Books Edited

  1. T. Bridges, M. D. Groves, D. P. Nicholls, Lectures on the Theory of Water Waves, London Mathematical Society Lecture Note Series, 426 (Cambridge University Press, 2016) download .
  2. P. Guyenne, D. P. Nicholls, C. Sulem, Hamiltonian Partial Differential Equations and Applications, Fields Institute Communications, 75 (Springer, 2015) download .

Journal Publications

Submitted

  1. D. P. Nicholls, X. Tong, "Simulation of Localized Surface Plasmon Resonances in Two Dimensions via Impedance-Impedance Operators" download .
  2. D. P. Nicholls, C. Perez-Arancibia, C. Turc, "Sweeping Preconditioners for the Iterative Solution of Quasiperiodic Helmholtz Transmission Problems in Layered Media" download .
  3. G. Ely, A. Malcolm, D. P. Nicholls, "Global Optimization for Full Waveform Inversion: Understanding Trade-offs and Parameter Choices" download .

To Appear

  1. D. P. Nicholls, "High-Order Spectral Simulation of Graphene Ribbons," Communications in Computational Physics download .
  2. Z. Ghiasi, J. Komperda, D. Li, A. Peyvan, D. P. Nicholls, and F. Mashayek, "Modal Explicit Filtering for Large Eddy Simulation in Discontinuous Spectral Element Method," Journal of Computational Physics download .

