Yekaterina Epshteyn

Associate Professor at the Department of Mathematics

The University of Utah

Numerical Methods for PDEs, Scientific Computing, Applied Mathematics

CVpdf

Brief Version of the Research Statementpdf

Research Interests:

- Numerical Methods for PDEs, Scientific Computing, Applied Mathematics
- Difference Potentials Method
- Central-Upwind Finite Volume Schemes
- Finite Element Methods
- Mathematical and Computational Modeling of Materials
- Computational Fluid Dynamics
- Shallow Water Models
- Flow in Porous Media, Multiphase Flow
- Biomedical Applications
## Gallery:

Some of the results that we obtained for two-phase flow simulation:

Below 2D view of saturation contour (left) and 3D view of pressure contour (right) at 350 days.

This is an example of heterogeneous benchmark problem (the permeability coefficient is discontinuous).

(Click on saturation picture to see the movie.)

Publications

REU Undergraduate Students: Alex Henabray (May 2014 - December 2014): Project "Numerical Solution of 1D Stefan Problem" (advised jointly with Jason Albright)

Camille Humphries (May 2013 - May 2014): Project "Central-Upwind Schemes for Shallow Water Models" (in Fall 2013 and Spring 2014 advised jointly with Jason Albright)

PhD Graduate Students: Kyle Steffen (Fall 2013 - present, co-advised with K. Golden)

Qing Xia (Fall 2014 - current)

Alumni: Jason Albright (Ph.D student 2011 - 2016), Starting Postdoc Position in October 2016 at the Theoretical Division at Los Alamos National Laboratory (LANL)

Patrick Bardsley (Ph.D student 2011 - 2016), Currently: Postdoctoral Fellow, Department of Mathematics and ICES, University of Texas, Austin

Michael Medvinsky (Postdoc Fall 2013 - May 2015), Currently: Research Assitant Professor, Department of Mathematics, North Carolina State University

Spencer Phippen (REU student May 2013 - January 2014, Project: "Difference Potentials Method for Interface Problems"), Currently: Software Engineer at Google

Recent Research Talks to Middle School Students, Spring 2013:

Project Youth - University of Utah (for 6th Graders from local schools), Spring 2013,Slides

The presentation "Fun Adventure in Applied Mathematics or What is Applied Mathematics?" was illustrated by experiments:

- Generating waves in a pan with a whole milk
- And experiments using soap bubbles

Applied Math Seminar, Fall 2016,html

MAC Websitehtml

Affiliated Faculty Member, Center for Quantitative Biology,html

Some Recent and Future Conferences:

Topics in Applied Nonlinear Analysis: Recent Advances and New Trends, Conference in honor of David Kinderlehrer's 75th birthday, July 18 - 20, 2016, Carnegie Mellon University

Prairie Analysis Seminar, September 25-26, 2015, Kansas State University

CMDS Investigators Workshop: At the Frontiers of Computation and Materials, Snowbird, Utah, USA, May 16, 2015

Pacific Northwest Numerical Analysis Seminar, PNWNAS, October 18 2014

IMA Hot Topics Workshop: Impact of Waves Along Coastlines, Minneapolis, October 14-17 2014, Poster

WhAM! A Research Collaboration Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations, IMA Special Workshop, Minneapolis, August 11-15 2014

CMDS 13, Continuum Models Discrete Systems, Salt Lake City, Utah, July 21-25 2014

ICOSAHOM 2014 , International Conference on Spectral and High Order Methods, Salt Lake City, Utah, June 23-27 2014

International Conference "Difference Schemes and Applications" in honor of 90th Birthday of Prof. Viktor Ryaben'kii, Moscow, Russia, May 27-31 2013, Program

Teaching:

- Fall 2016, Math 6610: Analysis of Numerical Methods I
- Fall 2016, Math 1311 : Accelerated Engineering Calculus I, Canvas
- Spring 2016, Math 1320-009: Engineering Calculus II
- Spring 2016, Math 1320-006: Engineering Calculus II
- Fall 2015, Math 7875-008 : Selected Topics in Numerical Methods for PDE
- Spring 2015, Math 6620 : Analysis of Numerical Methods II
- Fall 2014, Math 6610 : Analysis of Numerical Methods I
- Fall 2014, Math 1311 : Accelerated Engineering Calculus I
- Spring 2014, REU Math 4800 : Undergraduate Research in Mathematics: Selected Numerical Algorithms and Their Analysis, Poster
- Spring 2014, Math 5620 - Math 6865 : Introduction to Numerical Analysis II
- Fall 2013, Math 1311 : Accelerated Engineering Calculus I
- Spring 2013, Math 6630 : Numerical Solutions of Partial Differential Equations
- Fall 2012, Math 5750 - Math 6880 : Optimization
- Spring 2012, Math 6620 : Analysis of Numerical Methods II
- Spring 2012, Math 6790 : Case Studies in Computational Engineering and Science: Mathematics and Materials
- Fall 2011, Math 6610 : Analysis of Numerical Methods I
- Spring 2011, Math 6620 :Analysis of Numerical Methods II
- Fall 2010, Math 6610 : Analysis of Numerical Methods I
## Previous Teaching:

Carnegie Mellon University:- Spring 2010, Math 21-761: Numerical Methods for PDE: Finite Difference and Finite Volume Methods (graduate course)
- Fall 2009, Math 21-369: Numerical Methods (undergraduate course)
- Spring 2009, Math 21-369: Numerical Methods (undergraduate course)
- Fall 2008, Math 211-21: Integration and Differential Equations
- Spring 2008, Math 211-21:Integration and Differential Equations
- Fall 2007, Math 21-111:Calculus for Humanities Students I
University of Pittsburgh:- Teaching Assistant: Matrices and Linear Operators (Spring 2007)
- Grader: Finite Element Method (Spring 2007)
- Instructor: Calculus 1 (Summer 2005)
- Teaching Assistant: Calculus 1, 2 (Spring 2004, 2005-2006)

Contact Information

Department of MathematicsThe University of UtahSalt Lake City, UT 84112e-mail: epshteyn@math.utah.eduphone: (801) 585 - 1644

Last Modified: December, 2015