报告题目：A Filon-Clenshaw-Curtis-Smolyak Rule for Multi-Dimensional Oscillatory Integrals

报告时间：2022-10-13  14:30 - 15:30

报告人：伍智璋  香港大学

腾讯会议ID：528-209-866

Abstract：We combine the Smolyak technique for multi-dimensional interpolation with the Filon-Clenshaw-Curtis (FCC) rule for one-dimensional oscillatory integration, to obtain a new Filon-Clenshaw-Curtis-Smolyak (FCCS) rule for oscillatory integrals with linear phase over the d-dimensional cube [-1,1]d. By combining stability and convergence estimates for the FCC rule with error estimates for the Smolyak interpolation operator, we obtain an error estimate for the FCCS rule, consisting of the product of a Smolyak-type error estimate multiplied by a term that decreases with O(k-d ̅ ) , where k is the wavenumber and d ̅ is the number of oscillatory dimensions. If all dimensions are oscillatory, a higher negative power of k appears in the estimate. Numerical examples illustrate the theoretical properties of the FCCS rule, and include an example of a dimension-adaptive version of our method and an application of our method to an uncertainty quantification (UQ) problem for the Helmholtz equation. This is a joint work with I.G. Graham, D. Ma and Z. Zhang.