Peter K. Moore
Professor of Mathematics
Department of Mathematics
Southern Methodist University
Dallas, TX 75275

EDUCATION:

B.S. Mathematics, Michigan Technological University, Houghton, MI, 1981
M.S. Mathematics, Rensselaer Polytechnic Institute, Troy, NY, 1983

Ph.D. Mathematics, Rensselaer Polytechnic Institute, Troy, NY, 1988
PROFESSIONAL CAREER:
Sept. 1987 - June 1989, Postdoctoral Associate in Computer Science
        Rensselaer Polytechnic Institute
July  1989 - June 1994, Assistant Professor of Mathematics
        Tulane University
July  1994 - June 2000,  Associate Professor of Mathematics
        Tulane University
July  2000,  Professor of Mathematics
        Tulane University
August 2000 - August 2002, Associate Professor of Mathematics
         Southern Methodist University
Sept. 2002 - date, Professor of Mathematics
         Southern Methodist University
August 2005 - May 2009, Chair of the Mathematics Department
          Southern Methodist University
June 2009 - June 2010, Dean ad interim, Dedman College
          Southern Methodist University
July 2010 - date, Senior Associate Dean and Associate Dean of Academic Affairs, Dedman College
          Southern Methodist University
EDITOR:

         Editorial Board - Applied Numerical Mathematics,  January 2004 - December 2009.

RESEARCH INTERESTS:
Numerical analysis, especially adaptive techniques for partial differential equations and numerical ordinary differential/differential-algebraic equations, supercomputing.
TEACHING INTERESTS:
Calculus, differential equations, numerical analysis, modeling.
SERVICE:
Served on the Governor's K-16+ Mathematics Consortium on Mathematics, Louisiana, Spring 2000.

Member, Provost's Promotion and Tenure Committee, SMU, 2003-2005.

Member, Dean's Faculty Council, SMU, 2007-2009.

Organized honorary degree symposium on K-12 science/math/engineering education, SMU, 2008.
PUBLICATIONS:

M.Z. Haque and P.K. Moore, (2010) "Comparison of hp-adaptive error estimates for second order hyperbolic systems," J. Numer. Math. 18, 1-24.

P.K. Moore and M. Rangelova, (2010) "A posteriori error estimation for hp-adaptivity for fourth-order equations,"  Math. Comp. 79, 677-705.

P.K. Moore and W. Horsthemke, (2009) "Three-dimensional patterns in the Lengyel-Rabai-Epstein model of the CDIMA reaction," Chaos 19, 043116.

P.K. Moore, (2007) "The impact of parameter selection on the performance of an automatic adaptive code for solving reaction-diffusion equations in three dimensions," Numer. Alg. 46, 121-139.

P.K. Moore, (2007) "Solving regularly and singular perturbed reaction-diffusion equations in three space dimensions,'' J. Comp. Phys. 224, 601-615.

W. Horsthemke, C.E. Zachary and P.K. Moore, (2006) "Instabilities in networks of reactors coupled by photochemical feedback,"  Chem. Phys. Lett. 432, 457-461.

P.K. Moore, (2006) "Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for high-order methods in three space dimensions,'' Intern. J. Numer. Anal. Model. 3, 21-51.

P.K. Moore and W. Horsthemke, (2005) "Localized patterns in homogeneous networks of diffusively coupled reactors,'' Physica D. 206, 121-144.

S. Adjerid, P.K. Moore and J. Teresco, Eds. (2005) ADAPT'03: Adaptive Methods for Partial Differential Equations and Large-Scale Computation, Appl. Numer. Math. 52.

W. Horstkemke, K. Lam and P.K. Moore, (2004) "Network topology and Turing instabilities in small arrays of diffusively coupled reactors,'' Phys. Lett. A. 328,  444-451.

P.K. Moore, (2004) "An implicit interpolation error-based error estimation strategy for hp-adaptivity,''  J. Numer. Math. 12, 143-167.

