Nathan Louis Gibson Professor Department of Mathematics Kidder Hall 368 Oregon State University Corvallis, Oregon 97331-4605 USA (541) 737-4894 (Voice) (541) 737-0517 (Fax)

Teaching MTH 451/551-010 Fall 24 MTH 351-010 Winter 24 Archive Communications Publications Presentations Academic Advising Advising Info

Communications

Google Scholar Profile

PDFs for most papers can be found here.

• H Jiang, NL Gibson, Semismooth Newton methods with a shooting-like technique for solving a constrained free-boundary HJB equation, Journal of Computational and Applied Mathematics, Vol. 391, 113428, August 2021.

• Yong Chen, Nathan L Gibson, Arpan Biswas, An Li, Hamid Bashir, Erfaneh Sharif, Claudio Fuentes, Christopher Hoyle, Arturo S Leon, Christopher J Skypeck, Valuation of operational flexibility: A case study of Bonneville Power Administration, Energy Economics, Vol. 98, 105251, June 2021.

• B Johnson, NL Gibson, E Cotilla-Sanchez, A Coupled Karhunen-Loeve and Anisotropic Sparse Grid Interpolation Method for the Probabilistic Load Flow Problem Electric Power Systems Research, Volume 193, April 2021.

• P Hosseini, NL Gibson, D Chen, AS Leon,Flexible decision variables in multi-objective reservoir operation, International Journal of Computer Mathematics, Vol. 98, 11, March 2021.

• A Fisher, J Alvarez, NL Gibson, Analysis of methods for the Maxwell-random Lorentz model , Results in Applied Mathematics, Vol. 8, 100098, November 2020.

• A Biswas, Y Chen, N Gibson, C Hoyle, Bilevel Flexible-Robust Optimization for Energy Allocation Problems, ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg, Vol. 6, Iss. 3, September 2020. (pre-print).

• VA Bokil, NL Gibson, SL Nguyen, EA Thomann and EC Waymire, An Euler–Maruyama method for diffusion equations with discontinuous coefficients and a family of interface conditions, Journal of Computational and Applied Mathematics, April 2020. (pre-print).

• D. Chen, A. S. Leon, C. Fuentes, N. L. Gibson, H. Qin, "Incorporating Filters in Random Search Algorithms for the Hourly Operation of a Multireservoir System", Journal of Water Resources Planning and Management, Vol. 144, Iss. 2, Feb 2018. (pre-print).

• Erfaneh Sharifi, Hamid Bashiri, Arturo Leon, Yong Chen, and Nathan Gibson, "Valuation of flexibility for optimal reservoir operation", Open Water Journal, Vol. 4 : Iss. 2 , Article 5, 2017.

• Hamid Bashiri Atrabi, Erfaneh Sharifi, Arturo Leon, Yong Chen, and Nathan Gibson, "Quantification of Short-term Hydropower Generation Flexibility", Open Water Journal, Vol. 4 : Iss. 2 , Article 6, 2017.

• D Chen, AS Leon, P Hosseini, NL Gibson, C Fuentes, "Application of Cluster Analysis for Finding Operational Patterns of Multireservoir System During Transition Period", Journal of Water Resources Planning and Management, Vol. 143, Iss. 8, 2017. (pre-print).

• Duan Chen, Arturo S Leon, Nathan L Gibson, Parnian Hosseini, "Dimension reduction of decision variables for multireservoir operation: A spectral optimization model", Water Resources Research, 52 (1), 2016.

• V. A. Bokil, N. L. Gibson, D. A. McGregor and C. R. Woodside, "Toward Estimating Current Densities in Magnetohydrodynamic Generators", CCP 2014 Proceedings, Journal of Physics: Conference Series (JPCS), published by the IOP, vol. 640, number 012032, 2015. (pre-print).

• NL Gibson, "A Polynomial Chaos Method for Dispersive Electromagnetics", Communications in Computational Physics, vol. 18, issue 5, pp 1234-1263, 2015. (pre-print).

• VA Bokil, NL Gibson, V Gyrya, DA McGregor, "Dispersion reducing methods for edge discretizations of the electric vector wave equation", Journal of Computational Physics 287, 88-109, 2015. (pre-print).

• NL Gibson, C Gifford-Miears, AS Leon, VS Vasylkivska, "Efficient computation of unsteady flow in complex river systems with uncertain inputs", International Journal of Computer Mathematics 91 (4), 781-797, 2014. (pre-print).

• N. L. Gibson, P. Medina, M. Peszynska, and R. E. Showalter, "Evolution of phase transitions in methane hydrate", Journal of Mathematical Analysis and Applications, Volume 409, Issue 2, Pages 816–833, January 2014. PDF Online.

• M. G. McIntire , V. Vasylkivska, C. Hoyle, and N. L. Gibson, "Applying Robust Design Optimization to Large Systems", ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2014. (pre-print).

• Chen, Duan; Leon, Arturo; Gibson, Nathan L.; and Vasylkivska, Veronika S., "Using A Concurrent Hybrid Method To Optimize Short-Term Operation Of A Multi-Reservoir System With Multiple Objectives" (2014). Proceedings of 11th International Conference on Hydroinformatics, 2014, CUNY Academic Works.

