A new ADI-IIM scheme for solving two-dimensional wave equation with discontinuous coefficients

Ruitao Liu; Wanshan Li; Ruitao Liu; Wanshan Li

doi:10.3934/math.20241503

AIMS Mathematics

2024, Volume 9, Issue 11: 31180-31197. doi: 10.3934/math.20241503

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A new ADI-IIM scheme for solving two-dimensional wave equation with discontinuous coefficients

Ruitao Liu ,
Wanshan Li ^,

School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, China

Received: 30 August 2024 Revised: 21 October 2024 Accepted: 29 October 2024 Published: 01 November 2024
MSC : 65M06

A new alternating direction implicit immersed interface method (ADI-IIM) scheme was developed to solve the two-dimensional wave equation with discontinuous coefficients and sources. The alternating direction implicit (ADI) method was equipped with the immersed interface method (IIM) to recover the accuracy as well as maintaining the stability. Numerical experiments were carried out to verify the unconditional stability and the second-order accuracy both in time and space of the proposed scheme.
- alternating direction implicit method,
- immersed interface method,
- discontinuous coefficients,
- second-order accuracy,
- unconditional stability
Citation: Ruitao Liu, Wanshan Li. A new ADI-IIM scheme for solving two-dimensional wave equation with discontinuous coefficients[J]. AIMS Mathematics, 2024, 9(11): 31180-31197. doi: 10.3934/math.20241503

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Abstract

A new alternating direction implicit immersed interface method (ADI-IIM) scheme was developed to solve the two-dimensional wave equation with discontinuous coefficients and sources. The alternating direction implicit (ADI) method was equipped with the immersed interface method (IIM) to recover the accuracy as well as maintaining the stability. Numerical experiments were carried out to verify the unconditional stability and the second-order accuracy both in time and space of the proposed scheme.

References

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