Brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motion
Researchers in the field of numerical simulation of seismic wave motion have been suffering from the challenge in understanding and studying artificial boundary conditions (ABC), which is mainly attributed to the lack of systematic discussion and effective integration of ABC originating from various...
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| Format: | Article |
| Language: | zho |
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Editorial Office of Progress in Earthquake Sciences
2025-08-01
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| Series: | 地震科学进展 |
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| Online Access: | https://www.gjdzdt.cn/en/article/doi/10.19987/j.dzkxjz.2024-078 |
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| author | Xun Zhang Haojie Xing Ruixuan Zeng Xiaojun Li |
| author_facet | Xun Zhang Haojie Xing Ruixuan Zeng Xiaojun Li |
| author_sort | Xun Zhang |
| collection | DOAJ |
| description | Researchers in the field of numerical simulation of seismic wave motion have been suffering from the challenge in understanding and studying artificial boundary conditions (ABC), which is mainly attributed to the lack of systematic discussion and effective integration of ABC originating from various wave problems. To establish a systematic overall understanding of the essence of ABC and the basic performance of various specific ABC, we conducted a simple, intuitive, and logically clear discussion on the important issues of ABC, including their essence and primary methods, the theory of accuracy control, and numerical stability. ABC is essentially a collective name for all computation methods used to calculate the motion on an artificial boundary caused by out-going waves. The computational mode of ABC can be intuitively classified into three fundamental branches: space-time extrapolation, stress equilibrium on an artificial boundary, and regional attenuation. We discuss the similarities on the implementation pattern, the theory of accuracy control, and the numerical stability for the ABC in the same branch, as well as those discrepancies among different ABC branches. Consequently, a number of important issues associated with ABC are clarified, such as the following viewpoints. Liao’s time-space extrapolation rule is the most fundamental principle for the accuracy evaluations of all the extrapolation-type and stress-type ABC. The stability problem for Liao’s ABC applied in a finite-element wave motion simulation is mainly caused by the difficulty embedded in a combination of the boundary’s finite-difference-type formula and the inner-domain finite-element formula. Attenuation-type ABC provide an observation view angle that is completely different from that of extrapolation- and stress-type ABC; thus, they play an irreplaceable and unique role in artificial boundary problems. |
| format | Article |
| id | doaj-art-9da66a8bce514b588fa41e64e5572495 |
| institution | Kabale University |
| issn | 2096-7780 |
| language | zho |
| publishDate | 2025-08-01 |
| publisher | Editorial Office of Progress in Earthquake Sciences |
| record_format | Article |
| series | 地震科学进展 |
| spelling | doaj-art-9da66a8bce514b588fa41e64e55724952025-08-20T03:51:49ZzhoEditorial Office of Progress in Earthquake Sciences地震科学进展2096-77802025-08-0155843544510.19987/j.dzkxjz.2024-0782024-078Brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motionXun Zhang0Haojie Xing1Ruixuan Zeng2Xiaojun Li3State Key Laboratory of Bridge Engineering Safety and Resilience, Beijing University of Technology, Beijing 100124, ChinaInstitute of Geophysics, China Earthquake Administration, Beijing 100081, ChinaInstitute of Geophysics, China Earthquake Administration, Beijing 100081, ChinaState Key Laboratory of Bridge Engineering Safety and Resilience, Beijing University of Technology, Beijing 100124, ChinaResearchers in the field of numerical simulation of seismic wave motion have been suffering from the challenge in understanding and studying artificial boundary conditions (ABC), which is mainly attributed to the lack of systematic discussion and effective integration of ABC originating from various wave problems. To establish a systematic overall understanding of the essence of ABC and the basic performance of various specific ABC, we conducted a simple, intuitive, and logically clear discussion on the important issues of ABC, including their essence and primary methods, the theory of accuracy control, and numerical stability. ABC is essentially a collective name for all computation methods used to calculate the motion on an artificial boundary caused by out-going waves. The computational mode of ABC can be intuitively classified into three fundamental branches: space-time extrapolation, stress equilibrium on an artificial boundary, and regional attenuation. We discuss the similarities on the implementation pattern, the theory of accuracy control, and the numerical stability for the ABC in the same branch, as well as those discrepancies among different ABC branches. Consequently, a number of important issues associated with ABC are clarified, such as the following viewpoints. Liao’s time-space extrapolation rule is the most fundamental principle for the accuracy evaluations of all the extrapolation-type and stress-type ABC. The stability problem for Liao’s ABC applied in a finite-element wave motion simulation is mainly caused by the difficulty embedded in a combination of the boundary’s finite-difference-type formula and the inner-domain finite-element formula. Attenuation-type ABC provide an observation view angle that is completely different from that of extrapolation- and stress-type ABC; thus, they play an irreplaceable and unique role in artificial boundary problems.https://www.gjdzdt.cn/en/article/doi/10.19987/j.dzkxjz.2024-078numerical simulation of seismic wave motionartificial boundary conditiontheory of accuracy controlnumerical stabilitycomplex wave problems |
| spellingShingle | Xun Zhang Haojie Xing Ruixuan Zeng Xiaojun Li Brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motion 地震科学进展 numerical simulation of seismic wave motion artificial boundary condition theory of accuracy control numerical stability complex wave problems |
| title | Brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motion |
| title_full | Brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motion |
| title_fullStr | Brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motion |
| title_full_unstemmed | Brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motion |
| title_short | Brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motion |
| title_sort | brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motion |
| topic | numerical simulation of seismic wave motion artificial boundary condition theory of accuracy control numerical stability complex wave problems |
| url | https://www.gjdzdt.cn/en/article/doi/10.19987/j.dzkxjz.2024-078 |
| work_keys_str_mv | AT xunzhang briefdiscussionontheartificialboundaryconditionsinnumericalsimulationofseismicwavemotion AT haojiexing briefdiscussionontheartificialboundaryconditionsinnumericalsimulationofseismicwavemotion AT ruixuanzeng briefdiscussionontheartificialboundaryconditionsinnumericalsimulationofseismicwavemotion AT xiaojunli briefdiscussionontheartificialboundaryconditionsinnumericalsimulationofseismicwavemotion |