Simulation of 2D Acoustic Wave Propagation with Absorbing Boundary Condition

Abstract

In this work we design an algorithm to simulate the 2D acoustic wave (P wave) propagation in a medium with different regional velocities. We use the Generalized Conjugate Residual (GCR) algorithm to solve the trapezoidal time integration, where for a given time step of 0.01 seconds, the error is approximately 8% with respect to the reference. We further speed up the simulation by a factor of 900 by implementing a model reduction scheme using Proper Orthogonal Decomposition (POD). Lastly, to suppress the artificial reflections formed when the wave bounces off the fixed boundaries, we created two virtual absorbing layers by tapering the solution of nodes close to the corresponding boundaries after each time iteration. However, we note that the successful implementations of the model reduction and absorbing boundary condition are not compatible with each other and provide explanations for why and how to combine them in future work.