Appeared

  1. M. Kaplan and D. P. Nicholls, "A Nonlinear Least Squares Framework for Periodic Grating Identification with a High-Order Perturbation of Surfaces Implementation," Applied Numerical Mathematics, Volume 143, 20-34 (2019) download .
  2. Y. Hong, M. Otten, M. Min, S. Gray, and D. P. Nicholls, "Periodic Corrugations to Increase Efficiency of Thermophotovoltaic Emitting Structures," Applied Physics Letters, Volume 114, 053901 (2019) download .
  3. M. Ngom and D. P. Nicholls, "Well-Posedness and Analyticity of Solutions to a Water Wave Problem with Viscosity," Journal of Differential Equations, Volume 365, Issue 10, 5031-5065 (2018) download .
  4. D. P. Nicholls and X. Tong, "High-Order Perturbation of Surfaces Algorithms for the Simulation of Localized Surface Plasmon Resonances in Two Dimensions," Journal of Scientific Computing, Volume 76, Issue 3, 1370-1395 (2018) download .
  5. Y. Hong and D. P. Nicholls, "A High-Order Perturbation of Surfaces Method for Vector Electromagnetic Scattering by Doubly Layered Periodic Crossed Gratings," Journal of Computational Physics, Volume 372, 748-772 (2018) download .
  6. D. P. Nicholls, "Stable, High-Order Computation of Impedance-Impedance Operators for Three-Dimensional Layered Media Simulations," Proceedings of the Royal Society of London, A, Volume 474, 20170704 (2018) download .
  7. D. P. Nicholls, "Numerical Simulation of Grating Structures Incorporating Two-Dimensional Materials: A High-Order Perturbation of Surfaces Framework," SIAM Journal on Applied Mathematics, Volume 78, Issue 1, 19-44 (2018) download .
  8. X. Feng, J. Lin, and D. P. Nicholls, "An Efficient Monte Carlo-Transformed Field Expansion Method for Electromagnetic Wave Scattering by Random Rough Surfaces," Communications in Computational Physics, Volume 23, Number 3, 685-705 (2018) download .
  9. D. P. Nicholls, "On Analyticity of Linear Waves Scattered by a Layered Medium," Journal of Differential Equations, Volume 263, Issue 8, 5042-5089 (2017) download .
  10. Y. Hong and D. P. Nicholls, "A High-Order Perturbation of Surfaces Method for Scattering of Linear Waves by Periodic Multiply Layered Gratings in Two and Three Dimensions," Journal of Computational Physics, Volume 345, 162-188 (2017) download .
  11. D. P. Nicholls, "Numerical Solution of Diffraction Problems: A High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method," SIAM Journal on Numerical Analysis, Volume 55, Number 1, 144-167 (2017) download .
  12. Y. Hong and D. P. Nicholls, "A Stable High-Order Perturbation of Surfaces Method for Numerical Simulation of Diffraction Problems in Triply Layered Media," Journal of Computational Physics, Volume 330, 1043-1068 (2017) download .
  13. Y. He, M. Min, and D. P. Nicholls, "A Spectral Element Method with Transparent Boundary Condition for Periodic Layered Media Scattering," Journal of Scientific Computing, Volume 68, Issue 2, 772-802 (2016) download .
  14. D. P. Nicholls, "A High-Order Perturbation of Surfaces (HOPS) Approach to Fokas Integral Equations: Three Dimensional Layered-Media Scattering," Quarterly of Applied Mathematics, Volume 74, 61-87 (2016) download .
  15. D. P. Nicholls, S.-H. Oh, T. Johnson, and F. Reitich, "Launching Surface Plasmon Waves via Vanishingly Small Periodic Gratings," Journal of Optical Society of America, A, Volume 33, Issue 3, 276-285 (2016) download .
  16. D. P. Nicholls and V. Tammali, "A High-Order Perturbation of Surfaces (HOPS) Approach to Fokas Integral Equations: Vector Electromagnetic Scattering by Periodic Crossed Gratings," Applied Numerical Mathematics, Volume 101, 1-17 (2016) download .
  17. H. Borluk, H. Kalisch, and D. P. Nicholls, "A Numerical Study of the Whitham Equation as a Model for Steady Surface Water Waves," Journal of Computational and Applied Mathematics, Volume 296, 293-302 (2016) download .
  18. D. P. Nicholls, "A Method of Field Expansions for Vector Electromagnetic Scattering by Layered Periodic Crossed Gratings," Journal of Optical Society of America, A, Volume 32, Issue 5, 701-709 (2015) download .
