Convergence study of the -adaptive PUM and the -adaptive FEM applied to eigenvalue problems in quantum mechanics.

In this paper the -adaptive partition-of-unity method and the - and -adaptive finite element method are applied to eigenvalue problems arising in quantum mechanics, namely, the Schrödinger equation with Coulomb and harmonic potentials, and the all-electron Kohn-Sham density functional theory. The partition-of-unity method is equipped with an a posteriori error estimator, thus enabling implementation of error-controlled mesh refinement strategies. To that end, local interpolation error estimates are derived for the partition-of-unity method enriched with a class of exponential functions.

Development of a computational biomechanical model of the human upper-airway soft-tissues toward simulating obstructive sleep apnea.

Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnea (OSA). The anatomy of the tongue and other upper-airway tissues, and the ability to model their behavior, are central to such investigations. We present details of the construction and development of a soft-tissue model of the human upper airway, with the ultimate goal of simulating obstructive sleep apnea.