Delaminating quadrature method for multi-dimensional highly oscillatory integrals

A delaminating quadrature method for multi-dimensional highly oscillatory integrals is put forward. In comparison with the Levin method, the new method has the benefits of being numerically stable and having a high computational speed. Numerical experiments testified the advantages of this method.

[1]  G. Evans,et al.  An alternative method for irregular oscillatory integrals over a finite range , 1994 .

[2]  E. O. Tuck,et al.  A Simple “Filon-trapezoidal” rule , 1967 .

[3]  Sheehan Olver,et al.  Moment-free numerical approximation of highly oscillatory integrals with stationary points , 2007, European Journal of Applied Mathematics.

[4]  J. R. Webster,et al.  A comparison of some methods for the evaluation of highly oscillatory integrals , 1999 .

[5]  P. Grandclément.  Introduction to spectral methods , 2006, gr-qc/0609020.

[6]  W. Chew.  Waves and Fields in Inhomogeneous Media , 1990 .

[7]  A. Iserles,et al.  Efficient quadrature of highly oscillatory integrals using derivatives , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  A. Iserles,et al.  On the computation of highly oscillatory multivariate integrals with stationary points , 2006 .

[9]  Jie Shen,et al.  Spectral and High-Order Methods with Applications , 2006 .

[10]  Elsayed M. E. Elbarbary,et al.  Higher order pseudospectral differentiation matrices , 2005 .

[11]  R. Baltensperger.  Improving the accuracy of the matrix differentiation method for arbitrary collocation points , 2000 .

[12]  David Levin,et al.  Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations , 1982 .

[13]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[14]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[15]  A. ISERLES,et al.  ON THE COMPUTATION OF HIGHLY OSCILLATORY MULTIVARIATE INTEGRALS WITH CRITICAL POINTS , 2005 .

[16]  W. Cheney,et al.  Numerical analysis: mathematics of scientific computing (2nd ed) , 1991 .

[17]  L. Filon.  III.—On a Quadrature Formula for Trigonometric Integrals. , 1930 .

[18]  Sheehan Olver,et al.  Moment-free numerical integration of highly oscillatory functions , 2006 .

[19]  G. A. Evans,et al.  An expansion method for irregular oscillatory integrals , 1997, Int. J. Comput. Math..

[20]  C. Canuto.  Spectral methods in fluid dynamics , 1991 .

[21]  Ronald R. Coifman,et al.  On efficient computation of multidimensional oscillatory integrals with local Fourier bases , 2001 .

[22]  Tao Wang,et al.  A universal solution to one-dimensional oscillatory integrals , 2008, Science in China Series F: Information Sciences.

[23]  A. Tikhonov,et al.  Numerical Methods for the Solution of Ill-Posed Problems , 1995 .