W. Horsthemke and P.K. Moore, (2004) "Turing instability in inhomogeneous arrays of diffusively coupled reactors,'' J. Phys. Chem. A. 108, 2225-2231.

P.K. Moore, (2004) "Interpolation error-based a posteriori error estimation for p-refinement using first and second  derivative jumps,''  Appl. Numer. Math. 48, 63-82.

P.K. Moore, (2003) "Implicit interpolation error-based error estimation for reaction-diffusion equations in two space dimensions,''  Comp. Meth. Appl. Mech. Engrg. 192,4379-4401.

P.K. Moore, (2003) "An incomplete assembly with thresholding algorithm for systems of reaction-diffusion
equations in three space dimensions,''  J. Comput. Phys. 189,  130-158.

P.K. Moore,  (2003) "Applications of Lobatto polynomials to an adaptive finite element method: a posteriori error estimates for hp-adaptivity and grid-to-grid interpolation,''  Numer. Math. 94,  367-401.

P.K. Moore, (2001) "Interpolation error-based a posteriori error estimation in three dimensions: a first step,''  SMU Tech. Report 01-008, 1-33.

P.K. Moore, (2001) "Interpolation error-based a posteriori error estimation for two-point boundary value problems and parabolic equations in one space dimension,''  Numer. Math.  90, 149-177.

K. Skouibine, N. Trayanova and P. Moore,  (2000) "A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium,'' Math. Biosciences. 166, 85-100.

K. Skouibine, N. Trayanova and P. Moore, (2000) "Success and failure of the defibrillation shock: Insights from a simulation study,'' J. Cardiovascular Electrophysiology 11, 785-796.

P.K. Moore,  (2000) "An adaptive h-refinement finite element method for parabolic differential systems: some algorthmic considerations in solving in three space dimensions,'' SIAM J. Sci. Comput. 21,  1567-1586.

K. Skouibine, N. Trayanova and P. Moore, (1999) "Anode/cathode make and break phenomena during defibrillation: Does electroporation make a difference,''  IEEE Trans. BME. 46, 769-777.

P.K. Moore, (1999) "Finite difference methods and spatial a posteriori error estimates for solving parabolic equations in three dimensions on grids with irregular nodes,''  SIAM J. Numer. Anal.36, 1044-1064.

N. Trayanova, K. Skouibine and P. Moore, (1998) "Virtual electrode effects in defibrillation,'' Biophysics and Molecular Biology 69, 387-403.

P.K. Moore, L.R. Petzold and Y. Ren, (1998) "Regularization of index-one differential equations with rank deficient constraints,'' Comput. Math. Appl. 35, 43-61.

P.K. Moore and R.H. Dillon, (1996) "A comparison of several preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a high-order finite element method,'' Appl. Numer. Math. 20, 117-128.

J.E. Flaherty, P.K. Moore and J. Walter, (1995) "Adaptive methods for parabolic partial differential equations with applications to shear band formation,''  in Computational Mechanics '95 Theory and Applications 2, S.N. Atluri, G. Yagawa and T.A. Cruse, Eds., Springer Verlag, Heidelberg, 2487-2492.

P.K. Moore, (1995) "Comparison of adaptive methods for one-dimensional parabolic systems,'' Appl. Numer. Math. 16, 471-488.

J.E. Flaherty and P.K. Moore, (1995) "Integrated space-time adaptive hp-refinement methods for parabolic systems,'' Appl. Numer. Math. 16, 317-341.

P.K. Moore and L.R. Petzold, (1994) "A stepsize control strategy for stiff systems of ordinary differential equations,'' Appl. Numer. Math. 15, 449-463.

P.K. Moore, (1994) "A posteriori error estimation with finite element semi- and fully-discrete methods for nonlinear parabolic equations in one space dimension,'' SIAM J. Numer. Anal. 31, 149-169.

P.K. Moore and J.E. Flaherty, (1993) "High-order adaptive finite element-singly implicit Runge-Kutta methods for parabolic differential equations,'' BIT 33, 309-331.

