The present paper summarizes the generalized finite element method formulation and demonstrates some of its advantages over traditional finite element methods to solve complex, three-dimensional structural mechanics problems.
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)
A hybrid computational method for solving boundary-value problems is introduced which combines features of the meshless hp-cloud methods with features of conventional nite 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)
The idea that one can possibly develop computational models that predict the emergence, growth, or decline of tumors in living tissue is enormously intriguing as such predictions could revolutionize medicine and bring a new paradigm into the treatment and prevention of a class of the deadliest maladies affecting humankind. But at the heart of this subject… (More)
An adaptive feedback control system is presented which employs a computational model of bioheat transfer in living tissue to guide, in real-time, laser treatments of prostate cancer monitored by magnetic resonance thermal imaging. The system is built on what can be referred to as cyberinfrastructure-a complex structure of high-speed network, large-scale… (More)
In this paper the implementation of an adaptive mesh refinement scheme into an existing three-dimensional Eulerian hydrocode is described. The adaptive strategy is block-based, which was required in order to leave the existing data structure intact. The focus of this work is on the development of refinement and unrefinement procedures that are conservative… (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)