Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport

This course is offered under the auspices of MIT's Professional Education – Short Programs and will be held on the MIT campus June 14–16, 2009.

Description

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.

Course Outline

Sunday, June 14
0900–1030 Introduction to Reduced Basis Methodology [lecture/demo]
1030–1100 break
1100–1230 Introduction to rbMIT Software [lecture/demo]
1230–1330 lunch
1330–1500 Using Existing Worked Problems: Elliptic PDEs [lab]
Steady Heat Transfer (Conduction and Convection)
 Linear Elasticity (Equilibrium)
1500–1530 break
1530–1700 Using Existing Worked Problems: Parabolic PDEs [lab]
 Unsteady Heat Transfer (Conduction and Convection)

Monday, June 15
0900–1030 Pedagogical Approaches [group discussion]
1030–1100 break
1100–1230 User Inputs I: the "rbU" file [lecture/demo]
(Polygonal Geometries)
1230–1330 lunch
1330–1500 Creating New Worked Problems: Steady Heat Transfer [lab]
1500–1530 break
1530–1700 Creating New Worked Problems: Linear Elasticity [lab]
1700–1900 Reception

Tuesday, June 16
0900–1030 Creating New Worked Problems: Unsteady Heat Transfer [lab]
1030–1100 break
1100–1200 User Community/Collaborative Plans [group discussion]
1200–1230 User Inputs II: the "rbU" file [lecture/demo]
(Curved Geometries)
1230–1330 lunch
1330–1500 Creating New Worked Problems: Curved Geometries [lab]
1500–1530 break
1530–1630 Future Capabilities (acoustics, fluid flow, …) [lecture/demo]
1630–1700 Wrap-up

Prerequisites

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.)

Intended Audience

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

Tuition

Tuition is $1000. Scholarships are also available. The course is non-profit: all revenue net of the MIT Professional Institute expenses will support further development of the website.

Enrollment

The course will be offered if at least 8 participants are preregistered by 15 April 2009, and interested individuals are encouraged to contact Professor Tony Patera at patera@mit.edu. One can enroll for the course through MIT's Professional Education – Short Programs website.