Efficient Computation of Oscillatory Integrals via Adaptive Multiscale Local Fourier Bases
نویسندگان
چکیده
The integral ∫ L 0 e iνφ(s,t)f (s) ds with a highly oscillatory kernel (large ν, ν is up to 2000) is considered. This integral is accurately evaluated with an improved trapezoidal rule and effectively transcribed using local Fourier basis and adaptive multiscale local Fourier basis. The representation of the oscillatory kernel in these bases is sparse. The coefficients after the application of local Fourier transform are smoothed. Sometimes this enables us to obtain further compression with wavelets. 2000 Academic Press
منابع مشابه
Fast Directional Computation of High Frequency Boundary Integrals via Local FFTs
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the boundary. This paper presents a new fast algorithm for this task in two dimensions. This algorithm is built on top of directional low-rank approximations of the...
متن کاملEfficient computation of highly oscillatory integrals with Hankel kernel
In this paper, we consider the evaluation of two kinds of oscillatory integrals with a Hankel function as kernel. We first rewrite these integrals as the integrals of Fourier-type. By analytic continuation, these Fourier-type integrals can be transformed into the integrals on [0, + ), the integrands of which are not oscillatory, and decay exponentially fast. Consequently, the transformed integr...
متن کاملComputing Integrals of Highly Oscillatory Special Functions Using Complex Integration Methods and Gaussian Quadratures
An account on computation of integrals of highly oscillatory functions based on the so-called complex integration methods is presented. Beside the basic idea of this approach some applications in computation of Fourier and Bessel transformations are given. Also, Gaussian quadrature formulas with a modified Hermite weight are considered, including some numerical examples.
متن کاملEfficient computation of quadratic-phase integrals in optics.
We present a fast NlogN time algorithm for computing quadratic-phase integrals. This three-parameter class of integrals models propagation in free space in the Fresnel approximation, passage through thin lenses, and propagation in quadratic graded-index media as well as any combination of any number of these and is therefore of importance in optics. By carefully managing the sampling rate, one ...
متن کاملConstruction of Optimal Quadrature Formula for Numerical Calculation of Fourier Coefficients in Sobolev Space
Computation of integrals of strongly oscillating functions is one of the more important problems of numerical analysis, because such integrals are encountered in applications in many branches of mathematics as well as in other science such as quantum physics, flow mechanics and electromagnetism. Main examples of strongly oscillating integrands are encountered in different transformation, for ex...
متن کامل