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Runge-Kutta method

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Journal Article
Published: 10 March 2015
Bulletin of the Seismological Society of America (2015) 105 (2A): 657–675.
...Xiao Ma; Dinghui Yang; Guojie Song Abstract In a companion paper ( Ma et al. , 2014 ), we proposed a series of nearly analytic symplectic RungeKutta ( NSPRK ) methods with fourth‐order spatial accuracy and with second‐, third‐, and fourth‐order temporal accuracy. In this article, the NSPRK (2,4...
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Journal Article
Published: 02 September 2014
Bulletin of the Seismological Society of America (2014) 104 (5): 2206–2225.
...Xiao Ma; Dinghui Yang; Guojie Song; Meixia Wang Abstract In this article, a series of nearly analytic symplectic partitioned RungeKutta ( NSPRK ) methods for the 3D seismic‐wave equation are developed. First, the Hamiltonian formulations for acoustic and elastic‐wave equations are presented...
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Journal Article
Published: 01 December 2009
Bulletin of the Seismological Society of America (2009) 99 (6): 3340–3354.
...Dinghui Yang; Nian Wang; Shan Chen; Guojie Song Abstract A new explicit differentiator series method based on the implicit RungeKutta method, called the IRK - DSM in brief, is developed for solving wave equations. To develop the new algorithm, we first transform the wave equation, usually...
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Journal Article
Journal: Geophysics
Published: 21 October 2020
Geophysics (2020) 85 (6): S343–S355.
... of the numerical methods used to simulate the wavefields. Recently, a weighted Runge-Kutta discontinuous Galerkin (WRKDG) method has been developed to solve the wave equation, which is stable, explicit, and efficient in parallelization and suppressing numerical dispersion. By incorporating two different weights...
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Journal Article
Journal: Geophysics
Published: 29 June 2023
Geophysics (2023) 88 (5): T259–T270.
... and a fourth-order strong-stability-preserved Runge-Kutta (SSPRK) scheme is implemented in the temporal domain ( Wang et al., 2019b ). We derive the double-pole AODE unsplit CFS-PML expressions and formulate them as a first-order linear hyperbolic system, which is directly solved by the DG method. Furthermore...
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Journal Article
Journal: Geophysics
Published: 13 July 2021
Geophysics (2021) 86 (4): T261–T275.
...Xijun He; Dinghui Yang; Yanjie Zhou; Lei Yang; Xueyuan Huang ABSTRACT We have developed a Runge-Kutta discontinuous Galerkin (RKDG) method for solving wave equations in isotropic and anisotropic poroelastic media at low frequencies. First, the 2D Biot’s two-phase equations are transformed...
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Journal Article
Journal: Geophysics
Published: 03 August 2016
Geophysics (2016) 81 (5): T251–T263.
...Dinghui Yang; Xijun He; Xiao Ma; Yanjie Zhou; Jingshuang Li ABSTRACT The newly developed optimal nearly analytic discrete (ONAD) and the weighted Runge-Kutta discontinuous Galerkin (WRKDG) methods can effectively suppress the numerical dispersion caused by discretizing wave equations...
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Journal Article
Journal: Geophysics
Published: 13 December 2018
Geophysics (2019) 84 (1): T1–T11.
...-stepping methods, first, a second-order time-splitting algorithm solves the unstable part analytically and a Runge-Kutta method the regular equations. Alternatively, a first-order explicit Crank-Nicolson algorithm yields more stable solutions for low values of the thermal conductivity. These time-stepping...
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Journal Article
Journal: Geophysics
Published: 01 August 1987
Geophysics (1987) 52 (8): 1074–1084.
... method show that it is more accurate and efficient than standard integration techniques such as the Runge-Kutta method or the Taylor method. GeoRef, Copyright 2005, American Geological Institute. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States 1987 ...
Journal Article
Journal: Geophysics
Published: 01 December 1996
Geophysics (1996) 61 (6): 1895–1898.
