Short Programs

Real-Time Reliable Simulations for Heat Transfer and Continuum Mechanics: Educational Applications [2.09s]

Date: TBD, 2011 | Tuition: $1,000 (tentative) | Continuing Education Units (CEUs): 1.4 (tentative)

Course Summary

In this course we will describe, illustrate, and exercise methods and software for real-time reliable solution of heat transfer and continuum mechanics problems for application in education.

The course time will be divided into roughly three parts:

description and illustration of the underlying certified reduced basis methodology;
description and illustration of the associated rbMIT software; and
exercise of the rbMIT software in hands-on sessions.

Participants will learn to use and develop "worked problems" for in-lecture demonstrations (e.g. to visualize fields), homework assignments (e.g. to compare exact and approximate approaches), and semester projects (e.g. to optimize or design systems).

We provide on our website further information on the methodology and the rbMIT © MIT software, as well as examples of worked problems.

The rbMIT © MIT software, which works within Matlab® (optionally COMSOL Multiphysics®), is free for academic use. The package is simple to use: the user provides a high-level problem definition .m file; the software then performs all reduced basis procedures automatically to yield the necessary data and codes for Online real-time response. Automatic publication utilities are also provided.

Prerequisites:
Participants should be familiar with the partial differential equations of heat transfer and continuum mechanics, basic finite element techniques for discretization/solution of partial differential equations, and elementary matlab syntax and capabilities. No prior knowledge of reduced basis techniques is required.

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Learning Objectives

The participants of this course will be able to:

Describe the motivation for reduced basis methods and the contexts in which reduced basis methods are of interest.
List the basic Offline and Online steps required to develop a reduced basis "worked problem."
Perform visualization and output evaluation for existing "worked problems" by using the (Online) rbMIT software.
Develop new "worked problems" by using the (Offline/Online) rbMIT software.
Incorporate "worked problems" into educational applications, such as demonstrations and homework projects, in heat transfer and linear elasticity.

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Who Should Attend

Participants should be familiar with the physics and partial differential equations of heat transfer and continuum mechanics, very basic finite element techniques for discretization/solution of partial differential equations, and elementary matlab syntax and capabilities. No prior knowledge of reduced basis techniques is required. (Very optionally, some knowledge of LaTeX might be useful for dissemination.)

The course should be appropriate for university faculty and teaching staff as well as doctoral graduate students (as part of Teaching Assistant activities).

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Program Outline

Sunday, June 14:

Introduction to Reduced Basis Methodology [lecture/demo]
Introduction to rbMIT Software [lecture/demo]
Using Existing Worked Problems: Elliptic PDEs [lab]

Steady Heat Transfer (Conduction and Convection)
Linear Elasticity (Equilibrium)

Using Existing Worked Problems: Parabolic PDEs [lab]

Unsteady Heat Transfer (Conduction and Convection)

Monday, June 15:

Pedagogical Approaches [group discussion]
User Inputs I: the "rbU" file [lecture/demo]
- (Polygonal Geometries)
Creating New Worked Problems: Steady Heat Transfer [lab]
Creating New Worked Problems: Linear Elasticity [lab]
Reception

Tuesday, June 16:

Creating New Worked Problems: Unsteady Heat Transfer [lab]
User Community/Collaborative Plans [group discussion]
User Inputs II: the "rbU" file [lecture/demo]

(Curved Geometries)

Creating New Worked Problems: Curved Geometries [lab]
Future Capabilities (acoustics, fluid flow, …) [lecture/demo]
Wrap-up

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Course schedule

Class runs 10:00 am - 4:00 pm the first day and 9:00 am - 4:00 pm each subsequent day.

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On-site Courses

We can also offer this course for groups of employees at your location. Please contact the Short Programs office for further details.

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About The Lecturers

Anthony T. Patera
Tony Patera is Ford Professor of Engineering and Professor of Mechanical Engineering, Massachusetts Institute of Technology, and Co-Director of the MIT Center for Computational Engineering. He formerly served as Co-Director of the MIT Supercomputer Facility. Professor Patera received undergraduate and graduate degrees in Mechanical Engineering, and a doctorate in Applied Mathematics, all from MIT. He has published over 100 papers on scientific and engineering computation, computational methods, and numerical analysis, in particular spectral element, finite element, and reduced basis methods for partial differential equations; parallel processing; optimization; and applied mechanics, in particular fluid dynamics and transport phenomena, stability theory, and multicomponent media. His current research focuses on real-time, reliable solution of reduced basis approximation and a posteriori error estimation for parameterized PDEs. Professor Patera has received research awards nationally (AIAA) and internationally (Lombardy Academy of Arts and Sciences, Milan, Italy), as well as numerous teaching and education innovation awards at MIT. He has also developed fluid dynamics simulation software, the NEKTON code, used widely in universities, government laboratories, and industry, as well as the rbMIT software featured in this course.

For more information on Professor Patera's research please visit http://augustine.mit.edu.

Ngoc Cuong Nguyen
Cuong Nguyen is a Research Scientist in the Department of Aeronautics & Astronautics and the Department of Mechanical Engineering at MIT. He received his undergraduate degree from the Department of Aeronautical Engineering, HCMC University of Technology, and graduate and doctorate degrees in Computational Engineering from the Singapore-MIT Alliance, National University of Singapore. He has published papers in several research areas including reduced basis methods and a posteriori error estimation for parametrized partial differential equations, discontinuous Galerkin methods, multi-scale methods, turbulence modeling, and Bayesian analysis and uncertainty quantification. His current research focuses on scientific and engineering computation; numerical methods and analysis — in particular, finite element and multiscale methods for partial differential equations; optimization — in particular, band gap design for photonic and phononic crystals; applied mechanics — in particular, fluid dynamics, transport phenomena, and turbulence modeling; inverse problems — in particular, Bayesian analysis and uncertainty quantification for large-scale PDE-constrained systems. Dr Nguyen has co-developed and co-authored (with AT Patera, DBP Huynh, and G Rozza) the rbMIT software package featured in this course. He is a member of AIAA and SIAM.

For more information on Dr. Nguyen's research, please visit
http://web.mit.edu/cuongng/www/.

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Updates

This class is tentatively planned for 2010, depending on the level of interest. Email the Short Programs office to express your interest in taking this course. Please include your industry and learning goals.

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