Browsing by Author "Fernandez, Alvaro Agustin"
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Item An object-oriented framework for solving model problems using the sequential function approximation algorithm(2001) Fernandez, Alvaro Agustin; Meade, Andrew J., Jr.This dissertation describes and tests an Object-Oriented framework, written in Fortran 90, for the Sequential Function Approximation (SFA) algorithm. The SFA algorithm is a meshless method which places its basis functions in the domain sequentially, using optimization techniques. The framework described herein allows the user to define the domain, boundary conditions, and governing equations of 1-D and 2-D problems with minimal user coding, and to solve them using the SFA method. This work advances the state of knowledge in the fields of meshless methods in general and of the SFA method in particular. Unsteady transport problems are solved for the first time with the SFA method: diffusive, convective-diffusive, and purely convective problems are solved using a semi-discrete approach and stabilized with the Streamline-Upwind Petrov-Galerkin (SUPG) technique. Additionally, some light is shed on the role of consistency. SFA is placed within the broader context of meshless methods, and made consistent by transforming it into a sequentially solved Partition of Unity (POU) method. Consistency is experimentally found to improve the convergence behavior of all model problems solved. The improvement is most notable in problems with convection phenomena, although some improvement is seen even in purely diffusive problems. Other hypotheses regarding the SFA method are investigated as well.Item The application of feedforward artificial neural networks to function approximation and the solution of differential equations(1994) Fernandez, Alvaro Agustin; Meade, Andrew J., Jr.The increasing use of artificial neural networks and other connectionist systems in engineering, and the advantages obtained from that use, motivated the development of an approach wherein a single or multiple input feedforward artificial neural network with piecewise linear hard limit transfer functions could be directly "constructed." By viewing the network as a function approximator, algebraic constraint equations for the input and bias weights were derived which transformed the mathematical character of the net into one amenable to rigorous analysis without changing the architecture. Further application of the method of weighted residuals allowed direct solution for the output weights without any training. Ordinary and partial differential equations were solved using this method and the resulting accuracy and reliability verified. Further extension of this research will hopefully lead to the creation of adaptive engineering systems able to incorporate both governing equations and experimental data.