Fast accurate computation of the fully nonlinear solitary surface gravity waves. We present an easy to implement and fast algorithm for the computation of the steady solitary gravity wave solution of the free surface Euler equations in irrotational motion. First, the problem is reformulated in a fixed domain using the conformal mapping technique. Second, the problem is reduced to a single equation for the free surface. Third, this equation is solved using Petviashvili’s iterations together with pseudo-spectral discretisation. This method has a super-linear complexity, since the most demanding operations can be performed using a FFT algorithm. Moreover, when this algorithm is combined with the multi-precision floating point computations, the results can be obtained to any arbitrary accuracy.

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Ma, C. P.; Xu, G. D.; Duan, W. Y.: Study on the head-on collisions of two-dimensional trains of solitons (2020)
  2. Dinvay, Evgueni: On well-posedness of a dispersive system of the Whitham-Boussinesq type (2019)
  3. Durán, Angel; Dutykh, Denys; Mitsotakis, Dimitrios: On the multi-symplectic structure of Boussinesq-type systems. I: Derivation and mathematical properties (2019)
  4. Le, Uyen; Pelinovsky, Dmitry E.: Convergence of Petviashvili’s method near periodic waves in the fractional Korteweg-de Vries equation (2019)
  5. Papathanasiou, T. K.; Papoutsellis, Ch. E.; Athanassoulis, G. A.: Semi-explicit solutions to the water-wave dispersion relation and their role in the non-linear Hamiltonian coupled-mode theory (2019)
  6. Tong, Chao; Shao, Yanlin; Hanssen, Finn-Christian W.; Li, Ye; Xie, Bin; Lin, Zhiliang: Numerical analysis on the generation, propagation and interaction of solitary waves by a harmonic polynomial cell method (2019)
  7. Clamond, Didier; Dutykh, Denys: Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth (2018)
  8. Duchêne, Vincent; Nilsson, Dag; Wahlén, Erik: Solitary wave solutions to a class of modified Green-Naghdi systems (2018)
  9. Papoutsellis, Ch. E.; Charalampopoulos, A. G.; Athanassoulis, G. A.: Implementation of a fully nonlinear Hamiltonian coupled-mode theory, and application to solitary wave problems over bathymetry (2018)
  10. Mitsotakis, Dimitrios; Dutykh, Denys; Carter, John: On the nonlinear dynamics of the traveling-wave solutions of the Serre system (2017)
  11. Dutykh, Denys; Clamond, Didier; Durán, Angel: Efficient computation of capillary-gravity generalised solitary waves (2016)
  12. Zhou, B. Z.; Wu, G. X.; Meng, Q. C.: Interactions of fully nonlinear solitary wave with a freely floating vertical cylinder (2016)
  13. Murashige, Sunao; Choi, Wooyoung: High-order Davies’ approximation for a solitary wave solution in Packham’s complex plane (2015)
  14. Dutykh, Denys; Clamond, Didier: Efficient computation of steady solitary gravity waves (2014)
  15. Clamond, Didier; Dutykh, Denys: Fast accurate computation of the fully nonlinear solitary surface gravity waves (2013)