• V. A. Bokil and N. L. Gibson, "Convergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media", 11(4), 657-687, International Journal of Numerical Analysis and Modeling (IJNAM), 2014. (pre-print).
  OSU Technical Report version, 2013 (formerly http://hdl.handle.net/1957/38475).

• V. A. Bokil and N. L. Gibson, "Stability and Dispersion Analysis of High Order FDTD Methods for Maxwell's Equations in Dispersive Media", Contemporary Mathematics, Volume 586, 2013
  PDF Online.

• A. S. Leon, N. L. Gibson, and C. H. Gifford-Miears, “Toward reduction of uncertainty in complex multi-reservoir river systems”, Proceedings, XIX Intl Conference on Water Resources, 2012. (pre-print).

• M. J. Armentrout and N. L. Gibson, "Time Domain Parameter Distribution Estimation in Dispersive Media", Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2011), published by PIMS, 2011 , PDF Online.

• V. A. Bokil and N. L. Gibson, "Analysis of Spatial High-Order Finite Difference Methods for Maxwell's Equations in Dispersive Media", IMA Journal of Numerical Analysis, 32(3), 926-956, 2012, (first published online doi:10.1093/imanum/drr001, 2011), PDF Online. (pre-print).
  Proceedings version: "Analysis of High Order FDTD Methods For Maxwell's Equations in Dispersive Media", Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2011), published by PIMS, 2011 , PDF Online.
  OSU Technical Report version, 2013 (formerly http://hdl.handle.net/1957/13786).

• H.T. Banks, V.A. Bokil, and N.L.Gibson, "Analysis of stability and dispersion in a finite element method for Debye and Lorentz dispersive media", Numerical Methods for Partial Differential Equations, 25(4), pp 885-917, July 2009, PDF Online.

• H.T. Banks, V.A. Bokil, and N.L. Gibson, "Parameter estimation versus homogenization techniques in time-domain characterization of composite dielectrics", Journal of Inverse and Ill-Posed Problems, 15, no. 2, 117-135, 2007, PDF Online.

• H. T. Banks, N. L. Gibson, and W. P. Winfree, "2D Modeling of Pulsed THz Interrogation of SOFI with Knit Lines", Proceedings of Review of Progress in Quantitative NDE, 2007. (pre-print).

• H. T. Banks and N. L. Gibson, "Void detection in foam with knit lines using THz pulse interrogation", Mathematical and Computer Modelling 44, nos. 9-10, 807- 815, 2006, PDF Online.

• H. T. Banks and N. L. Gibson, "Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters", Quarterly of Applied Mathematics, 64, no. 4, 749-795, 2006, PDF Online.

• H. T. Banks, N. L. Gibson, and W. P. Winfree, "Gap detection with electromagnetic terahertz signals", Nonlinear Analysis: Real World Applications 6, no. 2, 381-416, 2005, PDF Online.

• H. T. Banks, V. A. Bokil, D. Cioranescu, N. L. Gibson, G. Griso, and B. Miara, "Homogenization of periodically varying coefficients in electromagnetic materials", Journal of Scientific Computing, 28, no. 2, 191-221, 2006, PDF Online.

• H. T. Banks and N. L. Gibson, "Well-posedness in Maxwell systems with distributions of polarization relaxation parameters", Applied Mathematics Letters 18, 423-430, 2005, PDF Online.

• S. Gavrilets and N. L. Gibson, "Fixation probabilities in a spatially heterogeneous environment", Population Ecology 44, no. 2, 51-58, 2002 PDF Online.

• Mathematics Graduate Student Seminar, OSU. Modeling and Simulation of Electromagnetics, May, 2023.

• Scientific Computing and Numerical Analysis minisymposium at 2021 SIAM PNW Conference, WSU Vancouver, WA. Optimization under uncertainty in magnetohydrodynamic generators, with Evan Rajbhandari and Rigel Woodside, May 2022.

• Applied and Computational Math Seminar, Portland State University, virtual. "Uncertainty Quantification Methods for Multiscale Modeling and Dimension Reduction" April, 2022.

• Mathematics Colloquium, Oregon State University, Corvallis, OR. Uncertainty Quantification Methods for Multiscale Modeling and Dimension Reduction, November, 2020.

• CCMA 2019, UNLV, Las Vegas, Nevada. Numerical Methods for Maxwell’s Equations with Random Polarization, October 2019.

• AMMCS 2019, Waterloo, Ontario, Canada. Analysis of Methods for the Maxwell-Random Lorentz Model, August 2019.

• Mathematics Graduate Student Seminar, OSU. Modeling and Simulation of Electromagnetics, Feb, 2019.

• "Numerical Methods for Dispersive Electromagnetics with Distributions of Parameters", in Recent Advances in Numerical Methods for Maxwell's Equations in Complex Media minisymposium, SIAM Annual Meeting, Portland, OR, July 2018.

• Polynomial Chaos for Dispersive Electromagnetics, in Topical Workshop on Computational Aspects of Time Dependent Electromagnetic Wave Problems in Complex Materials, ICERM, Providence, RI, June, 2018.

