Publications of David Nicholls
Operator expansions and constrained quadratic optimization for interface reconstruction: impenetrable periodic acoustic media.
Wave Motion,
51(1):23--40, 2014.
MR3127684
On ill-posedness of truncated series models for water waves.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.,
470(2166):20130849, 16, 2014.
MR3190218
The spectrum of finite depth water waves.
Eur. J. Mech. B Fluids,
46:181--189, 2014.
MR3200412
An operator expansions method for computing Dirichlet-Neumann operators in linear elastodynamics.
J. Comput. Phys.,
272:266--278, 2014.
MR3212272
Fokas integral equations for three dimensional layered-media scattering.
J. Comput. Phys.,
276:1--25, 2014.
MR3252567
Spectral stability of deep two-dimensional gravity-capillary water waves.
Stud. Appl. Math.,
130(2):81--107, 2013.
MR3023919
Synchrony dynamics across brain structures in limbic epilepsy vary between initiation and termination phases of seizures.
IEEE Transactions on Biomedical Engineering,
60(3):821-829, 2013.
Operator expansions and constrained quadratic optimization for interface reconstruction: impenetrable acoustic media.
Wave Motion,
1-30, 2013.
A discontinuous galerkin method for pricing american options under the constant elasticity of variance model.
SIAM Journal on Financial Mathematics,
1-14, 2013.
Three-dimensional acoustic scattering by layered media: a novel surface formulation with operator expansions implementation.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.,
468(2139):731--758, 2012.
MR2892310
An efficient and stable spectral method for electromagnetic scattering from a layered periodic structure.
J. Comput. Phys.,
231(8):3007--3022, 2012.
MR2897610
Well-posedness of a model for water waves with viscosity.
Discrete Contin. Dyn. Syst. Ser. B,
17(4):1113--1137, 2012.
MR2899939
Foreword [Special issue on ``Nonlinear Waves: Computation and Theory-IX, WAVES2009''].
Math. Comput. Simulation,
82(6):945, 2012.
MR2903336
Spectral stability of deep two-dimensional gravity water waves: repeated eigenvalues.
SIAM J. Appl. Math.,
72(2):689--711, 2012.
MR2914345
Numerical simulation of a weakly nonlinear model for internal waves.
Commun. Comput. Phys.,
12(5):1461--1481, 2012.
MR2927999
Three-dimensional acoustic scattering by layered media: a novel surface formulation with operator expansions implementation.
Proceedings of the Royal Society of London, A,
468:731-758, 2012.
An efficient and stable spectral method for electromagnetic scattering from a layered periodic structure.
Journal of Computational Physics,
231(8):3007-3022, 2012.
Numerical simulation of a weakly nonlinear model for internal waves.
Communications in Computational Physics,
12(5):1461-1481, 2012.
On stability of generalized short-crested water waves.
Physica D,
241:1406-1416, 2012.
Spectral stability of deep two-dimensional gravity-capillary water waves.
Studies in Applied Mathematics,
130:81-107, 2012.
A boundary perturbation method for recovering interface shapes in layered media.
Inverse Problems,
27(9):095009, 18, 2011.
MR2831891
Efficient enforcement of far-field boundary conditions in the transformed field expansions method.
J. Comput. Phys.,
230(22):8290--8303, 2011.
MR2835422
A field expansions method for scattering by periodic multilayered media.
Journal of the Acoustical Society of America,
129(4):1783-1793, 2011.
Spectral stability of traveling water waves: eigenvalue collision, singularities, and direct numerical simulation.
Physica D,
240(4-5):376-381, 2011.
Stable computation of the functional variation of the Dirichlet-Neumann operator.
J. Comput. Phys.,
229(3):906--920, 2010.
MR2566370
Numerical simulation of a weakly nonlinear model for water waves with viscosity.
J. Sci. Comput.,
42(2):274--290, 2010.
MR2578037
The domain of analyticity of Dirichlet-Neumann operators.
Proc. Roy. Soc. Edinburgh Sect. A,
140(2):367--389, 2010.
MR2608581
Traveling waves in deep water with gravity and surface tension.
SIAM J. Appl. Math.,
70(7):2373--2389, 2010.
MR2678043
A boundary perturbation method for vector electromagnetic scattering from families of doubly periodic gratings.
J. Sci. Comput.,
45(1-3):471--486, 2010.
MR2679809
Assessing instantaneous synchrony of nonlinear, nonstationary oscillators in the brain.
Journal of Neuroscience Methods,
186(1):42-51, 2010.
Detection of ocean bathymetry from surface wave measurements.
Eur. J. Mech. B Fluids,
28(2):224--233, 2009.
