Computational design for electromagnetic simulations

An automatic computational procedure has been developed to efficiently and accurately design the shape of complicated electromagnetic objects. These electromagnetic objects can be simulated for operation at high frequencies (~10 GHz), and can be comprised of dissimilar materials. The automated design procedure consists of linking together an original electromagnetic field simulation tool, an original adjoint routine for obtaining sensitivity derivatives, and an original grid-smoothing tool with an existing optimization package. The electromagnetic field simulation software employs a temporally and spatially higher-order accurate Streamline Upwind/Petrov-Galerkin finite-element method that numerically solves Maxwell’s equations in the time domain using implicit time stepping. The software for computing sensitivity derivatives employs a reverse-mode time-accurate discrete adjoint methodology that is formulated to automatically maintain consistency with the electromagnetic field simulation software. Grid smoothing is achieved using a spatially higher-order accurate Galerkin finite-element method that generates a numerical solution to the linear elastic equations. All computational solutions to the linear systems present in each software tool are obtained using the Generalized Minimum Residual algorithm with block diagonal preconditioning. Each software tool is implemented using a parallel processing paradigm and is therefore capable of being executed on a distributed memory supercomputer. The order of accuracy of the electromagnetic field simulation software has been determined by using comparisons with exact solutions. The field software’s results were compared to the exact iv solution of a rectangular resonant cavity. In all cases, the order properties of the field software exceed theoretical expectations when linear, quadratic, and cubic tetrahedral elements are employed to discretize the field. To demonstrate the consistency of the adjoint-based sensitivity derivates with those obtained directly from the field solver, derivatives have been extracted from the field software using a complex variable technique. The sensitivity derivatives from the reverse-mode time- accurate discrete adjoint method were then compared and demonstrated to agree to at least seven decimal places. As a demonstration of the assembled technologies, the optimization procedure successfully and efficiently modified the shape of two electromagnetic objects to reduce a specified cost function. A dielectric cube, under the influence of a propagating plane wave, was repositioned within a larger free space volume so that the field variables on the surface of the cube match desired values at a specified time. A similar demonstration case has also been conducted to modify the shape of a dielectric ellipsoid, under the same conditions as the cube

The Role of Computers in Research and Development at Langley Research Center

This document is a compilation of presentations given at a workshop on the role cf computers in research and development at the Langley Research Center. The objectives of the workshop were to inform the Langley Research Center community of the current software systems and software practices in use at Langley. The workshop was organized in 10 sessions: Software Engineering; Software Engineering Standards, methods, and CASE tools; Solutions of Equations; Automatic Differentiation; Mosaic and the World Wide Web; Graphics and Image Processing; System Design Integration; CAE Tools; Languages; and Advanced Topics

Virtual Reality Aided Mobile C-arm Positioning for Image-Guided Surgery

Image-guided surgery (IGS) is the minimally invasive procedure based on the pre-operative volume in conjunction with intra-operative X-ray images which are commonly captured by mobile C-arms for the confirmation of surgical outcomes. Although currently some commercial navigation systems are employed, one critical issue of such systems is the neglect regarding the radiation exposure to the patient and surgeons. In practice, when one surgical stage is finished, several X-ray images have to be acquired repeatedly by the mobile C-arm to obtain the desired image. Excessive radiation exposure may increase the risk of some complications. Therefore, it is necessary to develop a positioning system for mobile C-arms, and achieve one-time imaging to avoid the additional radiation exposure. In this dissertation, a mobile C-arm positioning system is proposed with the aid of virtual reality (VR). The surface model of patient is reconstructed by a camera mounted on the mobile C-arm. A novel registration method is proposed to align this model and pre-operative volume based on a tracker, so that surgeons can visualize the hidden anatomy directly from the outside view and determine a reference pose of C-arm. Considering the congested operating room, the C-arm is modeled as manipulator with a movable base to maneuver the image intensifier to the desired pose. In the registration procedure above, intensity-based 2D/3D registration is used to transform the pre-operative volume into the coordinate system of tracker. Although it provides a high accuracy, the small capture range hinders its clinical use due to the initial guess. To address such problem, a robust and fast initialization method is proposed based on the automatic tracking based initialization and multi-resolution estimation in frequency domain. This hardware-software integrated approach provides almost optimal transformation parameters for intensity-based registration. To determine the pose of mobile C-arm, high-quality visualization is necessary to locate the pathology in the hidden anatomy. A novel dimensionality reduction method based on sparse representation is proposed for the design of multi-dimensional transfer function in direct volume rendering. It not only achieves the similar performance to the conventional methods, but also owns the capability to deal with the large data sets

Deep Learning for Inverting Borehole Resistivity Measurements.

