Computational aspects of electromagnetic NDE phenomena

The development of theoretical models that characterize various physical phenomena is extremely crucial in all engineering disciplines. In nondestructive evaluation (NDE), theoretical models are used extensively to understand the physics of material/energy interaction, optimize experimental design parameters and solve the inverse problem of defect characterization. This dissertation describes methods for developing computational models for electromagnetic NDE applications. Two broad classes of issues that are addressed in this dissertation are related to (i) problem formulation and (ii) implementation of computers;The two main approaches for solving physical problems in NDE are the differential and integral equations. The relative advantages and disadvantages of the two approaches are illustrated and models are developed to simulate electromagnetic scattering from objects or inhomogeneities embedded in multilayered media which is applicable in many NDE problems. The low storage advantage of the differential approach and the finite solution domain feature of the integral approach are exploited. Hybrid techniques and other efficient modeling techniques are presented to minimize the storage requirements for both approaches;The second issue of computational models is the computational resources required for implementation. Implementations on conventional sequential computers, parallel architecture machines and more recent neural computers are presented. An example which requires the use of massive parallel computing is given where a probability of detection model is built for eddy current testing of 3D objects. The POD model based on the finite element formulation is implemented on an NCUBE parallel computer. The linear system of equations is solved using direct and iterative methods. The implementations are designed to minimize the interprocessor communication and optimize the number of simultaneous model runs to obtain a maximum effective speedup;Another form of parallel computing is the more recent neurocomputer which depends on building an artificial neural network composed of numerous simple neurons. Two classes of neural networks have been used to solve electromagnetic NDE inverse problems. The first approach depends on a direct solution of the governing integral equation and is done using a Hopfield type neural network. Design of the network structure and parameters is presented. The second approach depends on developing a mathematical transform between the input and output space of the problem. A multilayered perceptron type neural network is invoked for this implementation. The network is augmented to build an incremental learning network which is motivated by the dynamic and modular features of the human brain

Iterative methods for the saddle-point problem arising from the HC /EI formulation of the eddy current problem

This paper is concerned with the resolution of the linear system arising from a finite element approximation of the time-harmonic eddy current problem. We consider the HC/EI formulation introduced and analyzed in [2], where an optimal error estimate for the finite element approximation using edge elements of the first order is proved. We reduce the linear system by eliminating the Lagrange multiplier introduced in the insulator region. Two different iterative procedures are proposed: a modified SOR method and an Uzawa-like method. The finite element scheme has been implemented in Matlab and the two iterative procedures have been compared by solving four different test problems

An error-based variational approach to computational electromagnetics

Imperial Users onl

Mathematical and Algorithmic Aspects of Atmosphere-Ocean Data Assimilation

The nomenclature “data assimilation” arises from applications in the geosciences where complex mathematical models are interfaced with observational data in order to improve model forecasts. Mathematically, data assimilation is closely related to filtering and smoothing on the one hand and inverse problems and statistical inference on the other. Key challenges of data assimilation arise from the high-dimensionality of the underlying models, combined with systematic spatio-temporal model errors, pure model uncertainty quantifications and relatively sparse observation networks. Advances in the field of data assimilation will require combination of a broad range of mathematical techniques from differential equations, statistics, probability, scientific computing and mathematical modelling, together with insights from practitioners in the field. The workshop brought together a collection of scientists representing this broad spectrum of research strands

Micromagnetic modeling of magnetic nanostructures

Master'sMASTER OF ENGINEERIN

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

The 6th ECCOMAS Young Investigators Conference YIC2021 will take place from July 7th through 9th, 2021 at Universitat Politècnica de València, Spain. The main objective is to bring together in a relaxed environment young students, researchers and professors from all areas related with computational science and engineering, as in the previous YIC conferences series organized under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Participation of senior scientists sharing their knowledge and experience is thus critical for this event.YIC 2021 is organized at Universitat Politécnica de València by the Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) and the Sociedad Española de Matemática Aplicada (SEMA). It is promoted by the ECCOMAS.The main goal of the YIC 2021 conference is to provide a forum for presenting and discussing the current state-of-the-art achievements on Computational Methods and Applied Sciences,including theoretical models, numerical methods, algorithmic strategies and challenging engineering applications.Nadal Soriano, E.; Rodrigo Cardiel, C.; Martínez Casas, J. (2022). Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. https://doi.org/10.4995/YIC2021.2021.15320EDITORIA

