A fourth-order orthogonal spline collocation method for two-dimensional Helmholtz problems with interfaces

被引：1
作者：
Bhal, Santosh Kumar [1 ]
Danumjaya, Palla [1 ]
Fairweather, Graeme [2 ]
机构：
[1] BITS Goa Campus, Dept Math, Pilani 403726, Goa, India
[2] Amer Math Soc, Math Reviews, Ann Arbor, MI USA
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 36卷 / 06期
关键词：
almost block diagonal linear systems; discontinuous data; fast Fourier transforms; Helmholtz problems; matrix decomposition algorithm; optimal global convergence rates; orthogonal spline collocation; superconvergence; DIAGONAL LINEAR-SYSTEMS; FINITE-DIFFERENCE SCHEMES; MODIFIED ALTERNATE ROW; FORTRAN PACKAGES; GAUSSIAN POINTS; EQUATION;
D O I：
10.1002/num.22505
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Orthogonal spline collocation is implemented for the numerical solution of two-dimensional Helmholtz problems with discontinuous coefficients in the unit square. A matrix decomposition algorithm is used to solve the collocation matrix system at a cost ofO(N-2 log N)on anN x Npartition of the unit square. The results of numerical experiments demonstrate the efficacy of this approach, exhibiting optimal global estimates in various norms and superconvergence phenomena for a broad spectrum of wave numbers.
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收藏
页码：1811 / 1829
页数：19
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