## Computational and Applied Mathematics Seminar

## Location and Time

University of Wyoming, Ross Hall 247, Fridays from 4:10-5:00 (unless otherwise stated).

## Seminar Chairs

Professors Craig C. Douglas and Long Lee.

## Support

The CAM seminar series is currently supported through volunteers and the financial contributions by the UW Mathematics Department, MGNet.org, and and an energy grant from ExxonMobil.

## Schedule

For Fall, 2017, the speakers are as follows:

Date Speaker From/Note September 8 Xiukun Hu University of Wyoming September 14* Prof. Hiroshi Fujiwara Kyoto University September 22 Brad McCaskill University of Wyoming September 29 Prof. Xiaoming He Missouri University of Science and Technology October 6 October 13 Prof. Craig Douglas University of Wyoming October 20 October 27 Prof. Jan Mandel University of Colorado at Denver November 3 Novermber 10 Prof. Long Lee University of Wyoming Novermber 17 Prof. Man-Chung Yeung University of Wyoming December 1 * Thursday Colloquium in AG 1030

We are still looking for speakers for Fall 2017! The topics can be original research, a survey of an area, or an interesting paper or papers that would interest the CAM community.

The schedule, titles, and abstracts from Spring 2017 are here.

## Titles and Abstracts

## September 8

## GPU Accelerated Sequential Quadratic Programming

Xiukun Hu, University of WyomingNonlinear optimization problems arise in all industries. Accelerating optimization solvers is desirable. Efforts have been made to accelerate interior point methods for large scale problems. However, since the interior point algorithm used requires many function evaluations, the acceleration of the algorithm becomes less beneficial. We introduce a way to accelerate the sequential quadratic programming method, which is characterized by minimizing function evaluations, on graphical processing units.

## September 14

## Large Scale Numerical Simulation for Near-Infrared Light Propagation in Tissue on Modern Parallel Architectures

Prof. Hiroshi Fujiwara, Graduate School of Informatics, Kyoto UniversityIn this talk we discuss a feasibility of direct computation of the stationary radiative transport equation (RTE) for near-infrared (NIR) light propagation in human bodies. NIR light is poorly absorbed by tissue and is absorbed by hemoglobin, and it is expected to develop non-invasive monitoring of tissue activities. To this end, we have studied practical and reliable numerical methods for RTE which is a mathematical model of light propagation.

RTE is an integro-differential equation and light intensity depends on position and velocity in RTE. Therefore discretization leads essentially five dimensional large scale problems. Conventionally the Monte Carlo method and diffusion approximation have been used to save computational resources.

An upwind finite difference method and the block Gauss-Seidel iterative method are adopted in the current study. We show numerical results using a three dimensional MR image and compare computational times performed on a XeonPhi cluster and GPU nodes.

This work is based on a joint project with Prof. Yuusuke Iso, Prof. Nobuyuki Higashimori (Kyoto University), and the Human Brain Research Center in Kyoto University.

## September 22

## A Locally Conservative Stabilized Continuous Galerkin Finite Element Method for Two-Phase Flow in Poroelastic Subsurfaces

Brad McCaskill, Department of Mathematics, University of WyomingWe study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

## September 29

## Decoupled, Linear, and Energy Stable Finite Element Method for the Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model

Prof. Xiaoming He, Department of Mathematics and Statistics, Missouri University of Science and TechnologyIn this presentation, we discuss an efficient numerical approximation for a phase field model of the coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn-Hilliard-Navier-Stokes equations in the free flow region and Cahn-Hilliard-Darcy equations in the porous media region that are coupled by seven interface conditions. The coupled system is decoupled based on the interface conditions and the solution values on the interface from the previous time step. A fully discretized scheme with finite elements for the spatial discretization is developed to solve the decoupled system. In order to deal with the difficulties arising from the interface conditions, the decoupled scheme needs to be constructed appropriately for the interface terms and a modified discrete energy is introduced with an interface component. Furthermore, the scheme is linearized and energy stable. Hence, at each time step one only needs to solve a linear elliptic system for each of the two decoupled equations. Stability of the model and the proposed method is proved. Numerical experiments are presented to illustrate the features of the proposed numerical method and verify the theoretical conclusions.

## October 13

## Human Identification and Localization by Robots

Prof. Craig Douglas, Department of Mathematics, University of WyomingEnvironments in which mobile robots and humans must coexist tend to be quite dangerous to the humans. Many employers have resorted to separating the two groups since the robots move quickly and do not maneuver around humans easily resulting in human injuries. In this paper we provide a roadmap towards being able to integrate the two worker groups (human and robots) to increase both efficiency and safety.

Improved human to robot communication and collaboration has implications in multiple applications. For example:

(1) Robots that manage all aspects of dispensing items (e.g., drugs in pharmacies or supplies and tools in a remote workplace), reducing human errors.

(2) Dangerous location capable robots that triage injured subjects using remote sensing of vital signs.

(3) 'Smart' crash carts that move themselves to a required location in a hospital, in the field, or around in a remote location such as an offshore oil rig. Such carts help dispense drugs and tools, save time and money, and prevent accidents.This is joint work with Prof. Robert A. Lodder, University of Kentucky.

## October 27

## TBD

Prof. Jan Mandel, Department of Mathematics, University of Colorado at Denver...

## November 10

## TBD

Prof. Long Lee, Department of Mathematics, University of Wyoming...

## November 17

## TBD

Prof. Man-Chung Yeung, Department of Mathematics, University of Wyoming...