Research

Preprints:

  1. Matthew A. Cassini and Brittany Froese Hamfeldt. Numerical optimal transport from 1D to 2D using a non-local Monge-Ampere equation.
  2. Brittany Froese Hamfeldt.  A strong comparison principle for the generalised Dirichlet problem for Monge-Ampere.
  3. Yassine Boubendir, Jake Brusca, Brittany Froese Hamfeldt, and Tadanaga Takahashi.  Domain decomposition methods for the Monge-Ampere equation.

Refereed publications:

  1. Brittany Froese Hamfeldt and Axel G. R. Turnquist.  On the reduction in accuracy of finite difference schemes on manifolds without boundary.  IMA Journal of Numerical Analysis, 2023, .
  2. Jake Brusca and Brittany Froese Hamfeldt.  A convergent quadrature based method for the Monge-Ampere equation. SIAM Journal on Scientific Computing 45(3): A1097-A1124, 2023.
  3. Brittany Froese Hamfeldt and Axel G. R. Turnquist. A convergence framework for optimal transport on the sphere.  Numerische Mathematik, 151: 627-657, 2022.
  4. Brittany Froese Hamfeldt and Jacob Lesniewski. Convergent finite difference methods for fully nonlinear elliptic equations in three dimensions.  Journal of Scientific Computing, 90(35), 2022.
  5. Brittany Froese Hamfeldt and Jacob Lesniewski.  A convergent finite difference method for computing minimal Lagrangian graphs.  Communications on Pure and Applied Analysis, 21(2): 393-418, 2022.
  6. Brittany Froese Hamfeldt and Axel G. R. Turnquist.  Convergent numerical method for the reflector antenna problem via optimal transport on the sphere.  Journal of the Optical Society of America A, 38(11): 1704-1713, 2021
  7. Brittany Froese Hamfeldt and Axel G. R. Turnquist.  A convergent finite difference method for optimal transport on the sphere.  Journal of Computational Physics, 445(15), 2021.
  8. Brittany Froese Hamfeldt. Convergence framework for the second boundary value problem for the Monge-Ampere equation.  SIAM Journal on Numerical Analysis, 57(2): 945-971, 2019.
  9. Brittany Froese Hamfeldt. Convergent approximation of non-continuous surfaces of prescribed Gaussian curvature. Communications on Pure and Applied Analysis, 17(2): 671-707, 2018.
  10. Brittany Froese Hamfeldt and Tiago Salvador.  Higher-order adaptive finite difference methods for fully nonlinear elliptic equations. Journal of Scientific Computing 75(3): 1282-1306, 2018.
  11. Zexin Feng, Brittany D. Froese, Rongguang Liang, Dewen Cheng, and Yongtian Wang. Simplified freeform optics design for complicated laser beam shaping.  Applied Optics, 56(33): 9308-9314, 2017.
  12. Yunan Yang, Björn Engquist, Junzhe Sun, and Brittany D. Froese. Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion.  Geophysics, 83(1): R43-R62, 2018.
  13. Brittany D. Froese. Meshfree finite difference approximations for functions of the eigenvalues of the Hessian.  Numerische Mathematik, 138(1): 75-99, 2018.
  14. Jun Liu, Brittany D. Froese, Adam M. Oberman, and Mingqing Xiao.  A multigrid scheme for 3D Monge-Ampere equations. International Journal of Computer Mathematics, 94(9):1850-1866, 2017.
  15. Brittany D. Froese, Adam M. Oberman, and Tiago Salvador.  Numerical methods for the 2-Hessian elliptic partial differential equation.  IMA Journal of Numerical Analysis, 37(1):209-236, 2017.
  16. Jean-David Benamou and Brittany D. Froese.  Weak Monge-Ampere solutions of the semi-discrete optimal transportation problem. In Topological Optimization and Optimal Transport in the Applied Sciences, volume 17 of Radon Series on Computational and Applied Mathematics.  De Gruyter: 175-203, 2017.
  17. Björn Engquist, Brittany D. Froese, and Yunan Yang.  Optimal transport for seismic full waveform inversion.  Communications in Mathematical Science, 14(8):2309-2330, 2016.
  18. Zexin Feng, Brittany D. Froese, and Rongguang Liang.  Freeform illumination optics construction following an optimal transport map.  Applied Optics, 55(16):4301-4306, 2016.
  19. Zexin Feng, Brittany D. Froese, and Rongguang Liang.  A composite method for precise freeform optical beam shaping.  Applied Optics, 54(31):9364-9369, 2015.
  20. Zexin Feng, Brittany D. Froese, Chih-Yu Huang, Donglin Ma, and Rongguang Liang.  Creating unconventional geometric beams with large depth of field using double freeform-surface optics.  Applied Optics, 54(20):6277-6281, 2015.
  21. Björn Engquist, Brittany D. Froese, and Yen-Hsi Richard Tsai.  Fast sweeping methods for hyperbolic systems of conservation laws at steady state II.  Journal of Computational Physics, 286:70-86, 2015.
  22. Björn Engquist and Brittany D. Froese. Application of the Wasserstein metric to seismic signals.  Communications in Mathematical Science, 12(5):979-988, 2014.
  23. Jean-David Benamou, Brittany D. Froese, and Adam M. Oberman.  Numerical solution of the optimal transportation problem using the Monge-Ampère equation.  Journal of Computational Physics, 260:107-126, 2014.
  24. Björn Engquist, Brittany D. Froese, and Yen-Hsi Richard Tsai.  Fast sweeping methods for hyperbolic systems of conservation laws at steady state.  Journal of Computational Physics, 255:316-338, 2013.
  25. Brittany D. Froese and Adam M. Oberman.  Convergent filtered schemes for the Monge-Ampère partial differential equation.  SIAM Journal on Numerical Analysis, 51(1):423-444, 2013.
  26. Brittany D. Froese.  A numerical method for the elliptic Monge-Ampère equation with transport boundary conditions.  SIAM Journal on Scientific Computing, 34(3):A1432-A1459, 2012.
  27. Brittany D. Froese and Adam M. Oberman.  Convergent finite difference solvers for viscosity solutions of the elliptic Monge-Ampère equation in dimensions two and higher. SIAM Journal on Numerical Analysis, 49(4):1692-1714, 2011.
  28. Brittany D. Froese and Adam M. Oberman.  Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère Equation.  Journal of Computational Physics, 230(3):818-834, 2011.
  29. Jean-David Benamou, Brittany D. Froese, and Adam M. Oberman.  Two numerical methods for the elliptic Monge-Ampère Equation.  ESAIM: Mathematical Modelling and Numerical Analysis, 44(4):737-758, 2010.
  30. Brittany D. Froese and Adam M. Oberman.  Numerical averaging of non-divergence structure elliptic operators.  Communications in Mathematical Sciences, 7(4):785-804, 2009.

