Positions

Research Areas research areas

Selected Publications

Academic Article

Year Title
2020 HIGH-ORDER, DISPERSIONLESS "FAST-HYBRID" WAVE EQUATION SOLVER. PART I: O(1) SAMPLING COST VIA INCIDENT-FIELD WINDOWING AND RECENTERING.  SIAM Journal on Scientific Computing.  42:A1348-A1379. 2020
2016 WELL-POSED BOUNDARY INTEGRAL EQUATION FORMULATIONS AND NYSTROM DISCRETIZATIONS FOR THE SOLUTION OF HELMHOLTZ TRANSMISSION PROBLEMS IN TWO-DIMENSIONAL LIPSCHITZ DOMAINS.  Journal of Integral Equations and Applications.  28:395-440. 2016
2016 WINDOWED GREEN FUNCTION METHOD FOR LAYERED-MEDIA SCATTERING.  SIAM Journal on Applied Mathematics.  76:1871-1898. 2016
2014 The Fourier approximation of smooth but non-periodic functions from unevenly spaced data.  Advances in Computational Mathematics.  40:1073-1092. 2014
2012 Approximation error in regularized SVD-based Fourier continuations.  Applied Numerical Mathematics.  62:1790-1803. 2012
2012 Sobolev smoothing of SVD-based Fourier continuations.  Applied Mathematics Letters.  25:2227-2231. 2012
2011 A FAST ALGORITHM FOR FOURIER CONTINUATION.  SIAM Journal on Scientific Computing.  33:3241-3260. 2011
2010 High-order unconditionally stable FC-AD solvers for general smooth domains II. Elliptic, parabolic and hyperbolic PDEs; theoretical considerations.  Journal of Computational Physics.  229:3358-3381. 2010
2010 High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements.  Journal of Computational Physics.  229:2009-2033. 2010
2005 On the reconstruction of polycrystalline microstructures from two-point correlation statistics.  Journal of Computer-Aided Materials Design.  10:163-173. 2005
2004 Gradient-based non-linear microstructure design.  Journal of the Mechanics and Physics of Solids.  52:2569-2586. 2004
2004 Microstructure sensitive design of an orthotropic plate subjected to tensile load.  International Journal of Plasticity.  20:1561-1575. 2004
2004 Microstructures by design: linear problems in elastic-plastic design.  International Journal of Plasticity.  20:1577-1602. 2004
2001 Microstructure-sensitive design of a compliant beam.  Journal of the Mechanics and Physics of Solids.  49:1639-1663. 2001

Teaching Activities

  • Doctoral Research Taught course 2023
  • Graduate Partial Diff Eqns Taught course 2023
  • Mathematical Optimization Taught course 2023
  • Doctoral Research Taught course 2022
  • Intro to Engineering Computing Taught course 2022
  • Applied Functional Analysis Taught course 2022
  • Doctoral Research Taught course 2022
  • Mathematical Optimization Taught course 2022
  • Doctoral Research Taught course 2021
  • Intro to Numerical Methods I Taught course 2021
  • Mathematics and Apps in MATLAB Taught course 2021
  • Intro to Engineering Computing Taught course 2021
  • Intro to Engineering Computing Taught course 2021
  • Mathematics and Apps in MATLAB Taught course 2021
  • Intro to Numerical Methods I Taught course 2020
  • Mathematics and Apps in MATLAB Taught course 2020
  • Intro to Engineering Computing Taught course 2020
  • Applied Functional Analysis Taught course 2020
  • Mathematical Optimization Taught course 2020
  • Intro to Numerical Methods I Taught course 2019
  • Mathematics and Apps in MATLAB Taught course 2019
  • Calculus II Taught course 2019
  • Intro to Engineering Computing Taught course 2019
  • Mathematical Optimization Taught course 2019
  • Mathematical Optimization Taught course 2019
  • Mathematical Optimization Taught course 2019
  • Mathematics and Apps in MATLAB Taught course 2019
  • Intro to Numerical Methods I Taught course 2018
  • Mathematics and Apps in MATLAB Taught course 2018
  • Intro to Engineering Computing Taught course 2018
  • Applied Functional Analysis Taught course 2018
  • Intro to Engineering Computing Taught course 2018
  • Foundations of Applied Math Taught course 2017
  • Independent Study Taught course 2017
  • Mathematics and Apps in MATLAB Taught course 2017
  • Intro to Engineering Computing Taught course 2017
  • Intro to Engineering Computing Taught course 2017
  • Mathematics and Apps in MATLAB Taught course 2017
  • Mathematics and Apps in MATLAB Taught course 2017
  • Diff Equation w/Linear Algebra Taught course 2016
  • Mathematics and Apps in MATLAB Taught course 2016
  • Senior Seminar Taught course 2016
  • Calculus I Taught course 2016
  • Applied Functional Analysis Taught course 2016
  • Intro to Engineering Computing Taught course 2016
  • Rsrch Exp/Mathematics Taught course 2016
  • Intro to Numerical Methods I Taught course 2015
  • Intro to Numerical Methods I Taught course 2015
  • Introduction Numerical Methods Taught course 2015
  • Mathematics and Apps in MATLAB Taught course 2015
  • Intro to Engineering Computing Taught course 2015
  • Intro to Numerical Methods I Taught course 2015
  • Applied Functional Analysis Taught course 2014
  • Intro to Numerical Methods I Taught course 2014

    • Education And Training

  • B.S. Mechanical Engineering, Brigham Young University
  • M.S. Mechanical Engineering, Brigham Young University
  • Ph.D. Applied & Computational Mathematics, California Institute of Technology

    • Full Name

  • Mark Lyon