Publications of David Nicholls

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