Computational and Applied Mathematics seminar

Abstrakt finns enbart på engelska: In this talk, we take a look at the challenges involved in modeling the respiratory mechanics numerically. The focus is on the diaphragm, which is the main respiratory muscle, and which is very thin with respect to its size. Two main subproblems, geometry reconstruction and solution of elasticity PDEs in the geometry will be covered. We will discuss the choice of an unfitted oversampled radial basis function partition of unity method, and how it can help us in dealing with the thin geometry. We will discuss what kind of analysis we can use for this type of method. Finally, numerical results will be shown for linearly elastic model problems in the diaphragm geometry.