P.K. Moore and J.E. Flaherty, (1992) "An hp-adaptive method in space and time for parabolic equations,'' in Advances in Computer Methods for Partial Differential Equations VII, R. Vichnevetsky, D. Knight and G. Richter, Eds., IMACS, Rutgers.

P.K. Moore and J.E. Flaherty, (1992) "Adaptive local overlapping grid methods for parabolic systems in two space dimensions,'' J. Comput. Phys. 98, 54-63.

S. Adjerid, J.E. Flaherty, P.K. Moore and Y.J. Wang, (1992) "High-order adaptive methods for parabolic systems,'' Physica D 60, 94-111.

J.E. Flaherty, M. Benantar, R. Biswas and P.K. Moore, (1992) "Symbolic and parallel adaptive methods for partial differential equations,'' in Symbolic and Numerical Computation for Artificial Intelligence, B.R. Donald, D. Kapur and J.L. Mundy, Eds., Academic Press, London.

P.K. Moore and J.E. Flaherty, (1991) "High order adaptive solutions of parabolic equations I. singly implicit Runge-Kutta methods and error estimation,'' Tech. Report 91-12, Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY.

P.K. Moore and J.E. Flaherty, (1990) "A local refinement finite element method for one-dimensional systems,'' SIAM J. Numer. Anal. 27, 1422-1444.

P.K. Moore, C. Ozturan and J.E. Flaherty, (1989) "An environment for the parallel solution of parabolic partial differential equations,'' in Supercomputing '89: Supercomputing Structures and Computations I., L.P. Kartashev, S.I. Kartashev, Eds., 342-347.

J.E. Flaherty, P.K. Moore and C. Ozturan, (1989) "Adaptive overlapping grid methods for parabolic systems,'' in Adaptive Methods for Partial Differential Equations, J.E. Flaherty, P.J. Paslow, M.S. Shephard and J.D. Vasilakis, Eds., SIAM, Philadelphia.

P.K. Moore, C. Ozturan and J.E. Flaherty, (1989) "Towards the automatic numerical solution of partial differential equations,'' Mathematics and Computers in Simulation 31, 325-332.

M. Bieterman, J.E. Flaherty and P.K. Moore, (1986) "Adaptive refinement methods for non-linear parabolic partial differential equations,'' in Accuracy Estimates and Adaptivity for Finite Elements, I. Babuska, O.C. Zienkiewcz, J.R. Gago and E.R. de Oliveira, Eds., J Wiley & Sons, Chichester.

J.E. Flaherty and P.K. Moore, (1984) "An adaptive local refinement finite element method for parabolic partial differential equations,'' in Proceedings of AFREC, 2, 139-152.

ABSTRACTS:
K. Skouibine, N. Trayanova and P. Moore, (1998) "Success and failure of the defibrillation shock: Does it depend on the fiber field,'' in Proceedings - 20th International Conference - IEEE/EMBS, 428-431.
K. Skouibine, N. Trayanova and P. Moore, (1997) "Reorganization and termination of a spiral wave reentry following a defibrillation shock,'' in Proceedings - 19th International Conference - IEEE/EMBS, 13-14.
CONFERENCES AND INVITED LECTURES:
Presented a colloquium talk at Baylor University, October, 2008, Waco, TX.

Presented a minisymposium talk at the SIAM Annual Meeting, July, 2008, San Diego, CA.

Presented an invited special session talk at the 7th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, May, 2008, Arlington, TX.

Presented a talk at the applied math seminar at Wayne State University, April 2008, Detroit, MI.

Presented a colloquium talk at Oakland University, April 2008, Rochester, MI.

Participated in the AMS Committee on Science Policy Forum and visited with congressional staff to discuss funding for science and mathematics, April 2007, Washington D.C.

Presented a seminar talk at Texas A&M University, April 2007, College Station, TX.

Presented a paper at FEMTEC 2006,  December 2006, UTEP, El Paso, TX.

Presented an invited minisymposium talk at MAFELAP06, June 2006, Brunel University, Uxbridge, England.

