Graduate Students Seminar

Speaker 1: Ahmet Aydin

Title

A Monolithic Solver for the Unsteady Navier-Stokes Equations

Abstract

Consider the unsteady, time dependent, Navier-Stokes Equations which govern fluid dynamics. The spatial discretization is achieved using Taylor-Hood elements, where biquadratic basis functions are applied to the velocity components and bilinear basis functions to the pressure components. For time discretization, the unconditionally stable backward Euler method is employed. Rather than solving the system sequentially at each time step, the algebraic systems across all time steps are combined into a single monolithic system. The resulting system is solved using Picard iteration.

Speaker 2: Haoyu Ren

Title

Literature review on nonparametric methods for doubly robust estimation of continuous treatment effects

Abstract

Continuous treatments (e.g.doses) arise often in practice,but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We develop a novel kernel smoothing approach that requires only mild smoothness assumptions on the effect curve and still allows for misspec- ification of either the treatment density or outcome regression. We derive asymptotic properties and give a procedure for data-driven bandwidth selection. The methods are illustrated via sim- ulation and in a study of the effect of nurse staffing on hospital readmissions penalties.