parameterization for three-dimensional optimum design in aerodynamics by using the so-called "Free-Form Deformation" approach based on 3D tensorial B\'ezier parameterization. The proposed procedure leads to efficient numerical simulations with highly reduced computational costs

Smooth parametric surfaces and n-sided patches

The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed

Discontinuities in numerical radiative transfer

Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of the stationary radiative transfer equation is particularly challenging in such situations, because standard numerical methods may perform very inefficiently in the absence of local smoothness. However, a rigorous investigation of the numerical treatment of the radiative transfer equation in discontinuous media is still lacking. The aim of this work is to expose the limitations of standard convergence analyses for this problem and to identify the relevant issues. Moreover, specific numerical tests are performed. These show that discontinuities in the atmospheric physical parameters effectively induce first-order discontinuities in the radiative transfer equation, reducing the accuracy of the solution and thwarting high-order convergence. In addition, a survey of the existing numerical schemes for discontinuous ordinary differential systems and interpolation techniques for discontinuous discrete data is given, evaluating their applicability to the radiative transfer problem

Comparison between specialized quadrature rules for method of moments with NURBS modelling applied to periodic multilayer structures

A comparison between Ma-Rokhlin-Wandzura (MRW) and double exponential (DE) quadrature rules for numerical integration of method of moments (MoM) matrix entries with singular behavior is presented for multilayer periodic structures. Non Uniform Rational B-Splines (NURBS) modelling of the layout surfaces is implemented to provide high-order description of the geometry. The comparison is carried out in order to show that quadrature rule is more suitable for MoM matrix computation in terms of sampling, accuracy of computation of MoM matrix, and CPU time consumption. The comparison of CPU time consumption shows that the numerical integration with MRW samples is roughly 15 times faster than that numerical integration using DE samples for results with similar accuracies. These promising results encourage to carry out a comparison with results obtained in previous works where a specialized approach for the specific analysis of split rings geometries was carried out. This previous approach uses spectral MoM version with specific entire domain basis function with edge singularities defined on split ring geometry. Thus, the previous approach provides accurate results with low CPU time consumption to be compared. The comparison shows that CPU time consumption obtained by MRW samples is similar to the CPU time consumption required by the previous work of specific analysis of split rings geometries. The fact that similar CPU time consumptions are obtained by MRW quadrature rules for modelling of general planar geometries and by the specialized approach for split ring geometry provides an assessment for the usage of the MRW quadrature rules and NURBS modelling. This fact provides an efficient tool for analysis of reflectarray elements with general planar layout geometries, which is suitable for reflectarray designs under local periodicity assumption where a huge number of periodic multilayer structures have to be analyzed.Agencia Estatal de InvestigaciónJunta de Comunidades de Castilla-La Manch

Multisided generalisations of Gregory patches

We propose two generalisations of Gregory patches to faces of any valency by using generalised barycentric coordinates in combination with two kinds of multisided Bézier patches. Our first construction builds on S-patches to generalise triangular Gregory patches. The local construction of Chiyokura and Kimura providing G1 continuity between adjoining Bézier patches is generalised so that the novel Gregory S-patches of any valency can be smoothly joined to one another. Our second construction makes a minor adjustment to the generalised Bézier patch structure to allow for cross-boundary derivatives to be defined independently per side. We show that the corresponding blending functions have the inherent ability to blend ribbon data much like the rational blending functions of Gregory patches. Both constructions take as input a polygonal mesh with vertex normals and provide G1 surfaces interpolating the input vertices and normals. Due to the full locality of the methods, they are well suited for geometric modelling as well as computer graphics applications relying on hardware tessellation

Movimientos simétrico lineales esféricos segmentados para interpolación de orientaciones en planificación de trayectorias de herramienta en CNC de 5 Ejes

RESUMEN: Este artículo emplea biarcos cuaterniónicos para interpolar un conjunto de orientaciones con restricciones de velocidad angular. La curva cuaterniónica resultante representa un movimiento simétrico lineal esférico segmentado con continuidad C1 . El propósito de este esfuerzo es poner en uso los movimientos simétrico lineales desde el punto de vista de aproximación e interpolación de movimiento y presentar su potencial aplicación en la simulación de mecanizado por Control Numérico Computarizado (CNC) y planeación de trayectorias de herramienta. Los biarcos cuaterniónicos pueden ser usados para aproximar curvas B-spline cuaterniónicas que representan movimientos esféricos racionales, los cuales tienen aplicaciones en planeación de trayectorias de robots, en CAD/CAM y en gráficas por computador.ABSTRACT: This paper employs quaternion biarcs to interpolate a set of orientations with angular velocity constraints. The resulting quaternion curve represents a piecewise line-symmetric spherical motion with C1 continuity. The purpose of this effort is to put line-symmetric motions into use from the viewpoint of motion approximation and interpolation, and to present their potential applications in Computerized Numerical Control (CNC) machining simulation and tool path planning. Quaternion biarcs may be used to approximate B-spline quaternion curves that represent rational spherical motions that have applications in robot path planning, CAD/CAM and computer graphics