... computed traveltimes with the amplitude information attached to it in two dimensions. (2) Finite-difference methods (Reshel and Kosloff, 1986; Vidale, 1988; van Trier and Symes, 1991). These solve the eikonal equation directly by using different numerical schemes such as the Runge-Kutta method, wavefront...
Journal Article
Published: 01 April 1969
Bulletin of the Seismological Society of America (1969) 59 (2): 909–922.
... order Runge-Kutta method of comparable accuracy. An analysis also is made of the errors introduced at various stages in the calculation of spectra so that allowable errors can be prescribed for the numerical integration. Using the proposed method of computing or other methods of comparable accuracy...
Journal Article
Published: 01 November 2009
Earthquake Spectra (2009) 25 (4): 899–925.
... Runge-Kutta method with an adaptive step size control. An analytical solution is obtained for the first time for a special case of periodic torsional pounding. Results of our numerical simulations reveal that torsional pounding tends to be much more complex and unpredictable than translational pounding...
Image
Flow diagram of the adaptive timestep <span class="search-highlight">method</span> that was used in this study, w...
Published: 05 October 2021
Figure 3. Flow diagram of the adaptive timestep method that was used in this study, which was inspired by the fourth‐order RungeKutta method ( Press and Teukolsky, 1992 ). The color version of this figure is available only in the electronic edition.
Journal Article
Published: 05 November 2019
Bulletin of the Seismological Society of America (2019) 109 (6): 2746–2754.
.... For all further calculations, the fourth‐order RungeKutta method with a timestep of 1 s was used. In addition to its accuracy, it is significantly faster than using a timestep of 0.1 s with the other lower‐order methods. The moment tensor solutions of large earthquakes are often obtained...
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Journal Article
Published: 09 March 2022
Bulletin of the Seismological Society of America (2022) 112 (3): 1197–1223.
... performance. In this study, we develop an efficient parallel weighted RungeKutta discontinuous Galerkin (WRKDG) method on unstructured meshes for solving 3D seismic wave equations. The DG method we use is based on the first‐order formulation of a hyperbolic system with an explicit weighted RungeKutta time...
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Journal Article
Journal: Geophysics
Published: 10 April 2019
Geophysics (2019) 84 (3): T167–T179.
... of symplectic methods to formulate symplectic partitioned Runge-Kutta (SPRK) + CPML and nearly analytic SPRK (NSPRK) + CPML, both of which are properly synchronized. To further investigate their validity, the two algorithms are then applied to acoustic and elastic wave simulations in typical geologic models...
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Journal Article
Journal: Geophysics
Published: 08 October 2018
Geophysics (2018) 83 (6): T301–T311.
...-called convolutional PML (CPML). We have developed the corresponding CPML conditions with nonconstant grid compression parameter, and used its combination algorithms specifically with the symplectic partitioned Runge-Kutta and the nearly analytic SPRK methods for solving second-order seismic wave...
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Journal Article
Journal: Geophysics
Published: 27 May 2019
Geophysics (2019) 84 (4): T193–T206.
... equations, the nearly-analytic symplectic partitioned Runge-Kutta (NSPRK) method has been combined with split-field PML (SPML) and convolutional complex-frequency shifted PML (C-CFS-PML) previously to model acoustic and short-time elastic wave modelings, not yet successfully applied to long-time elastic...
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Journal Article
Journal: Geophysics
Published: 13 March 2019
Geophysics (2019) 84 (3): T133–T145.
... third-order symplectic partitioned Runge-Kutta scheme so that it preserves the Hamiltonian structure of the wave equation in long-term simulations. Consequently, the symplectic IPDG method combines the advantages of discontinuous Galerkin method and the symplectic time integration. We investigate...
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Journal Article
Published: 10 March 2020
Bulletin of the Seismological Society of America (2020) 110 (2): 754–762.
.... The authors sincerely thank Dinghui Yang in Computing Geophysics Lab of Tsinghua University for provided the analytical solution in the article. The authors also sincerely thank Ma Xiao for discussion and revising the nearly analytic symplectically partitioned RungeKutta method (NSPRK) series code and two...
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