An accurate and efficient local one-dimensional method for the 3D acoustic wave equation

• Autorzy: Wu Mengling , Jiang Yunzhi , Ge Yongbin

Identyfikatory

DOI

10.1515/dema-2022-0148

• Języki publikacji: EN

Abstrakty

EN

We establish an accurate and efficient scheme with four-order accuracy for solving three-dimensional (3D) acoustic wave equation. First, the local one-dimensional method is used to transfer the 3D wave equation into three one-dimensional wave equations. Then, a new scheme is obtained by the Padé formulas for computation of spatial second derivatives and the correction of the truncation error remainder for discretization of temporal second derivative. It is compact and can be solved directly by the Thomas algorithm. Subsequently, the Fourier analysis method and the Lax equivalence theorem are employed to prove the stability and convergence of the present scheme, which shows that it is conditionally stable and convergent, and the stability condition is superior to that of most existing numerical methods of equivalent order of accuracy in the literature. It allows us to reduce computational cost with relatively large time step lengths. Finally, numerical examples have demonstrated high accuracy, stability, and efficiency of our method.

Słowa kluczowe

EN

local one-dimensional; wave equation; variable coefficients; high accuracy compact difference scheme; stability; convergence

PL

równanie falowe; współczynnik zmienny; schemat różnicowy; stabilność; zbieżność

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 528--552
• Opis fizyczny: Bibliogr. 38 poz., rys., tab., wykr.

Twórcy

autor

Wu Mengling

• Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, 750021, China

autor

Jiang Yunzhi

• Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, 750021, China
• Basic Courses Teaching and Research Department, Yingkou Institute of Technology, Yingkou, 115100, China

autor

Ge Yongbin

• Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, 750021, China

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).