139 p.El subsuelo terrestre está formado por diferentes materiales, principalmente por rocas porosas que posiblemente contienen minerales y están rellenas de agua salada y/o hidrocarburos. Por lo general, las formaciones que crean estos materiales son irregulares y con materiales de diferentes propiedades mezclados en el mismo estrato.Uno de los principales objetivos en geofísica es determinar las propiedades petrofísicas del subsuelo de la Tierra. De este modo, las compañías pueden determinar la localización de las reservas de hidrocarburos para maximizar su producción o descubrir localizaciones óptimas para el almacenamiento de hidrógeno o el depósito de CO$_2$. Para este propósito, las compañías registran mediciones electromagnéticas utilizando herramientas de Medición Durante Perforación (LWD por sus siglas en inglés -- Logging While Drilling), las cuales son capaces de recabar datos mientras se lleva a cabo el proceso de prospección. Los datos obtenidos se procesan para producir un mapa del subsuelo de la Tierra. Basándose en el mapa generado, el operador ajusta en tiempo real la trayectoria de la herramienta de prospección para seguir explorando objetivos de explotación, incluidos los yacimientos de petróleo y gas, y maximizar la posterior productividad de las reservas disponibles. Esta técnica de ajuste en tiempo real se denomina geo-navegación.Hoy en día, la geo-navegación desempeña un papel esencial en geofísica. Sin embargo, requiere la resolución de problemas inversos en tiempo real. Esto supone un reto, ya que los problemas inversos suelen estar mal planteados.Existen múltiples métodos tradicionales para resolver los problemas inversos, principalmente, los métodos basados en el gradiente o en la estadística. Sin embargo, estos métodos tienen graves limitaciones. En particular, a menudo necesitan calcular el problema inverso cientos de veces para cada conjunto de mediciones, lo que es computacionalmente caro en problemas tridimensionales (3D).Para superar estas limitaciones, proponemos el uso de técnicas de Aprendizaje Profundo (DL por sus siglas en inglés -- Deep Learning) para resolver los problemas inversos. Aunque la etapa de entrenamiento de una Red Neuronal Profunda (DNN por sus siglas en inglés Deep Neural Network) puede requerir mucho tiempo, una vez que la red está correctamente entrenada puede predecir la solución en una fracción de segundo, facilitando las operaciones de geo-navegación en tiempo real. En la primera parte de esta tesis, investigamos las funciones de pérdida apropiadas para entrenar una DNN cuando se trata de un problema inverso.Además, para entrenar adecuadamente una DNN que se aproxime a la solución inversa, necesitamos un gran conjunto de datos que contenga la solución del problema directo para muchos modelos terrestres diferentes. Para crear dicho conjunto de datos, necesitamos resolver una Ecuación en Derivadas Parciales (PDE por sus siglas en inglés -- Partial Differential Equation) miles de veces. La creación de un conjunto de datos puede llevar mucho tiempo, especialmente para los problemas bidimensionales y tridimensionales, ya que la resolución de la PDE mediante métodos tradicionales, como el Método de Elementos Finitos (FEM por sus siglas en inglés -- Finite Element Method), es computacionalmente caro. Por lo tanto, queremos reducir el coste computacional de la construcción de la base de datos necesaria para entrenar la DNN. Para ello, proponemos el uso de métodos de Análisis Isogeométrico refinado (rIGA por sus siglas en inglés -- refined Isogeometric Analysis).Además, exploramos la posibilidad de utilizar técnicas de DL para resolver PDE, que es la limitación computacional principal al resolver problemas inversos. Nuestro objetivo principal es desarrollar un simulador rápido para resolver PDE paramétricas. Como primer paso, en esta tesis analizamos los problemas de cuadratura que aparecen al resolver PDE utilizando DNN y proponemos diferentes métodos de integración para superar estas limitacionesbca