J. Tinsley Oden

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The analysis of complex three-dimensional structural components has become a common task in recent years at several industries, like, automotive, aerospace, naval, nuclear, etc. However, the analysis of this class of problems using traditional finite element methods still poses several difficulties. It is a common practice in the industry to use automatic(More)
A hybrid computational method for solving boundary-value problems is introduced which combines features of the meshless Äj?-cloud methods with features of conventional finite elements. The method admits straightforward nonuniform hp-type approximations, easy implementation of essential boundary conditions, is robust under severe distortions of the mesh, and(More)
Abstract In this work, we propose to extend the Arlequin framework to couple particle and continuum models. Three different coupling strategies are investigated based on the L2 norm, H1 seminorm, and H1 norm. The mathematical properties of the method are studied for a one-dimensional model of harmonic springs, with varying coefficients, coupled with a(More)
Laser surgery, or laser-induced thermal therapy, is a minimally invasive alternative or adjuvant to surgical resection in treating tumors embedded in vital organs with poorly defined boundaries. Its use, however, is limited due to the lack of precise control of heating and slow rate of thermal diffusion in the tissue. Nanoparticles, such as nanoshells, can(More)
Elevating the temperature of cancerous cells is known to increase their susceptibility to subsequent radiation or chemotherapy treatments, and in the case in which a tumor exists as a well-defined region, higher intensity heat sources may be used to ablate the tissue. These facts are the basis for hyperthermia based cancer treatments. Of the many available(More)
It is common knowledge that the accuracy with which computer simulations can depict physical events depends strongly on the choice of the mathematical model of the events. Perhaps less appreciated is the notion that the error due to modeling can be defined, estimated, and used adaptively to control modeling error, provided one accepts the existence of a(More)