Evaluation of Localization Strategies with Method of Approximate Particular Solutions Without Mesh

Nelson F Chaverra, Maria C Martínez, Juan D Rios, Julian M Granados

Abstract


En el presente trabajo, se evalúan varios esquemas de localización con  el Método de Soluciones Particulares Aproximadas (MAPS). Este método sin malla utiliza soluciones particulares de una ecuación auxiliar de Poisson no homogénea para aproximar la variable dependiente. Problemas de difusión con condiciones de frontera tipo Dirichlet y Neumann son abordados para evaluar el desempeño de la formulación local mediante el uso de vecindades en forma de cruz, cruz alargada y circular. Los resultados obtenidos con las vecindades en forma de cruz muestran una mayor estabilidad con respecto al parámetro de forma. Las estrategias de localización muestran un mejor desempeño en problemas con condiciones de frontera de Dirichlet, mientras que la formulación global obtiene mejores resultados en problemas de difusión con condiciones de frontera de Neumann.


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