A space-time dual-pairing summation-by-parts framework for forward and adjoint wave equations
This work addresses wave propagation problems for computational physics and engineering, offering a novel numerical framework with potential applications in inverse problems, but it appears incremental as it builds on existing SBP and SAT techniques.
The paper tackled the problem of forward and adjoint wave propagation by proposing a space-time dual-pairing summation-by-parts (DP-SBP) numerical framework, achieving high-order accuracy with natural dissipation and enabling adjoint-consistent approximations for inverse problems, as verified through numerical experiments in one and two dimensions.
In this paper, we propose the first of its kind space-time dual-pairing summation by parts (DP-SBP) numerical framework for forward and adjoint wave propagation problems. This novel approach enables us to achieve spatial and temporal high order accuracy while naturally introducing dissipation in time. Within this framework, initial and boundary conditions are weakly imposed using the simultaneous approximation term (SAT) technique. Fully discrete energy estimates are derived, ensuring the stability of the resulting numerical scheme. Furthermore, the proposed space-time numerical framework allows us to construct adjoint consistent fully discrete numerical approximations, which can be applied to solve inverse wave propagation problems. We provide numerical experiments in one and two spatial dimensions to verify the theoretical analysis and demonstrate convergence of numerical errors.