A New Computational Approach for Wave Propagation

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Wave motion is the key mechanism of interest to many fields of science, such as mechanics, acoustics, seismology, oceanography, coastal and offshore engineering, electromagnetism, etc. Despite an extreme variety of physical appearances of wave phenomena, mathematical models and numerical methods implemented from them face reliability and accuracy concerns, especially at high frequencies and under impact loadings. This award will support research on a new numerical approach with optimal accuracy for wave propagation. The new modeling technique will be able to provide accurate solutions for a broad range of civil and military applications related to national health and security, respectively, where wave propagation is a concern. The project will provide opportunities to educate and train graduate and undergraduate students on the theoretical and modeling aspects of wave propagation, with a focus on underrepresented students. A workshop on dynamic behavior will also be developed for high school teachers under this project.Many modern numerical techniques based on weak-form formulations of partial differential equations do not provide optimal accuracy in the discrete equations. This leads to a prohibitively large computation time for real-world wave propagation problems. In this project, a novel high-order numerical approach for wave propagation on Cartesian meshes for irregular domains will be directly formulated in terms of discrete equations with unknown coefficients. These coefficients are calculated by the minimization of the local truncation error and provide the optimal order of accuracy. Some of the important applications will include high-frequency wave propagation in the Hopkinson Bar and elastic wave propagation in the vicinity of crack tips and defects. Due to stationary Cartesian meshes, there will be no need to remesh the domain for a moving crack. The moving crack will be treated by the corresponding high-order boundary conditions on the same Cartesian grid.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.