Reports:

  1. Brittany D. Froese.  Generalised finite difference methods for Monge-Ampere equations.  Oberwolfach Report, 7:42-45, 2017.
  2. Jean-David Benamou, Brittany D. Froese, and Adam M. Oberman.  Numerical solution of the second boundary value problem for the Monge-Ampere equation.  INRIA Report, 2012.

Theses:

  1. Numerical methods for the elliptic Monge-Ampère equation and optimal transport, Ph.D. Thesis, Simon Fraser University, 2012.
  2. Numerical methods for two second order elliptic equations, Master's Thesis, Simon Fraser University, 2009.
  3. Homotopy analysis method for axisymmetric flow of a power law fluid past a stretching sheet, Bachelor's Thesis, Trinity Western University, 2007.

Grants:

  1. NSF DMS-2308856
    Approximation of transport maps from local and non-local Monge-Ampere equations
    July 1, 2023 - June 30, 2026
    $379,703
  2. NSF DMS-1751996
    CAREER: Generated Jacobian Equations in Geometric Optics and Optimal Transport
    July 1, 2018 - June 30, 2023
    $400,000
  3. NSF DMS-1619807
    Meshfree Finite Difference Methods for Nonlinear Elliptic Equations
    September 1, 2016 - August 31, 2019
    $149,974
  4. Simons Foundation Collaboration Grant for Mathematicians
    Numerical Methods for Optimal Transportation
    September 1, 2016 - August 31, 2017
    $7,000