Department of Mathematics

• 


• R. Ingram
  
  310 Thackeray Hall
  University of Pittsburgh
  Pittsburgh, PA 15260
  
  e-mail: rni1@pitt.edu
  
  
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• Academic Adviser
  
  Dr. William Layton

Ross Nicholas Ingram

Research Overview:

I am interested in the application of mathematics to solve physical problems including fluid-thermodynamics in pebble bed nuclear reactors, optimal placement of wind turbines, biological flows (e.g. modeling onset of open-angle glaucoma), electrically conducting flows, reactor physics (flux-nuclide evolution), and image processing. In particular, I apply techniques of real and numerical analysis to study differential equations and their discretizations - this allows for rigorous error and stability estimation of various schemes.

Publications and Technical Reports:

Ingram, R., Unconditional convergence of high-order extrapolations of the Crank-Nicolson, finite-element method for the Navier-Stokes equations (old revision), University of Pittsburgh, Department of Mathematics, Jul. 2010, (submitted, International Journal of Numerical Analysis and Modeling, Jul. 2011). Ingram, R., A new linearly extrapolated Crank-Nicolson time-stepping scheme for the NSE, (draft), University of Pittsburgh, Department of Mathematics, Jun. 2011, (submitted, Mathematics of Computation, Jun. 2011). Yuksel, G. and Ingram, R., Numerical Analysis of a Finite Element, Crank-Nicolson discretization for MHD Flows at Small Magnetic Reynolds Numbers (draft), (submitted, International Journal of Numerical Analysis and Modeling, Jun. 2010). Ingram, R., A Mixed Finite Element Approximation of Stokes-Brinkman and NS-Brinkman Equation for Non-Darcian Flows, (old revision), SIAM J. Numer. Anal. 49, pp. 491-520, 2011. Ingram, R., Layton, W.J., Mays, N., Analysis of Iterated Tikhonov: Defect Correction for Ill-Posed Problems (old revision), University of Pittsburgh, Department of Mathematics, Aug. 2008, (under revision). Ingram, R., Wheeler, M.F., Yotov, I., A Multipoint Mixed Finite Element Method on Hexahedra, (draft), SIAM J. Numer. Anal., Vol. 48, Issue 4, pp. 1281-1312, 2010. Ingram, R., Tutwiler, R.L., "An Application in Hyperspectral Image Processing," Applied Research Laboratory, Technical Report, Apr. 2002. Ingram, R.N., Lewis, A.S., Tutwiler, R.L., An automatic nonlinear correlation approach for processing of hyperspectral images, International Journal of Remote Sensing, Vol. 25, Number 22, 2004, 4981-4998(18).

Research Talks, Posters, and Workshops

Ingram R. "Convergence Analysis of Crank-Nicolson, Finite Element Discretizations of the Navier-Stokes Equations: Avoiding time-step restrictions," SIAM Annual Meeting, Pittsburgh Convention Center, July 12-16, 2010. Ingram, R.N. "A Limitation of the Brinkman model for porous media flows," International Workshop on Fluid Dynamics, University of Waseda, March 8 - 16, 2010. Ingram, R.N. "The Brinkman-Boussinesq model for natural convection in complicated domains," Computational Mathematics Seminar, University of Pittsburgh , November 10, 2009. Ingram, R.N. "The Brinkman model for fast, viscous, and turbulent flows in porous media ," IMA workshop on Flowing Complex Fluids: Rheological Measurements and Constitutive Modeling , Institute of Mathematics and its Applications at University of Minnesota, September 14-18, 2009. Ingram, R.N. "Uncoupling Accuracy and Stability in Tikhonov Regularization Parameter Selection," ICAM Mini-Conference , Virginia Tech University, February 21, 2009. Ingram, R.N. "Sensitivity Relation in an Iterated Tikhonov Regularization Scheme," Varga Conference, Kent State University, Oct. 18, 2008. Brain Imaging Workshop, Mathematical Biosciences Institute at the Ohio State University, Jun. 9-13, 2008.