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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)

We review and extend the theory and methodology of a posteriori error estimation and adaptivity for modeling error for certain classes of problems in linear and nonlinear mechanics. The basic idea is that for a given collection of physical phenomena a rich class of mathematical models can be identified, including models that are sufficiently refined and… (More)

- J. T. Oden, C. A. Duarte, O. C.Zienkiewicz, TWJHUHimoir gTATEMHCl, C. A. M. Duarte
- 2007

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)

- Paul T. Bauman, Hachmi Ben Dhia, Nadia Elkhodja, J. T. Oden, Serge Prudhomme
- 2008

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)

- Yusheng Feng, David Fuentes, +6 authors J. Tinsley Oden
- Engineering with Computers
- 2008

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)

- J T Oden, K R Diller, +13 authors Y Zhang
- Numerical methods for partial differential…
- 2007

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)

- J. T. ODEN, YUSHENG FENG
- 1997

In this paper, the development and implementation of highly parallelizable domain decomposition solvers for adaptive hp finite element methods is discussed. Two-level orthogonalization is used to obtain a reduced system which is preconditioned by a coarse grid operator. The condition number of the preconditioned system, for Poisson problems in two space… (More)

- J. Tinsley Oden
- Scholarpedia
- 2010

- J. Tinsley Oden, Serge Prudhomme, Albert Romkes, Paul T. Bauman
- SIAM J. Scientific Computing
- 2006

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)

- J. T. Oden, C. T. Reddy
- 2006