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  Project abstracts can be viewed from the CD-ROM which is enclosed or the SMA website (  
  AMM&NS Programme HPCES Programme IMST Programme MEBCS Programme  
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  HPCES Programme  
Expertise: Numerical methods for partial differential equations
Output Bounds for Partial Differential Equations
Project Advisor
Assoc Prof Khoo Boo Cheong
Project Advisor (MIT) :
Prof Jaime Peraire
Duration :
December 2000 to December 2004

Project Abstract:

This project focuses on the development of methods for the efficient calculation of lower and upper bounds to outputs which are functionals of the solutions to partial differential equations. Such methods are extremely useful in engineering design where outputs, such as temperatures, displacements and stresses are needed at critical locations, provided of course that the methods are accurate, efficient and inexpensive. Obviously, coarse element discretizations are inexpensive but rather inaccurate, while fine element discretizations are accurate but expensive. The aim is to find methods which possess both accurate and inexpensive characteristics, and which can also be implemented with little difficulty in multiprocessor environments. In particular, the primary objective of this project is to extend the recent work of Patera and Peraire to fracture mechanics problems, where lower and upper bounds to stress intensity factors will be of importance to fracture-resistant design. This has been successfully achieved for stress intensity factors in homogeneous and bimaterial crack problems obtained with the displacement extrapolation method, and for J-integral with a novel method which can treat the quadratic functionals. Now we are computing the bounds to the exact values of J-integral.

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