Summary: Fast Evaluation of 2­D and 3­D Oscillatory Integrals with Local Fourier Bases
A. Averbuch 1 , E. Braverman 2;3 , R. Coifman 3 , M. Israeli 2;4
1 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
2 Computer Science Department, Technion, Haifa 32000, Israel.
3 Department of Mathematics, Yale University, New Haven, CT 06520­8283, USA
AMS Subject Classification: 65T, 65D30, 42B
Abstract
The 2­D surface integral Z
S
Z
e
išOE(x;y;r;t) f(r; t) ds
and the 3­D volume integral
Z Z
V
Z
e išOE(x;y;z;q;r;t) f(q; r; t) dq dr dt
with a highly oscillatory kernel (large š) are represented in the local Fourier basis. The
representation of the oscillatory kernels in this basis is sparse. This opens new ways to fast
computations of these integrals. The present paper is an extension of our previous paper

Source: Averbuch, Amir - School of Computer Science, Tel Aviv University

Collections: Computer Technologies and Information Sciences