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Localized radial basis function methods for PDEs in thin volumes

Banff International Research Station for Mathematical Innovation and Discovery

This work was initiated because we wanted to simulate the biomechanics of the respiratory system. The main muscle that drives the respiration is the diaphragm which has an aspect ratio of approximately 1:100 of the length and thickness scales. There are several practical challenges to deal with. Creating a smooth representation of the geometry extracted from medical images; generating anisotropic scattered nodes within the thin volume; applying physically relevant boundary conditions; and solving the (non-linear) elasticity equations. In this talk, I will show results for the geometry representation as well as analysis of and results for a simplified anisotropic linear elasticity problem.

Mathematics; Numerical analysis; Partial differential equations; Women and early careers in math

video/mp4

Author affiliation: Uppsala U.

2019-11-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72249

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/