| 带尖角的障碍声波散射区域的反演 |
| |
| 引用本文： | 张梅东,王连堂.带尖角的障碍声波散射区域的反演[J].纯粹数学与应用数学,2009,25(3):610-616. |
| |
| 作者姓名： | 张梅东 王连堂 |
| |
| 作者单位： | 张梅东(防灾科技学院基础部,河北,燕郊,065201);王连堂(西北大学数学系,陕西,西安,710127) |
| |
| 摘 要： | 对带尖角的障碍声波散射区域进行了反演，其前提条件是整体场满足奇次Dirichlet边界条件．在用Nystrom方法解正问题的过程中，由于采用等距网格积分给尖角处带来很差的收敛性，这是因为双层位势的积分算子的核在尖角处有Mellin型奇性，不再是紧算子；为此采用梯度网格，数值例子表明该处理方法的有效可靠性．
|
| 关 键 词： | 尖角 反演 Dirichlet边界条件 Nystrm方法 |
The reconstruction of scattering domain with a corner of acoustic waves |
| |
| Institution: | ZHANG Mei-dong , WANG Lian-tang (1.Department of Basic Courses, Institute of Disaster Prevention Science and Technology, Yanjiao 065201, China; 2.Department of Mathematics, Northwest University, Xi＇an 710069, China) |
| |
| Abstract: | The reconstruction of the scattering domain with a corner of acoustic waves is presented in this paper, it is assumed that the total field satisfied homogenous Dirichlet boundary condition ;in direct problem by NystrSm ,due to the singularity of the solution at the corner ,a quadrature method based on an equidistant grid only very poor convergence.The kernel of double - layer integral operator in a domain with a corner has a Mellin type singularity at the corner and no longer is compact in the space of continuous function.Hence graded mesh is used.Numerical examples indicate that this method is accurate and simple to use. |
| |
| Keywords: | sharped-corner reconstruction Dirichlet boundary condition NystrSm method |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
