Resumen de Desarrollo y optimización de un generador de mallas superficiales y/o volumétricas para aplicaciones de simulación electromagnética
- español
En esta tesis, se estudia el problema de la discretización de modelos geométricos complejos mediante elementos de formas simples y tamaños homogéneos, conocido como mallado. El objetivo es el mallado orientado a la simulación con métodos de análisis electromagnético, concretamente, el Método de los Momentos y la Óptica Física, utilizada para el cálculo del campo radiado por objetos complejos. Para ello, se ha desarrollado un algoritmo de generación de mallas superficiales que descompone los modelos geométricos en elementos cuadrangulares y triangulares conformados a los cuerpos originales, con una resolución de mallado que depende de la longitud de onda de análisis. Con este método, se garantiza una discretización robusta y fiable del modelo geométrico original. También se presenta un algoritmo de mallado volumétrico para discretizar objetos cerrados con hexaedros homogéneos, con el objetivo de modelar objetos volumétricos dieléctricos. Para poder trabajar con formas arbitrarias, se ha utilizado el modelado mediante superficies paramétricas no racionales (NURBS), ya que permite un alto nivel de detalle con una formulación matemática relativamente sencilla y bastante robusta. Con el objetivo de maximizar la interoperabilidad de los métodos de mallado, se propone un algoritmo de interpolación que permite convertir mallas de puntos de paso a curvas o superficies paramétricas. La generación de mallas es un proceso costoso en términos de recursos de CPU, por lo que los métodos presentados en esta tesis han sido paralelizados. También se exponen técnicas de preprocesado de los modelos geométricos y de postprocesado de las mallas, que garantizan que las mallas finales cumplan todos los requisitos impuestos por los núcleos de análisis electromagnético con las mejores prestaciones posibles. En la sección de resultados se validan las técnicas expuestas en este trabajo.
- English
In this thesis, the problem of discretization of geometric complex models by means of simple shapes and homogeneous sizes elements is studied, better known as meshing, and that is necessary in multiple software applications. Geometric models rendering is an example aimed at graphic visualization, in which arbitrary objects are approximated by means of basic shapes to facilitate the representation with new objects with the same appearance that the original ones. Another application, in which this project has been really focused, is the analysis of geometric models with numerical techniques that require simplifying the original geometries with elements of specific characteristics to ensure reliable results, such as thermal analysis, fluid dynamics, etc.
The aim of this project is the meshing simulation-oriented with electromagnetic analysis methods, in particular, the Method of Moments and the Physical Optics, applied to the calculation of the scattered field of any complex object. To do that, a superficial meshing algorithm has been implemented which breaks the geometric models down into quadrangular or triangular body-fitted elements, with a resolution mesh that depends on the wavelength analysis. With this method, a robust and reliable original geometric model discretization is guaranteed. A volumetric meshing algorithm to break closed objects down into homogeneous hexahedrons is also shown, with the aim of modelling dielectric volumetric objects.
To be able to work with arbitrary shapes, the non-rational parametric surfaces (NURBS) modelling has been used, as this provides a high level detail with a relatively simple and robust mathematical formulation. Although most of Computer Aided Geometric Designs tools use parametric surfaces, there are some tools that only work with grid of points on curves or surfaces. With the aim of maximizing the interoperability of the meshing methods, an interpolation algorithm that permits to convert grid points to parametric curves or surfaces is proposed. Mesh generation is a heavy process in terms of CPU resources, so the methods proposed in this thesis have been parallelized. Furthermore, a new optimization technique of the superficial meshing process is presented, that consists in a multilevel mesh generation, and allows reducing widely the meshing resources. Additional preprocessing and postprocessing techniques of the input geometric models and output meshes are also presented, respectively, that guarantee that the final meshes achieve all requirements imposed by the electromagnetic analysis kernels with the best features.
To verify all methods proposed in this thesis, a simulation collection is gathered, in which results of simulating some superficial meshes obtained with the developed algorithm are compared to other ones generated with commercial meshing tools. Meshing times are also analysed when the speeding up techniques proposed in thisproject are used or not
