Semantic Scholar Open Access 2020 5 sitasi

Super-exponential growth rates of condition number in the boundary knot method for the Helmholtz equation

Liping Zhang Zi-Cai Li Hung‐Tsai Huang Zhen Chen

Abstrak

Abstract The boundary knot method (BKM) is applied to the Helmholtz equation in 2D bounded simply-connected domains, to show high accuracy of the solutions obtained by not many fundamental solutions (FS) used. When the Bessel function is chosen as the FS, the optimal polynomial convergence rates are obtained for disk domains. Moreover, the bounds of condition number (Cond) are derived for disk domains, to show a super-exponential growth via the number of FS used. The super-exponential growth of Cond is new and intriguing in the numerical methods for partial differential equations (PDE). It is also imperative for the BKM that good numerical solutions may be achieved by balancing accuracy and instability. Numerical experiments are carried out to support the analysis made. Comparisons between the BKM and the MFS are also made.

Topik & Kata Kunci

Computer Science Mathematics

Penulis (4)

Liping Zhang

Zi-Cai Li

Hung‐Tsai Huang

Zhen Chen

Format Sitasi

APA MLA BibTeX

Zhang, L., Li, Z., Huang, H., Chen, Z. (2020). Super-exponential growth rates of condition number in the boundary knot method for the Helmholtz equation. https://doi.org/10.1016/j.aml.2020.106333

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Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Total Sitasi: 5×
Sumber Database: Semantic Scholar
DOI: 10.1016/j.aml.2020.106333
Akses: Open Access ✓