A New Natural Boundary Element Method for the 2D Viscoelastic Wave Equation

Fei Teng

doi:10.62762/JNSPM.2025.358007

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Volume 1, Issue 1, Journal of Numerical Simulations in Physics and Mathematics

Volume 1, Issue 1, 2025

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Journal of Numerical Simulations in Physics and Mathematics, Volume 1, Issue 1, 2025: 32-41

Open Access | Research Article | 30 June 2025

A New Natural Boundary Element Method for the 2D Viscoelastic Wave Equation

Fei Teng 1 *

1 College of Arts and Sciences, Shanghai Dianji University, Shanghai 201306, China

* Corresponding Author: Fei Teng, [email protected]

DOI: 10.62762/JNSPM.2025.358007

Received: 07 June 2025, Accepted: 18 June 2025, Published: 30 June 2025

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Abstract

The natural boundary element (NBE) method is herein mainly adopted to compute the numerical solutions of the viscoelastic wave equation in a two-dimensional (2D) unbounded domain. To this end, a new time semi-discrete (TSD) scheme is constructed for the viscoelastic wave equation, and the existence, stability, and error estimates of the time semi-discretized solutions are analyzed. Subsequently, based on the natural boundary naturalization principle, a fully discrete NBE scheme is established. The existence and stability of the fully discrete NBE solutions are examined, and the errors between the analytical solution and the fully discrete NBE solutions are estimated. Finally, several numerical experiments are conducted to verify the effectiveness of the NBE method in solving the viscoelastic wave equation in the 2D unbounded domain.

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Keywords

natural boundary element

viscoelastic wave equation

existence and stability

error estimate

Data Availability Statement

Data will be made available on request.

Funding

This work was supported by the National Natural Science Foundation of China under Grant 11671106.

Conflicts of Interest

The author declares no conflicts of interest.

Ethical Approval and Consent to Participate

Not applicable.

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APA Style

Teng, F. (2025). A New Natural Boundary Element Method for the 2D Viscoelastic Wave Equation. Journal of Numerical Simulations in Physics and Mathematics, 1(1), 32–41. https://doi.org/10.62762/JNSPM.2025.358007

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TY  - JOUR
AU  - Teng, Fei
PY  - 2025
DA  - 2025/06/30
TI  - A New Natural Boundary Element Method for the 2D Viscoelastic Wave Equation
JO  - Journal of Numerical Simulations in Physics and Mathematics
T2  - Journal of Numerical Simulations in Physics and Mathematics
JF  - Journal of Numerical Simulations in Physics and Mathematics
VL  - 1
IS  - 1
SP  - 32
EP  - 41
DO  - 10.62762/JNSPM.2025.358007
UR  - https://www.icck.org/article/abs/JNSPM.2025.358007
KW  - natural boundary element
KW  - viscoelastic wave equation
KW  - existence and stability
KW  - error estimate
AB  - The natural boundary element (NBE) method is herein mainly adopted to compute the numerical solutions of the viscoelastic wave equation in a two-dimensional (2D) unbounded domain. To this end, a new time semi-discrete (TSD) scheme is constructed for the viscoelastic wave equation, and the existence, stability, and error estimates of the time semi-discretized solutions are analyzed. Subsequently, based on the natural boundary naturalization principle, a fully discrete NBE scheme is established. The existence and stability of the fully discrete NBE solutions are examined, and the errors between the analytical solution and the fully discrete NBE solutions are estimated. Finally, several numerical experiments are conducted to verify the effectiveness of the NBE method in solving the viscoelastic wave equation in the 2D unbounded domain.
SN  - 3068-9082
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -

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@article{Teng2025A,
  author = {Fei Teng},
  title = {A New Natural Boundary Element Method for the 2D Viscoelastic Wave Equation},
  journal = {Journal of Numerical Simulations in Physics and Mathematics},
  year = {2025},
  volume = {1},
  number = {1},
  pages = {32-41},
  doi = {10.62762/JNSPM.2025.358007},
  url = {https://www.icck.org/article/abs/JNSPM.2025.358007},
  abstract = {The natural boundary element (NBE) method is herein mainly adopted to compute the numerical solutions of the viscoelastic wave equation in a two-dimensional (2D) unbounded domain. To this end, a new time semi-discrete (TSD) scheme is constructed for the viscoelastic wave equation, and the existence, stability, and error estimates of the time semi-discretized solutions are analyzed. Subsequently, based on the natural boundary naturalization principle, a fully discrete NBE scheme is established. The existence and stability of the fully discrete NBE solutions are examined, and the errors between the analytical solution and the fully discrete NBE solutions are estimated. Finally, several numerical experiments are conducted to verify the effectiveness of the NBE method in solving the viscoelastic wave equation in the 2D unbounded domain.},
  keywords = {natural boundary element, viscoelastic wave equation, existence and stability, error estimate},
  issn = {3068-9082},
  publisher = {Institute of Central Computation and Knowledge}
}

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