Design and development of solid-state functional materials for Na-ion batteries

This Thesis addresses new functional materials for Na-ion battery (NIB) applications. Since the breakthrough of Li-ion battery (LIB), extensive research has been focusing on alternatives to Lithium, based on cheaper and widespread elements for sustainable energy storage solutions. In this context, the effective large-scale deployment of NIB requires great efforts in the development of good Na+ host anodes, high-energy cathodes and safe electrolytes. New components must ensure enhanced efficiency in the NIB operating processes (i.e., Na+ insertion/extraction at the electrode/electrolyte interface and Na+ transport through the electrolyte) for empowering high energy density and long-term cycle stability. Here, we present NIB materials optimization through an innovative approach, based on computational methods that are directly related to experiments. Our aim is to unveil the most important features that can affect the material capabilities towards Na+ uptake, transport and storage. During the research activity at Università di Napoli Federico II, state-of-the-art DFT methods have been employed to investigate the structure-property relationship of solid-state nanoelectrodes. Our studies on TiO2 anatase and MoS2/graphene 2D-heterostructure reveals that sodiation mechanisms are driven by intrinsic structural features. Migration barriers are directly correlated to structure-dependent descriptors, such as the accessible area for the intercalating Na+ at TiO2 surfaces, and the S coordination around the migrating Na+ within MoS2/graphene interface. From these outcomes, we provide new design strategies to improve the electrode efficiency upon sodiation, for example suggesting the preferential growth of TiO2 along the (001) direction or the introduction of S vacancies in MoS2 monolayers. On the cathode side, we unveil the charge compensation mechanism occurring in NaxNi0.25Mn0.68O2 upon desodiation, with a major focus on the O-redox chemistry at very low Na loads. Molecular O2 is predicted to be released from Mn-deficient sites in the bulk cathode via formation of superoxo-species and preferential breaking of labile Ni-O bonds. We prove that increasing M-O covalency via suitable doping would prevent O2 loss and allows to fully recover a reversible process. Research stages at ENS de Lyon and the R&D laboratory of Lithops s.r.l. have been dedicated to the optimization of electrolyte materials. By development and application of polarizable force fields in molecular dynamics simulations, we report reliable predictions of Na+ diffusion and solvation properties into the PyrFSI room-temperature ionic liquid (RT-IL). We combine RT-ILs with cross-linked PEO matrix to obtain highly conductive polymeric membranes. Galvanostatic cycling of Na metal based cells containing these innovative polymer electrolytes and state-of-the-art electrodes shows promising performances and paves the route to further assessment of efficient cells. The foreseen integration of these studies will provide new understanding on the complex charge transfer processes occurring at the electrode/electrolyte interface during battery functioning. The new knowledge on electrochemical behavior of advanced materials will be key for boosting the NIB technology in the near future

Numerical Simulation

Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

Supercomputing in Aerospace

Topics addressed include: numerical aerodynamic simulation; computational mechanics; supercomputers; aerospace propulsion systems; computational modeling in ballistics; turbulence modeling; computational chemistry; computational fluid dynamics; and computational astrophysics

Robotic manipulation of cloth: mechanical modeling and perception

(Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.(Esp) En este trabajo estudiamos varios problemas matemáticos relacionados con la manipulación robótica de textiles. En primer lugar, desarrollamos un modelo continuo libre de 'locking' para la simulación física de textiles inextensibles. Presentamos una novedosa discretización usando 'elementos finitos' de nuestras restricciones de inextensibilidad resultando en un tratamiento unificado de mallados triangulares y cuadrangulares de la tela. A continuación, explicamos cómo incorporar contactos, autocolisiones y fricción en las ecuaciones de movimiento, de modo que las fuerzas de fricción y las restricciones de inextensibilidad y colisiones puedan integrarse implícitamente y sin ningún desacoplamiento. Desarrollamos un 'solver' de tipo 'conjunto-activo' adaptado a nuestro problema no lineal que tiene en cuenta las restricciones activas pasadas para acelerar la resolución de los contactos no resueltos y, además, puede inicializarse desde cualquier punto no necesariamente factible. Posteriormente, nos embarcamos en la validación empírica del modelo desarrollado. Grabamos en un entorno de laboratorio -con cámaras de profundidad y sistemas de captura de movimiento- los movimientos de siete tipos de textiles (entre los que se incluyen, por ejemplo, algodón, tela vaquera y poliéster) de varios tamaños y a diferentes velocidades, terminando con más de 80 grabaciones. Los escenarios considerados son todos dinámicos e implican sacudidas y torsiones rápidas de los textiles, colisiones con obstáculos e incluso golpes con una varilla cilíndrica. Finalmente, comparamos las grabaciones con las simulaciones dadas por nuestro modelo inextensible, y encontramos que, de media, el error es del orden de 1 cm incluso para las telas más grandes (DIN A2) y los escenarios más complicados. Además, también abordamos otros problemas relevantes para la manipulación robótica de telas, como son la percepción y la clasificación de sus estados. Presentamos un algoritmo de reconstrucción basado en la teoría de Morse que procede directamente de una nube de puntos para obtener una descomposición celular de una superficie con o sin borde: los resultados son una parametrización a trozos de la superficie de la tela como una unión de celdas de Morse. A partir de la descomposición celular puede deducirse inmediatamente la topología de la superficie. Por último, estudiamos el espacio de configuración de un trozo de tela: dado que el estado original de la tela es plano, el conjunto de estados posibles bajo la hipótesis de inextensibilidad es el conjunto de superficies desarrollables isométricas a una fija. Demostramos que una curva genérica simple, cerrada y regular a trozos en el espacio puede ser el borde de un número finito de superficies desarrollables con curvatura media no nula. Inspirándonos en este resultado, introducimos las coordenadas dGLI, una representación de dimensión baja del estado de un pedazo de tela basada en una derivada direccional de la integral de enlazamiento de Gauss. Estas coordenadas -calculadas a partir de la posición del borde de la tela- permiten distinguir cambios cualitativos clave en distintas secuencias de plegado.Postprint (published version