An efficient algorithm for wave propagation in dynamic 3D configurations

Abstract

We consider a model problem in which the motion of particles is examined using data carried by waves interacting with the particles. Such problems arise, for example, when tracer particles are carried by a fluid, and their position is detected using scattered light or sound waves. The time evolution of the model can be revealed by simulating the detected wave at a series of snapshots in time as their motion evolves, akin to a motion picture. In our model problem, for proof of concept, the motion of the particles is described by a simple second order ordinary differential equation, but the wave propagation simulation is extremely challenging because the governing partial differential equation must be solved in an unbounded region subject to boundary conditions on the particle boundaries, which change position as the motion of the particles evolves. The principal aim of this work is to demonstrate the use of a fast surrogate for the solution of the wave propagation partial differential equation, and we demonstrate both the accuracy of the surrogate and its efficiency. The efficiency is crucial to allow the simulation of the wave propagation to keep up with the frame rate of the simulation.

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