Rechercher

sur ce site


Accueil du site > Résumés des séminaires > Labo > Improving convergence in numerical analysis using observers - Applications in cardiac modeling

Improving convergence in numerical analysis using observers - Applications in cardiac modeling

We propose an observer-based approach to circumvent the issue of unbounded approximation errors - with respect to the length of the time window considered - in the discretization of wave-like equations in bounded domains, which covers the cases of the wave equation per se and of linear elasticity as well as beam, plate and shell formulations, and so on. Namely, taking advantage of some measurements available on the system over time, we adopt a strategy inspired from sequential data assimilation and by which the discrete system is dynamically corrected using the discrepancy between the solution and the measurements. In addition to the classical cornerstones of numerical analysis made up by stability and consistency, we are thus led to incorporating a third crucial requirement pertaining to observability - to be preserved through discretization. Numerical assessments confirm the a priori error estimates found in the theory, and we will also present a real-life application of the approach with the model of a beating heart and measurements provided by medical imaging.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46