| Abstract: |
| Eikonal and transport equations arise from using the geometrical-optics ansatz in solving wave equations in the high-frequency regime. In attenuating media, the unknowns are complex-valued so that the real and imaginary parts are coupled with each other. In this talk, we present an effective fast sweeping solver for solving the two equations. Based on a specially designed numerical Hamiltonian, we develop a fast Gauss-Seidel iterative scheme, and establish its convergence theory. Numerical experiments are carried out to demonstrate the effectiveness of the new scheme. |
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