16th CISM-IUTAM Summer School on: Advanced Integral Equation Methods in Computational Mechanics
July 7, 2008 — July 11, 2008
Coordinator:
- Marc Bonnet (Ecole Polytechnique - CNRS, Palaiseau Cedex, France)
The field equations governing many problems of continuum solid or fluid mechanics, acoustics, electromagnetism… can be reformulated in terms of integral equations using classical concepts of mathematical physics. This approach leads to numerical solution techniques, most notably the boundary element method (BEM) that is well known for providing very accurate results while its maximal efficiency is achieved under relatively simple constitutive assumptions. Integral equation-based solution techniques are especially efficient for dealing with spatial regions which are of large extension or complex geometry, or which involve unknown or moving objects, either as a stand-alone tool or in association with other solution techniques (usually the FEM). They are in particular often employed for solving wave propagation problems.
This course aims at presenting, discussing and demonstrating recent advances in the field of integral equation methods in computational mechanics. A major progress accomplished over the last few years, with considerable impact on applications, has been the formulation of fast solution methods, which overcome the limitations caused by fully-populated matrices and heavy numerical integration in traditional BEM techniques and allow to run million-DOF problems on ordinary personal computers. Hence, considerable attention is devoted in the present proposal to this topic (lectures by Bonnet and Nishimura, and also parts of lectures by Frangi and Rodin). Many current applications of integral equations are made within BEM-FEM coupled formulations (Clouteau) and/or address coupled multiphysics problems (Frangi). Another currently very active area of computational mechanics, namely that involving stochastic modelling, is also addressed (within the specific scope of this summer school) in the lectures by Clouteau on wave propagation in random media. The integral-equation treatment of continuous and discrete periodic media (including its fast-solution component) presented by Rodin has important applications in the computational mechanics of materials. Finally, integral equation formulations for elastic wave propagation are instrumental in the definition of new, non-iterative and computationally fast, wave-based imaging techniques of (visco-)elastic media, based on linear sampling or topological sensitivity (Guzina).
This session is primarily aimed at researchers (from academy or industry) and doctoral students involved in computational methodologies and their applications in fields such as engineering mechanics, geophysics, non-destructive evaluation and electrical engineering.