The time‐domain Lippmann–Schwinger equation and convolution quadrature
Abstract
We consider time‐domain acoustic scattering from a penetrable medium with a variable sound speed. This problem can be reduced to solve a time‐domain volume Lippmann–Schwinger integral equation. Using convolution quadrature in time and trigonometric collocation in space, we can compute an approximate solution. We prove that the time‐domain Lippmann–Schwinger equation has a unique solution and prove conditional convergence and error estimates for the fully discrete solution for globally smooth sound speeds. Preliminary numerical results show that the method behaves well even for discontinuous sound speeds. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 517–540, 2015
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 12, 2014
- Source ID
- 10.1002/num.21921
Entities
People
- Armin Lechleiter
- Peter Monk
Organizations
- Air Force Office of Scientific Research
- National Science Foundation
- University of Bremen
- University of Delaware