Presented an invited minisymposium talk at the 8th US National Conference on Computational Mechanics, July 2005, Austin, TX.

Presented a series of ten lectures over one week at the Facultad de Matematicas, Universidad Autonoma de Yucatan, July 2005, Merida, Mexico.

Presented a colloquium at the University of Texas at San Antonio, October 2004, San Antonio, TX.

Presented a seminar and colloquium at Tulane University, November 2003, New Orleans, LA.

Presented a seminar at the Institute for Computational Engineering and Sciences, October 2003, Austin, TX.

Co-organizer of ADAPT'03: Adaptive Methods for Partial Differential Equations and Large-Scale Computation conference, October 2003, Troy, NY.

Presented an invited minisymposium talk at the 7th US National Congress on Computational Mechanics, July 2003, Albuquerque, NM.

Presented an invited talk at the IMACS Workshop on Adaptive Methods for PDEs, Fields Institute, University of Toronto, August 2002, Toronto, Canada.

Presented a short talk at the Texas Finite Element Rodeo at Texas A&M University, March 2002, College Station, TX.

Presented a seminar at SCOREC, Rensselear Polytechnic Institute, July 2001, Troy NY.

Presented a seminar at the Mathematical Research Branch, NIDDK, National Institutes of Health, March 2001, Bethesda, MD.

Presented a short talk at the Texas Finite Element Rodeo, Southern Methodist University, March 2001, Dallas, TX.

Presented an invited talk at the Applied Math Seminar at Colorado State University, February 2001, Fort Collins, CO.

Presented a student seminar at Baylor University, November 2000, Waco, TX.

Presented a seminar at the University of Texas at Arlington,  October 2000, Arlington,TX.

Presented a colloquium at Texas Christian University, October 2000, Ft. Worth, TX.

Presented a student seminar at University of Dallas, September 2000, Dallas, TX.

Presented a colloquium at Southern Methodist University, February 2000,  Dallas TX.

Presented a seminar at SCOREC, Rensselaer Polytechnic Institute, January 2000,  Troy, NY.

Presented an invited talk at the Scientific Computing Seminar, University of Southern Mississippi, December 1999, Hattiesburg, MS.
Presented an invited talk at the Applied Math Seminar, Duke University, December 1999, Durham, NC.
Presented a talk at the Annual Meeting of the Pi Mu Epsilon Chapter of Southeastern Louisiana University, May 1999, Hammond, LA.
Presented a colloquium at Temple University, March 1999, Philadelphia, PA.
Presented a colloquium at Emory University, February 1999, Atlanta, GA.
Presented a seminar at the Cardiac Rhythm Management Laboratory, February, 1999, University of Alabama at Birmingham, Birmingham, AL.
Presented a paper at the First Southern Symposium on Computing, December 1998, University of Southern Mississippi, Hattiesburg, MS.

Presented a colloquium at the University of New Orleans, May 1998, New Orleans, LA.

Presented a colloquium at Southeastern Louisiana University, April 1998, Hammond, LA.

Presented a colloquium at Calvin College, August 1997, Grand Rapids, MI.

Presented an invited lecture and colloquium at Louisiana State University, September 1996, Baton Rouge, LA.

Presented an invited talk at the Workshop on the Method of Lines for Time Dependent Problems, University of Kentucky, June 1995, Lexington, KY.

Presented a seminar at Xavier University, October 1994, New Orleans, LA.

Presented a seminar at the Army High Performance Computing Research Center, October 1993, Minneapolis, MN.

Presented a paper at the IMA Summer Program on Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations, July 1993, Minneapolis, MN.

Presented a seminar at SCOREC and the Computer Science Department, Rensselaer Polytechnic Institute, May 1993, Troy, NY.

Presented a paper at the ISSAC workshop, U.C. Berkeley, July 1992, Berkeley, CA.

Presented a paper at the Seventh IMACS International Conference, June 1992, Rutgers, NJ.

Presented a paper at the SCOREC workshop, Rensselaer Polytechnic Institute, October 1991, Troy, NY.

