Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2025 Dec 11.
doi: 10.1038/s41598-025-32321-2. Online ahead of print.

A time-domain Runge-Kutta dual reciprocity boundary element method for scalar wave propagation problem

Fenglin Zhou  1   2 , Jiehua Deng  1 , Junfeng Man  1 , Yu Qin  3 , Jianghong Yu  3   4 , Yijing Zhang  5 , Wenyuan Li  6
Affiliations
Free article

A time-domain Runge-Kutta dual reciprocity boundary element method for scalar wave propagation problem

Fenglin Zhou et al. Sci Rep. .
Free article

Abstract

This paper presents a combined approach utilizing the dual reciprocity boundary element method (DRBEM) and the fourth-order Runge-Kutta method (RKM) to address acoustic radiation problems. Within the dual reciprocity framework, a radial basis function (RBF) is introduced to convert the domain integral into a boundary integral form. Following boundary element discretization, a system of second-order ordinary differential equations (ODEs) is derived. These are subsequently transformed into a set of first-order ODEs (Euler equations) via the introduction of an intermediate variable. The fourth-order Runge-Kutta method is then employed to numerically integrate the resulting system. The validity and accuracy of the proposed method are demonstrated through two numerical examples involving acoustic wave propagation in different structural domains.

Keywords: Acoustic radiation; Dual reciprocity boundary element method; Radial basis function; Runge-Kutta method.

PubMed Disclaimer

Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

References

    1. Rao, S. M. & Raju, P. K. Application of the method of moments to acoustic scattering from multiple bodies of arbitrary shape[J]. J. Acoust. Soc. Am. 86 (3), 1143–1148 (1989).
    1. Liu, X. et al. A fast multipole boundary element method for half-space acoustic problems in a subsonic uniform flow[J]. Eng. Anal. Boundary Elem. 137, 16–28 (2022).
    1. Kirkup The boundary element method in acoustics: A Survey[J]. Appl. Sci. 9 (8), 1642 (2019).
    1. Ergin, A. A., Shanker, B. & Michielssen, E. The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena[J]. IEEE Antennas Propag. Mag. 41 (4), 39–52 (1999).
    1. Chen, W., Li, J. & Fu, Z. Singular boundary method using time-dependent fundamental solution for scalar wave equations[J]. Comput. Mech. 58 (5), 717–730 (2016).

LinkOut - more resources