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Volume 13, Issue 6
Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals

Wenzhen Qu, Hongwei Gao & Yan Gu

Adv. Appl. Math. Mech., 13 (2021), pp. 1398-1417.

Published online: 2021-08

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  • Abstract

In this paper, a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena. In the derivation of the present approach, the second order time derivative of the physical quantity in the wave equation is treated as a substitution variable. Based on the temporal discretization with the Krylov deferred correction (KDC) technique, the original wave problem is then converted into the modified Helmholtz equation. The transformed boundary value problem (BVP) in space is efficiently simulated by using the meshless generalized finite difference method (GFDM) with Taylor series after truncating the second and fourth order approximations. The developed scheme is finally verified by four numerical experiments including cases with complicated domains or the temporally piecewise defined source function. Numerical results match with the analytical solutions and results by the COMSOL software, which demonstrates that the developed KDC-GFDM can allow large time-step sizes for wave propagation problems in long-time intervals.

  • AMS Subject Headings

35L05, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-1398, author = {Qu , WenzhenGao , Hongwei and Gu , Yan}, title = {Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {6}, pages = {1398--1417}, abstract = {

In this paper, a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena. In the derivation of the present approach, the second order time derivative of the physical quantity in the wave equation is treated as a substitution variable. Based on the temporal discretization with the Krylov deferred correction (KDC) technique, the original wave problem is then converted into the modified Helmholtz equation. The transformed boundary value problem (BVP) in space is efficiently simulated by using the meshless generalized finite difference method (GFDM) with Taylor series after truncating the second and fourth order approximations. The developed scheme is finally verified by four numerical experiments including cases with complicated domains or the temporally piecewise defined source function. Numerical results match with the analytical solutions and results by the COMSOL software, which demonstrates that the developed KDC-GFDM can allow large time-step sizes for wave propagation problems in long-time intervals.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0178}, url = {http://global-sci.org/intro/article_detail/aamm/19428.html} }
TY - JOUR T1 - Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals AU - Qu , Wenzhen AU - Gao , Hongwei AU - Gu , Yan JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1398 EP - 1417 PY - 2021 DA - 2021/08 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0178 UR - https://global-sci.org/intro/article_detail/aamm/19428.html KW - Wave equation, Krylov deferred correction technique, large time-step, long-time simulation, generalized finite difference method. AB -

In this paper, a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena. In the derivation of the present approach, the second order time derivative of the physical quantity in the wave equation is treated as a substitution variable. Based on the temporal discretization with the Krylov deferred correction (KDC) technique, the original wave problem is then converted into the modified Helmholtz equation. The transformed boundary value problem (BVP) in space is efficiently simulated by using the meshless generalized finite difference method (GFDM) with Taylor series after truncating the second and fourth order approximations. The developed scheme is finally verified by four numerical experiments including cases with complicated domains or the temporally piecewise defined source function. Numerical results match with the analytical solutions and results by the COMSOL software, which demonstrates that the developed KDC-GFDM can allow large time-step sizes for wave propagation problems in long-time intervals.

Qu , WenzhenGao , Hongwei and Gu , Yan. (2021). Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals. Advances in Applied Mathematics and Mechanics. 13 (6). 1398-1417. doi:10.4208/aamm.OA-2020-0178
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