Presented a colloquium at North Carolina State University, January 1991, Raleigh, NC.

Presented a paper at the Annual SIAM Meeting, July 1990, Chicago, IL.

Presented a paper at the Conference on Expert Systems for Numerical Computing, December 1998, W. Lafayette, IN.

Presented a paper at the Conference on Adaptive Methods for Partial Differential Equations, October 1988, Troy, NY.

Presented a paper at the International Conference on Accuracy Estimates and Adaptive Refinements in Finite Element Computations, June 1984, Lisbon, Portugal.
 

RESEARCH SUPPORT:
Principal Investigator, NSF/MRI, 8/1/05-7/31/06, $197,575, "Acquisition of Scientific Computing Equipment: Enhancing Research in Applied Mathematics and Computation."

Principal Investigator, NSF/DMS, 8/5/03-8/4/04, $5,000, "Conference on Adaptive Methods for Partial Differential Equations and Large-Scale Computation.''

Principal Investigator, NSF/DMS, 8/1/02-7/31/05, $110,985, "Enhancing the Performance of Hp-adaptive Methods for Parabolic and Elliptic Systems.''

Principal Investigator, NSF/SCREMS-DMS, 9/1/01-8/31/04, $60,000, "Enhancement of Scientific Computing
Equipment: Research in Applied Mathematics and Computation.''

Principal Investigator, President's Partners Grant, SMU, 6/1/01-5/31/02, $1,800, ``Three-dimensional
graphics for modeling physical and biological systems.''

Principal Investigator, NSF/DMS, 7/1/99-6/30/02, $73,914, "Adaptive Methods for Systems of Reaction-Diffusion Equations.''

Principal Investigator, BOR/LEQSF (1999-2001), 6/99-6/01, $77,354, ``Enhancement of Scientific Computing Equipement: Department of Mathematics, Tulane University."
Co-Principal Investigator, NSF/GIG, 9/1997-8/2000, $528,779, "Computational Science in Biomedical Systems.''

Co-Principal Investigator, DOE-EM/FG, 6/93-2/97, $172,044 (1st year), $236,865 (2nd year), $192,322 (3rd year), $192,899 (4th year), $260,000 (5th year), "Pore-Level Flow, Transport, Aggolomeration, and Reaction Kinetics of Microorganisms.''

Principal Investigator, NSF/SCREMS-DMS, 8/1/96-7/31/97, $36,452, "Enhancement of Scientific Computing Equipment: Research in Applied Mathematics and Statistics.''

Principal Investigator, BOR/LEQSF (1996-1997), 6/1/96-6/30/97, $79,647, "Enhancement of Scientific Computing Equipment: Department of Mathematics, Tulane University.''

Co-Principal Investigator, ONR (DOD), 9/93-9/94, $121,814, "Enhancement of Research Computing Equipment: Department of Mathematics.''

Co-Principal Investigator, NSF/DUE, 9/94-8/96, $6,500, "Applied Mathematics and Linear Algebra in an Electronic Classroom.''

Co-Principal Investigator, LEQSF (1993-94), 6/93-5/94, $83,662, "Enhancement of Scientific Computing Equipment.''

Co-Principal Investigator, NSF/SCREMS-DMS, 6/1/91-11/92, $41,111, "Enhancement of Scientific Computing Equipment.''

PH.D. STUDENTS:
Christina Dekany, Zia Haque, current.

Kwan Lam, November 2007, Pattern Formation in Non-Linear Chemical Systems.

Marina Rangelova, May 2007, Error Estimates for Fourth Order Partial Differential Equations.


Earl Packard, June 1998, Finite Difference Approximations for Parabolic Systems on Grids with Irregular Nodes.

Kirill Skouibine, May 1998, Mathematical Modeling of Spiral Wave Reentry and Defibrillation Shocks in Ventricular Myocardium.

Hongyi Yu, May 1997, Domain Decomposition Multiplicative Schwarz Method and Local Adaptive Mesh Refinement Strategy for Solving a Class of Nonlinear Parabolic Equations.