Numerical Analysis and Scientific Computing Seminar | Elisabeth Larsson, Meshfree methods for modeling the human respiratory system

MC 5417 and Zoom (For link please contact ddelreyfernandez@uwaterloo.ca)  

Speaker

Professor Elisabeth Larsson Department of Information Technology of Uppsala University

Title

Meshfree methods for modeling the human respiratory system

Abstract

In this talk, I will talk about a long-term project to model the mechanics of the human respiratory system accurately. The geometries and the displacements of the different participating muscles and organs are assumed to be smooth, which indicates that it could be effective to use high-order accurate numerical simulation methods for this application. We are investigating whether meshfree methods based on radial basis function (RBF) approximation are competitive. The main muscle of the respiratory system is the diaphragm, and this is the component that we have so far focused on. The diaphragm is a thin structure, with a complex geometry, which poses some specific numerical challenges. I will discuss an improved method to reconstruct thin geometries from noisy point cloud data using a radial basis function partition of unity method (RBF-PUM). The reconstructed object surface is represented as the zero-level set of a function defined in the ambient space and can be made infinitely smooth. Then I will discuss two different approaches to solving PDEs in such geometries. The first approach RBF-PUM is based on the same tools as were used for the geometry and the second is using stencil-based RBF-FD approximations. Both numerical experiments and theoretical results for the two methods will be included.