Publications

1. D. P. Nicholls and J. Shen, "A Rigorous Numerical Analysis of the Transformed Field Expansion Method," in preparation.
2. C. Fazioli and D. P. Nicholls, "Stable, High-Order Numerical Simulation of Variations of Dirichlet-Neumann Operators," in preparation.
3. M. Kakleas and D. P. Nicholls, "Numerical Simulation of a Model for Water Waves with Viscosity," in preparation.
4. D. P. Nicholls, "A Rapid Boundary Perturbation Algorithm for Scattering by Families of Rough Surfaces," submitted. download (361 k)
5. B. Hu and D. P. Nicholls, "The Domain of Analyticity of Dirichlet-Neumann Operators," submitted. download (1.67 M)
6. D. P. Nicholls, "Spectral Data for Traveling Water Waves: Singularities and Stability," submitted. download (503 k)
7. T. Binford, D. P. Nicholls, N. Nigam, and T. Warburton, "Exact Non-Reflecting Boundary Conditions on General Domains and hp-Finite Elements," submitted. download (374 k)
8. D. P. Nicholls and M. Taber, "Detection of Ocean Bathymetry from Surface Wave Measurements," European Journal of Mechanics B/Fluids (to appear). download (288 k)
9. J. Gorsky and D. P. Nicholls, "A Small Dispersion Limit to the Camassa-Holm Equation: A Numerical Study," Mathematics and Computers in Simulation (to appear). download (1.1 M)
10. 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 (423 k)
11. 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 (231 k)
12. 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 (253 k)
13. 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 (300 k)
14. 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 (392 k)
15. 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 (1.64 M)
16. D. P. Nicholls, "Boundary Perturbation Methods for Water Waves," GAMM-Mitteilungen, Volume 30, Number 1, 44-74 (2007). download (1.47 M)
17. 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 (187k)
18. 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 (270 k)
19. 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 (234k)
20. 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 (647k)
21. 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 (216k)
22. 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 (265k)
23. 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 (360k)
24. 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 (383k)
25. 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 (716k)
26. 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 (296k)
27. 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 (584k)
28. 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 (635k)
29. 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 (940k)
30. D. P. Nicholls and F. Reitich, "Analytic Continuation of Dirichlet-Neumann Operators," Numerische Mathematik, Volume 94, Number 1, 107-146 (2003). download (417k)
31. D. P. Nicholls and F. Reitich, "A Stable High-Order Perturbative Method for the Computation of Dirichlet-Neumann Operators," Journal of Computational Physics, Volume 170, Number 1, 276-298 (2001). download (157k)
32. 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 (344k)*
33. D. P. Nicholls, "On Hexagonal Gravity Water Waves," Mathematics and Computers in Simulation, Volume 55, Number 4-6, 567-575 (2001). download (417k)
34. 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 (343k)
35. D. P. Nicholls, "Traveling Water Waves: Spectral Continuation Methods with Parallel Implementation," Journal of Computational Physics, Volume 143, Number 1, 224-240 (1998). download (262k)