  19. D. P. Nicholls and A. Sward, "A Discontinuous Galerkin Method for Pricing American Options Under the Constant Elasticity of Variance Model," Communications in Computational Physics, Volume 17, Issue 3, 761-778 (2015) download .
  20. D. Ambrose and D. P. Nicholls, "Fokas Integral Equations for Three Dimensional Layered-Media Scattering," Journal of Computational Physics, Volume 276, 1-25 (2014) download .
  21. D. P. Nicholls, F. Reitich, T. Johnson, S.-H. Oh, "Fast High-Order Perturbation of Surfaces (HOPS) Methods for Simulation of Multi-Layer Plasmonic Devices and Metamaterials," Journal of Optical Society of America, A, Volume 31, Issue 8, 1820-1831 (2014) download .
  22. Z. Fang and D. P. Nicholls, "An Operator Expansions Method for Computing Dirichlet-Neumann Operators in Linear Elastodynamics," Journal of Computational Physics, Volume 272, 266-278 (2014) download .
  23. B. Akers and D. P. Nicholls, "The Spectrum of Finite Depth Water Waves," European Journal of Mechanics B/Fluids, Volume 46, 181-189 (2014) download .
  24. D. Ambrose, J. Bona, and D. P. Nicholls, "On Ill-Posedness of Truncated Series Models for Water Waves," Proceedings of the Royal Society of London, A, Volume 470, 1-16 (2014) download .
  25. A. Malcolm and D. P. Nicholls, "Operator Expansions and Constrained Quadratic Optimization for Interface Reconstruction: Impenetrable Acoustic Media," Wave Motion, Volume 51, 23-40 (2014) download .
  26. T. Sobayo, A. Fine, E. Gunnar, C. Kazlauskas, D. P. Nicholls, and D. Mogul, "Synchrony Dynamics across Brain Structures in Limbic Epilepsy Vary Between Initiation and Termination Phases of Seizures," IEEE Transactions on Biomedical Engineering, Volume 60, Number 3, 821-829 (2013) download .
  27. B. Akers and D. P. Nicholls, "Spectral Stability of Deep Two-Dimensional Gravity-Capillary Water Waves," Studies in Applied Mathematics, Volume 130, 81-107 (2012) download .
  28. T. McBride and D. P. Nicholls, "On Stability of Generalized Short-Crested Water Waves," Physica D, Volume 241, 1406-1416 (2012) download .
  29. R. Canning and D. P. Nicholls, "Numerical Simulation of a Weakly Nonlinear Model for Internal Waves," Communications in Computational Physics, Volume 12, Number 5, 1461-1481 (2012) download .
  30. B. Akers and D. P. Nicholls, "Spectral Stability of Deep Two-Dimensional Gravity Water Waves: Repeated Eigenvalues," SIAM Journal on Applied Mathematics, Volume 72, Number 2, 689-711 (2012) download .
  31. Y. He, D. P. Nicholls, and J. Shen, "An Efficient and Stable Spectral Method for Electromagnetic Scattering from a Layered Periodic Structure," Journal of Computational Physics, Volume 231, Number 8, 3007-3022 (2012) download .
  32. D. P. Nicholls, "Three-Dimensional Acoustic Scattering by Layered Media: A Novel Surface Formulation with Operator Expansions Implementation," Proceedings of the Royal Society of London, A Volume 468, 731-758 (2012) download .
  33. D. Ambrose, J. Bona, and D. P. Nicholls, "Well-Posedness of a Model for Water Waves with Viscosity," Discrete and Continuous Dynamical Systems, Series B, Volume 17, Number 4, 1113-1137 (2012) download .
  34. D. P. Nicholls, "Efficient Enforcement of Far-Field Boundary Conditions in the Transformed Field Expansions Method," Journal of Computational Physics, Volume 230, Number 22, 8290-8303 (2011) download .
  35. A. Malcolm and D. P. Nicholls, "A Boundary Perturbation Method for Recovering Interface Shapes in Layered Media," Inverse Problems, Volume 27, Number 9, 095009 (2011) download .
  36. A. Malcolm and D. P. Nicholls, "A Field Expansions Method for Scattering by Periodic Multilayered Media," Journal of the Acoustical Society of America, Volume 129, Number 4, 1783-1793 (2011) download .
  37. D. P. Nicholls, "Spectral Stability of Traveling Water Waves: Eigenvalue Collision, Singularities, and Direct Numerical Simulation," Physica D, Volume 240, Issues 4-5, 376-381 (2011) download .
  38. D. P. Nicholls and J. Orville, "A Boundary Perturbation Method for Vector Electromagnetic Scattering from Families of Doubly Periodic Gratings," Journal of Scientific Computing, Volume 45, Number 1, 471-486 (2010) download .
