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Colloquium - Choi

A-Posteriori Finite Element Bound Method Devised by an Adaptive Refinement, the Direct Equilibration and Parallel Computing Strategies for the Multi-Physical, Multi-Scale and Multi-Dimensional Partial Differential Equations
Hae-Won Choi
University of Toronto
3/28/2005
10:00am-11:00am
NCAR

As numerical techniques widely are applied to multi-physical, multi-scale and multi-dimensional engineering applications, the ability to compute solutions and furthermore the ability to quantify the accuracy of underlying mathematical models seem to be of significant importance for robust and reliable numerical simulations. Over the last two decades, a number of endeavors have focused on the challenge for development and improvement of notable error estimation and adaptive refinement methods. Significant progress has been dedicated in recent years by the use of the advanced a-posteriori finite element error estimation technique termed the bound method. This novel technique provides fast yet robust, reliable and efficient bounds to the "output" of underlying partial differential equations (PDEs) as well as naturally yields a local error indicator, which estimates numerical error for given mathematical models, leading to construct economical and optimized meshes for computations. The bound method in this work is applied to the multi-physical, micro-scale and multi-dimensional PDEs, in particular to facilitate engineering applications governed by the incompressible Navier-Stokes and Energy equations. Furthermore, the bound method devised by advanced numerical strategies, such as an adaptive refinement, the direct equilibration and parallel computing techniques, will address inter-disciplinary and emerging applications: heat and mass transport phenomena in an array of electronic chip devices and heat exchangers; as well as fluidic motion flow and species transport phenomena of the electro-osmotic flow in microchannels for integrated microfluidic systems such as biochip and Lap-on-chip devices.

This talk is sponsored by the National Center for Atmospheric Research Scientific Computing Division and will be held in the Chapman Room at the Mesa Lab.

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