CASPER Seminar: "On fast multipole methods for Volterra integral equations with highly oscillatory kernels"

DateNovember 14, 2018Time2:30 - 3:30 pm
LocationBaylor Research & Innovation Collaborative (BRIC), room 3160
Description

Baylor University and CASPER present:

Ms. Qiangyang Zhang
Visiting Scholar, Department of Mathematics
Baylor University and CASPER

On fast multipole methods for Volterra integral equations with highly oscillatory kernels

Abstract:

This talk explores the fast multipole methods (FMMs) to accelerate the approximation for weakly singular Volterra integral equations with highly oscillatory trigonometric kernels. By constructing the fast translation path, the FMM is utilized to speed up the iterative method, which reduces the complexity from $O(N^{2})$ to $O(N)$. Especially, we use the collocation method to discretize the Volterra integral equation with constants and linear elements respectively, then apply the GMRES to solve the dense and non-symmetric linear system. In addition, the highly oscillatory integrals derived from the algorithm are calculated effectively by the steepest descent method. The proposed method shows that the numerical solutions become more accurate as the frequency increases. Both of the optimal convergence rates of truncation and the error bounds analysis are represented in the end.

Bio:

Ms. Zhang is a doctoral candidate in Computational Mathematics at Central South University, China. She is currently doing research with Dr. Tim Sheng at Baylor University as a visiting scholar.

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PublisherCASPER
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