  39. B. Akers and D. P. Nicholls, "Traveling Waves in Deep Water with Gravity and Surface Tension," SIAM Journal on Applied Mathematics, Volume 70, Number 7, 2373-2389 (2010) download .
  40. B. Hu and D. P. Nicholls, "The Domain of Analyticity of Dirichlet-Neumann Operators," Proceedings of the Royal Society of Edinburgh A, Volume 140, Number 2, 367-389 (2010) download .
  41. C. Fazioli and D. P. Nicholls, "Stable Computation of Variations of Dirichlet-Neumann Operators," Journal of Computational Physics, Volume 229, Number 3, 906-920 (2010) download .
  42. M. Kakleas and D. P. Nicholls, "Numerical Simulation of a Weakly Nonlinear Model for Water Waves with Viscosity," Journal of Scientific Computing, Volume 42, Number 2, 274-290 (2010) download .
  43. A. S. Fine, D. P. Nicholls, and D. J. Mogul, "Assessing Instantaneous Synchrony of Nonlinear, Nonstationary Oscillators in the Brain," Journal of Neuroscience Methods, Volume 186, Number 1, 42-51 (2010) download .
  44. J. Gorsky and D. P. Nicholls, "A Small Dispersion Limit to the Camassa-Holm Equation: A Numerical Study," Mathematics and Computers in Simulation, Volume 80, Number 1, 120-130 (2009) download .
  45. D. P. Nicholls and J. Shen, "A Rigorous Numerical Analysis of the Transformed Field Expansion Method," SIAM Journal on Numerical Analysis, Volume 47, Number 4, 2708-2734 (2009) download .
  46. T. Binford, D. P. Nicholls, N. Nigam, and T. Warburton, "Exact Non-Reflecting Boundary Conditions on Perturbed Domains and hp-Finite Elements," Journal of Scientific Computing, Volume 39, Number 2, 265-292 (2009) download .
  47. D. P. Nicholls, "Spectral Data for Traveling Water Waves: Singularities and Stability," Journal of Fluid Mechanics, Volume 624, 339-360 (2009) download .
  48. D. P. Nicholls, "A Rapid Boundary Perturbation Algorithm for Scattering by Families of Rough Surfaces," Journal of Computational Physics, Volume 228, Number 9, 3405-3420 (2009) download .
  49. D. P. Nicholls and M. Taber, "Detection of Ocean Bathymetry from Surface Wave Measurements," European Journal of Mechanics B/Fluids, Volume 28, Number 2, 224-233 (2009) download .
  50. D. P. Nicholls and F. Reitich, "Boundary Perturbation Methods for High-Frequency Acoustic Scattering: Shallow Periodic Gratings," Journal of the Acoustical Society of America, Volume 123, Number 5, 2531-2541 (2008) download .
  51. D. P. Nicholls and M. Taber, "Joint Analyticity and Analytic Continuation for Dirichlet-Neumann Operators on Doubly Perturbed Domains," Journal of Mathematical Fluid Mechanics, Volume 10, Number 2, 238-271 (2008) download .
  52. C. Fazioli and D. P. Nicholls, "Parametric Analyticity of Functional Variations of Dirichlet-Neumann Operators," Differential and Integral Equations, Volume 21, Number 5-6, 541-574 (2008) download .
  53. P. Guyenne and D. P. Nicholls, "A High-Order Spectral Method for Nonlinear Water Waves over Bottom Topography," SIAM Journal on Scientific Computing, Volume 30, Number 1, 81-101 (2007) download .
  54. D. P. Nicholls, "Spectral Stability of Traveling Water Waves: Analytic Dependence of the Spectrum," Journal of Nonlinear Science, Volume 17, Number 4, 369-397 (2007) download .
  55. Q. Fang, D. P. Nicholls, and J. Shen, "A Stable, High-Order Method for Three-Dimensional Bounded-Obstacle Scattering," Journal of Computational Physics, Volume 224, Number 2, 1145-1169 (2007) download .
  56. D. P. Nicholls, "Boundary Perturbation Methods for Water Waves," GAMM-Mitteilungen, Volume 30, Number 1, 44-74 (2007) download .
  57. L. Chindelevitch, D. P. Nicholls and N. Nigam, "Error Analysis and Preconditioning for an Enhanced DtN-FE Algorithm for Exterior Scattering Problems," Journal of Computational and Applied Mathematics, Volume 204, 493-504 (2007) download .
  58. D. P. Nicholls and N. Nigam, "Error Analysis of an Enhanced DtN-FE Method for Exterior Scattering Problems," Numerische Mathematik, Volume 105, Number 2, 267-298 (2006) download .
  59. D. P. Nicholls and J. Shen, "A Stable, High-Order Method for Two-Dimensional Bounded-Obstacle Scattering," SIAM Journal on Scientific Computing, Volume 28, Issue 4, 1398-1419 (2006) download .