MR2494864
Spectral data for travelling water waves: singularities and stability.
J. Fluid Mech.,
624:339--360, 2009.
MR2496379
Exact non-reflecting boundary conditions on perturbed domains and $hp$-finite elements.
J. Sci. Comput.,
39(2):265--292, 2009.
MR2506654
A rapid boundary perturbation algorithm for scattering by families of rough surfaces.
J. Comput. Phys.,
228(9):3405--3420, 2009.
MR2513839
A rigorous numerical analysis of the transformed field expansion method.
SIAM J. Numer. Anal.,
47(4):2708--2734, 2009.
MR2551143
A small dispersion limit to the Camassa-Holm equation: a numerical study.
Math. Comput. Simulation,
80(1):120--130, 2009.
MR2573272
Joint analyticity and analytic continuation of Dirichlet-Neumann operators on doubly perturbed domains.
J. Math. Fluid Mech.,
10(2):238--271, 2008.
MR2411413
Parametric analyticity of functional variations of Dirichlet-Neumann operators.
Differential Integral Equations,
21(5-6):541--574, 2008.
MR2483268
Boundary perturbation methods for high-frequency acoustic scattering: shallow periodic gratings.
Journal of the Acoustical Society of America,
123(5):2531-2541, 2008.
Boundary perturbation methods for water waves.
GAMM-Mitt.,
30(1):44--74, 2007.
MR2324394
Error analysis and preconditioning for an enhanced DtN-FE algorithm for exterior scattering problems.
J. Comput. Appl. Math.,
204(2):493--504, 2007.
MR2324475
A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering.
J. Comput. Phys.,
224(2):1145--1169, 2007.
MR2330309
Spectral stability of traveling water waves: analytic dependence of the spectrum.
J. Nonlinear Sci.,
17(4):369--397, 2007.
MR2337757
A high-order spectral method for nonlinear water waves over moving bottom topography.
SIAM J. Sci. Comput.,
30(1):81--101, 2007/08.
MR2377432
Stable, high-order computation of traveling water waves in three dimensions.
Eur. J. Mech. B Fluids,
25(4):406--424, 2006.
MR2241379
A stable high-order method for two-dimensional bounded-obstacle scattering.
SIAM J. Sci. Comput.,
28(4):1398--1419 (electronic), 2006.
MR2255463
Error analysis of an enhanced DtN-FE method for exterior scattering problems.
Numer. Math.,
105(2):267--298, 2006.
MR2262759
Hamiltonian long-wave expansions for water waves over a rough bottom.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.,
461(2055):839--873, 2005.
MR2121939
On analyticity of travelling water waves.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.,
461(2057):1283--1309, 2005.
MR2147749
Numerical simulation of solitary waves on plane slopes.
Math. Comput. Simulation,
69(3-4):269--281, 2005.
MR2152259
Analyticity of Dirichlet-Neumann operators on Hölder and Lipschitz domains.
SIAM J. Math. Anal.,
37(1):302--320 (electronic), 2005.
MR2176934
Exact non-reflecting boundary conditions on general domains.
J. Comput. Phys.,
194(1):278--303, 2004.
MR2033387
Shape deformations in rough surface scattering: cancellations, conditioning, and convergence.
Journal of the Optical Society of America, A,
21(4):590--605, 2004.
Shape deformations in rough surface scattering: improved algorithms.
Journal of the Optical Society of America, A,
21(4):606--621, 2004.
Solitary wave interactions of the Euler-Poisson equations.
J. Math. Fluid Mech.,
5(1):92--118, 2003.
MR1966646
Analytic continuation of Dirichlet-Neumann operators.
Numer. Math.,
94(1):107--146, 2003.
MR1971215
Traveling gravity water waves in two and three dimensions.
Eur. J. Mech. B Fluids,
21(6):615--641, 2002.
MR1947187
On hexagonal gravity water waves.
Math. Comput. Simulation,
55(4-6):567--575, 2001.
MR1831395
Stability of high-order perturbative methods for the computation of Dirichlet-Neumann operators.
J. Comput. Phys.,
170(1):276--298, 2001.
MR1843612
A new approach to analyticity of Dirichlet-Neumann operators.
Proc. Roy. Soc. Edinburgh Sect. A,
131(6):1411--1433, 2001.
MR1869643
Travelling two and three dimensional capillary gravity water waves.
SIAM J. Math. Anal.,
32(2):323--359 (electronic), 2000.
MR1781220
Traveling water waves: spectral continuation methods with parallel implementation.
J. Comput. Phys.,
143(1):224--240, 1998.
MR1624696