Abstract
We explore time-based solvers for linear standing-wave problems, especially the oscillatory Helmholtz equation. Here, we show how to accelerate the convergence properties of timestepping. We introduce a new time-based solver that we call phase-adjusted time-averaging (PATA), which we couple to timestepping to form the PATA-TS solver. Numerical experiments indicate that the PATA-TS solver is faster than the PATA solver and timestepping by a factor of 1.2 and 1.5 or more, respectively. We also explain why the PATA-TS solver is robust, efficient, and easy to program for a variety of practical applications.
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Ganguly, K., Orszag, S.A. A New Time-Based Iterative Solver for Linear Standing-Wave Problems. Journal of Scientific Computing 14, 329–346 (1999). https://doi.org/10.1023/A:1023252514987
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DOI: https://doi.org/10.1023/A:1023252514987