  60. D. P. Nicholls and F. Reitich, "Stable, High-Order Computation of Traveling Water Waves in Three Dimensions," European Journal of Mechanics B/Fluids, Volume 25, Number 4, 406-424 (2006) download .
  61. B. Hu and D. P. Nicholls, "Analyticity of Dirichlet-Neumann Operators on Hölder and Lipschitz Domains," SIAM Journal on Mathematical Analysis, Volume 37, Number 1, 302-320 (2005) download .
  62. D. P. Nicholls and F. Reitich, "On Analyticity of Traveling Water Waves," Proceedings of the Royal Society of London A, Volume 461, Number 2057, 1283-1309 (2005) download .
  63. W. Craig, P. Guyenne, D. P. Nicholls and C. Sulem, "Hamiltonian Long Wave Expansions for Water Waves over a Rough Bottom," Proceedings of the Royal Society of London A, Volume 461, Number 2055, 839-873 (2005) download .
  64. P. Guyenne and D. P. Nicholls, "Numerical Simulation of Solitary Waves on Plane Slopes," Mathematics and Computers in Simulation, Volume 69, 269-281 (2005) download .
  65. D. P. Nicholls and F. Reitich, "Shape Deformations in Rough Surface Scattering: Improved Algorithms," Journal of the Optical Society of America, A, Volume 21, Issue 4, 606-621 (2004) download .
  66. D. P. Nicholls and F. Reitich, "Shape Deformations in Rough Surface Scattering: Cancellations, Conditioning, and Convergence," Journal of the Optical Society of America, A, Volume 21, Issue 4, 590-605 (2004) download .
  67. D. P. Nicholls and N. Nigam, "Exact Non-Reflecting Boundary Conditions on General Domains," Journal of Computational Physics, Volume 194, Number 1, 278-303 (2004) download .
  68. M. Haragus, D. P. Nicholls, and D. H. Sattinger, "Solitary Wave Interactions of the Euler-Poisson Equations," Journal of Mathematical Fluid Mechanics, Volume 5, 92-118 (2003) download .
  69. W. Craig and D. P. Nicholls, "Traveling Gravity Water Waves in Two and Three Dimensions," European Journal of Mechanics B/Fluids, Volume 21, Number 6, 615-641 (2002) download .
  70. D. P. Nicholls and F. Reitich, "Analytic Continuation of Dirichlet-Neumann Operators," Numerische Mathematik, Volume 94, Number 1, 107-146 (2003) download .
  71. D. P. Nicholls and F. Reitich, "Stability of High-Order Perturbative Methods for the Computation of Dirichlet-Neumann Operators," Journal of Computational Physics, Volume 170, Number 1, 276-298 (2001) download .
  72. D. P. Nicholls and F. Reitich, "A New Approach to Analyticity of Dirichlet-Neumann Operators," Proceedings of the Royal Society of Edinburgh A, Volume 131, Number 6, 1411-1433 (2001) download .
  73. D. P. Nicholls, "On Hexagonal Gravity Water Waves," Mathematics and Computers in Simulation, Volume 55, Number 4-6, 567-575 (2001) download .
  74. W. Craig and D. P. Nicholls, "Traveling Two and Three Dimensional Capillary Gravity Water Waves," SIAM Journal on Mathematical Analysis, Volume 32, Number 2, 323-359 (2000) download .
  75. D. P. Nicholls, "Traveling Water Waves: Spectral Continuation Methods with Parallel Implementation," Journal of Computational Physics, Volume 143, Number 1, 224-240 (1998) download .

Refereed Conference Proceedings

Appeared

  1. G. Ely, A. Malcolm, D. P. Nicholls, "Combining Global Optimization and Boundary Integral Methods to Robustly Estimate Subsurface Velocity Models," Society of Exploration Geophysicists, 2015, xx-xx (2015) download .
  2. A. Fine, D. P. Nicholls, and D. Mogul, "Modulation of Instantaneous Synchrony During Seizures by Deep Brain Stimulation," Engineering in Medicine and Biology Society, 2009, 3310-3313 (2009) download .
  3. A. Fine, D. P. Nicholls, and D. Mogul, "Analysis of Instantaneous Synchrony During Seizures," Neural Engineering, 2009, 490-493 (2009) download .

Book Chapters

Appeared

  1. D. P. Nicholls, "High-Order Perturbation of Surfaces (HOPS) Short Course: Boundary Value Problems," Lectures on the Theory of Water Waves, London Mathematical Society Lecture Note Series, 426 (Cambridge University Press, 2016) download .
  2. D. P. Nicholls, "High-Order Perturbation of Surfaces (HOPS) Short Course: Analyticity Theory," Lectures on the Theory of Water Waves, London Mathematical Society Lecture Note Series, 426 (Cambridge University Press, 2016) download .