Elementos finitos com resolução simplificada de sistemas de equações lineares para dispositivos fotônicos / Finite elements with simplified solutions of linear systems of equations for photonic devices

AUTOR(ES)

Kleucio Claudio

DATA DE PUBLICAÇÃO

2010

RESUMO

The Finite Element Method is one of the most popular numerical tools in electromagnetics. Implicit schemes require the solution of sparse linear equation systems, this step demands a lot of computational time. This work proposes alternatives enhancements to obtain better computational performance of such implicit schemes. This was made through the improvement of direct and iterative methods, for problems which may be interpreted as perturbations of a given original one. This is very important specially in the optimization process of devices, due to the fact that one needs to solve many linear systems with little changes at each step, to explore the search space, so many perturbed linear systems are solved to obtain the optimum device. For direct methods the Small Rank Adjustment technique was used, while for iterative methods, the Preconditioned Gradient Stabilized Biconjugate Method reusing the preconditioner, were adopted. The applications were focused on the design of photonic devices, like couplers, filters, demultiplexers, etc.

ASSUNTO(S)

linear equations iterative methods (mathematics) métodos de elementos finitos fotônicos equações lineares métodos iterativos (matemática) finite element method photonic

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