Seminar on numerical methods
Thursday, September 28, 2017
11:00-11:50 am, Room SL406
Alfa R.H. Heryudono (University of Massachusetts Dartmouth)
Numerical collocation method for simulating 1-D PDE model of human tear film dynamics
Abstract. The one dimensional case for a single lubrication-type equation modeling the dynamics of the human tear film in a blink cycle has been proposed by Braun et al. The equations must be solved on time varying domain and they are of nonlinear, fourth-order in space, and first order in time. We describe the implementation of pseudospectral collocation methods to compute its numerical solutions on a transformed domain and to impose the third-order boundary conditions arising from flux conditions at both end points. At the end, we present some numerical results for full and partial blink cases and compare them with experimental data. This talk is also suitable for undergraduate students who have taken or are currently taking numerical PDE course.