We develop and analyze a new approach for simultaneously computing multiple solutions to the Helmholtz equation for different frequencies and different forcing functions. The new Multi-Frequency WaveHoltz (MFWH) algorithm is an extension of the original WaveHoltz method and both are based on time-filtering solutions to an associated wave-equation. With MFWH, the different Helmholtz solutions are computed simultaneously by solving a single wave equation combined with multiple time filters. The MFWH algorithm defines a fixed-point iteration which can be accelerated with Krylov methods such as GMRES. The solution of the wave equation can be efficiently solved with implicit time-stepping using as few as five time-steps per period. Discretization errors in time can be completely removed by various adjustments. Numerical results are given to confirm the convergence theory when solving energy conserving problems.

About the speaker:

Francis Appiah is a third-year Ph.D. student in the Department of Mathematical Sciences at Rensselaer Polytechnic Institute. His research focuses on developing methods to simultaneously solve Helmholtz equations across multiple frequencies and forcing functions.

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