Quadratic spline collocation method and efficient preconditioner for the Helmholtz equation with the Sommerfeld boundary conditions

被引：3
|
作者：
Luo, Wei-Hua [1 ,2 ]
Huang, Ting-Zhu [1 ]
Li, Liang [1 ]
Li, Hou-Biao [1 ]
Gu, Xian-Ming [1 ]
机构：
[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China
[2] Neijiang Normal Univ, Data Recovery Key Lab Sichuan Prov, Neijiang 641112, Sichuan, Peoples R China
来源：
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2016年 / 33卷 / 03期
关键词：
Helmholtz equations; Sommerfeld boundary conditions; Quadratic spline collocation; Polynomial preconditioner; PARTIAL-DIFFERENTIAL EQUATIONS; ORDER;
D O I：
10.1007/s13160-016-0225-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, using the quadratic spline collocation method (QSC), we numerically solve the Helmholtz equations with the Sommerfeld boundary conditions. By reordering the unknowns, we obtain a 3 x 3 block linear system. Then, we introduce a two-step preconditioner based on the approximate inverse block polynomial preconditioner. Theoretical analysis show this preconditioner can largely gather the eigenvalues around 1. Numerical examples are presented to test the error of QSC method and check the efficiency of the presented preconditioner.
引用
收藏
页码：701 / 720
页数：20
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