• AMS Western Section Meeting "Analysis of Methods for Dispersive Electromagnetics with Distributions of Parameters", Apr 2018.

• Applied Mathematics and Computation Seminar, Oregon State University, Corvallis, OR. "Uncertainty Quantification Methods with Applications", Mar 2018.

• Applied Mathematics and Computation Seminar, Oregon State University, Corvallis, OR. "Gradient-based Methods for Optimization", Feb 2018.

• SIAM PNW Meeting Modeling Dispersive Materials with Parameter Distributions in the Lorentz Model, October, 2017.

• Inverse Problems for Distributions of Parameters in PDE Systems , REU 2017

• SIAM Conference on Optimization. Flexible Decision Variables in Reservoir Operation, May, 2017.

• Mathematics Graduate Student Seminar, OSU. Modeling and Simulation of Electromagnetics, April, 2017.

• Mathematics Graduate Student Seminar, OSU. Uncertainty Quantification Techniques in PDE Systems, April, 2016.

• Invited Speaker, “Quantification of Uncertainties in Materials Science”, NIST, Gaithersburg, MD, January 14-15, 2016.

• Invited Speaker, 2015 PNW Numerical Analysis Seminar, Western Washington University, Bellingham, Washington. "Polynomial Chaos Approach for Dispersive Electromagnetics", October 17, 2015.

• Invited Speaker, Mechanical, Industrial and Manufaturing Engineering Graduate Student Seminar, OSU. "Uncertainty Quantification Techniques in PDE Systems", March 6, 2015.

• Pacific Coast Carbon Storage / Computational Energy Science Research Closeout Meeting, NETL. Finding Arcs in MHD Generators, October 29, 2014.

• Mathematics Graduate Student Seminar, OSU. Research Projects in Math Modeling and Numerical Analysis, May, 2014.

• Cascade Computational and Applied Mathematics Seminar, OSU. "Polynomial Chaos Approach for Maxwell’s Equations in Dispersive Media ", April 5, 2014.

• Mathematics Colloquium, Oregon State University, Corvallis, OR. Uncertainty Quantification Techniques in PDE Systems, November, 2013.

• "Numerical Modeling Methane Hydrate Evolution", in Recent Developments in Numerical Methods for PDEs minisymposium, invited by Yekaterina Epshteyn and Fengyan Li, SIAM Annual Meeting, San Diego, CA, July 2013.

• Applied Mathematics and Computation Seminar, Oregon State University, Corvallis, OR. "Polynomial Chaos Approach for Maxwell's Equations in Dispersive Media", March, 2013.

• Mathematics Graduate Student Seminar, OSU. Modeling and Simulation of Microwaves in Biological Material, April, 2012.

• Applied Mathematics and Computation Seminar, Oregon State University, Corvallis, OR. "Gradient-based Methods for Optimization": Part 1 Part 2, October, 2011.

• Mathematics Graduate Student Seminar, OSU. Modeling and Simulation of Microwaves in Biological Material, May, 2011.

• Applied Mathematics and Computation Seminar, Oregon State University, Corvallis, OR. "Stochastic Spectral Approaches to Bayesian Inference", March, 2011.

• 2011 Joint Mathematics Meeting, New Orleans, LA. "Electromagnetic Relaxation Time Distribution Inverse Problems in the Time-domain", AMS-SIAM Special Session on Control and Inverse Problems for Partial Differential Equations minisymposium, organized by M. L. Joyner, January 2011.

• 2011 Joint Mathematics Meeting, New Orleans, LA. MAA Panel Discussion: The benefits of hosting a regional undergraduate mathematics conference. "Northwest Undergraduate Mathematics Symposium", January, 2011.

• Waves Seminar, NJIT. Polynomial Chaos Approach for Simulations in Dispersive Media , September, 2010.

• Mathematics Colloquium, Reed College, Portland, OR. Inverse Problems for Distributions of Parameters in PDE Systems, Nov 2010.

• Solid-state and Optics Seminar, Oregon State University, Corvallis, OR. "Approximating Dispersive Mechanisms Using the Debye Model with Distributions of Dielectric Parameters", October, 2008.

• Applied Mathematics and Computation Seminar, Oregon State University, Corvallis, OR. "Gradient-based Methods for Optimization": Part 1 Part 2, November, 2007.

• Conference on Applied Inverse Problems 2007: Theoretical and Computational Aspects, University of British Columbia Campus Vancouver, Canada. Electromagnetic Characterization of Damage in Complex Dielectrics, Identification of Defects and Cracks Minisymposium organized by Shiro Kubo, June 2007.

• Mathematics REU, Oregon State University, Corvallis, OR. Finding damage in Space Shuttle foam, July, 2007.

• Mathematics Colloquium, Oregon State University, Corvallis, OR. Electromagnetic characterization of damage in Space Shuttle foam, March, 2007.

• Applied Mathematics and Computation Seminar, Oregon State University, Corvallis, OR. Inverse Problem for Distributions of Dielectric Parameters, November, 2006.