Applied and Computational Math Seminar: Fast recovery of far-field time-domain signals from near-field data

Speaker:Scott Field, University of Massachusetts - Dartmouth
Title: Fast recovery of far-field time-domain signals from near-field data

Abstract: Time-domain simulation of linear hyperbolic partial differential equations on a finite computational domain requires the introduction of a fictitious outer boundary. A long-standing challenge in the computation of waves is to identify the far-field or asymptotic signal. From data recorded on a sphere defined by the radius r1 we seek to recover the far-field signal which would reach large distances r2 including infinity. Far-field signals are particularly important as they encode information about the physical system. In this talk, I show how far-field signal recovery is handled with a time-domain convolution of the solution recorded on a sphere r1 with a kernel. A kernel which describes signal recovery for the ordinary (acoustic) wave equation can be written in closed-form. Using rational approximation techniques developed by Alpert, Greengard and Hagstrom (AGH) this kernel can be "compressed" as a compact sum-of-poles in the frequency domain. For linear hyperbolic PDEs where one does not know a closed-form kernel representation, the AGH technique continues to provide numerically generated kernels. We use this approach to compute signals generated from binary black hole systems where the analytic kernel is not known. 

Time: Thursday, May 4, 2017, 1:00-2:00 p.m. (NOTE SPECIAL TIME!)

Place: Exploratory Hall, Room 3301 (NOTE SPECIAL ROOM!)