An explicit marching-on-in-time scheme for solving the time domain Kirchhoff integral equation.

Abstract
A fully explicit marching-on-in-time (MOT) scheme for solving the time domain Kirchhoff (surface) integral equation to analyze transient acoustic scattering from rigid objects is presented. A higher-order Nyström method and a PE(CE)m-type ordinary differential equation integrator are used for spatial discretization and time marching, respectively. The resulting MOT scheme uses the same time step size as its implicit counterpart (which also uses Nyström method in space) without sacrificing from the accuracy and stability of the solution. Numerical results demonstrate the accuracy, efficiency, and applicability of the proposed explicit MOT solver.

Citation
Chen, R., Sayed, S. B., Alharthi, N., Keyes, D., & Bagci, H. (2019). An explicit marching-on-in-time scheme for solving the time domain Kirchhoff integral equation. The Journal of the Acoustical Society of America, 146(3), 2068–2079. doi:10.1121/1.5125259

Acknowledgements
This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No 2016-CRG5-2953. The authors would like to thank the King Abdullah University of Science and Technology Supercomputing Laboratory (KSL) for providing the required computational resources.

Publisher
Acoustical Society of America (ASA)

Journal
The Journal of the Acoustical Society of America

DOI
10.1121/1.5125259

Additional Links
http://asa.scitation.org/doi/10.1121/1.5125259

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