Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations  

作　　者：程攀 黄晋 王柱 

机构地区：[1]School of Science,Chongqing Jiaotong University [2]School of Mathematical Sciences,University of Electronic Science and Technology of China [3]Department of Mathematics,Virginia Polytechnic Institute and State University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2011年第12期1505-1514,共10页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.10871034);the Natural Science Foundation Project of Chongqing(No.CSTC20-10BB8270);the Air Force Office of Scientific Research(No.FA9550-08-1-0136);the National Science Foundation(No.OCE-0620464)

摘　　要：This paper presents mechanical quadrature methods （MQMs） for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O（h3） and low computation complexity. Moreover, the mechanical quadrature methods are simple without computing any singular integration. A nonlinear system is constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system are proved based on an asymptotical compact theory and the Stepleman theorem. Using the h3-Richardson extrapolation algorithms （EAs）, the accuracy to the order of O（h5） is improved. To slove the nonlinear system, the Newton iteration is discussed extensively by using the Ostrowski fixed point theorem. The efficiency of the algorithms is illustrated by numerical examples.This paper presents mechanical quadrature methods （MQMs） for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O（h3） and low computation complexity. Moreover, the mechanical quadrature methods are simple without computing any singular integration. A nonlinear system is constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system are proved based on an asymptotical compact theory and the Stepleman theorem. Using the h3-Richardson extrapolation algorithms （EAs）, the accuracy to the order of O（h5） is improved. To slove the nonlinear system, the Newton iteration is discussed extensively by using the Ostrowski fixed point theorem. The efficiency of the algorithms is illustrated by numerical examples.

关 键 词：Helmholtz equation mechanical quadrature method Newton iteration nonlinear boundary condition 

分 类 号：O175.5[理学—数学]