Preconditioned conjugate gradient methods for the solution of Love’s integral equation with very small parameter
作者:
Highlights:
•
摘要
In this paper, we propose efficient numerical methods for the solution of the following Love’s integral equation f(x)+1π∫−11c(x−y)2+c2f(y)dy=1,x∈[−1,1],where c>0 is a very small parameter. We introduce a new unknown function h(x)=f(x)−0.5 as in Lin et al. (2013), and then apply a composite Gauss–Legendre quadrature to the resulting integral equation as in Pastore (2011). The coefficient matrix of corresponding linear system is a nonsymmetric block matrix with Toeplitz blocks. We transform the nonsymmetric linear system into a symmetric linear system and introduce a preconditioner which is a block matrix with circulant blocks. Spectral properties of relevant matrices are analyzed and numerical results are presented to illustrate the efficiency of the proposed methods.
论文关键词:65F10,65F15,Love’s integral equation,Composite Gauss–Legendre quadrature,Block matrix with Toeplitz blocks,Preconditioned conjugate gradient method
论文评审过程:Received 19 July 2016, Revised 9 January 2017, Available online 29 June 2017, Version of Record 14 July 2017.
论文官网地址:https://doi.org/10.1016/j.cam.2017.06.020