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A controllability method for Maxwell's equations

Abstract : We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the controllability method determines iteratively a periodic solution in the time domain. At each conjugate gradient iteration, the gradient of the cost functional is simply computed by running any time-dependent simulation code forward and backward for one period, thus leading to a non-intrusive implementation easily integrated into existing software. Moreover, the proposed algorithm automatically inherits the parallelism, scalability, and low memory footprint of the underlying time-domain solver. Since the time-periodic solution obtained by minimization is not necessarily unique, we apply a cheap post-processing filtering procedure which recovers the time-harmonic solution from any minimizer. Finally, we present a series of numerical examples which show that our algorithm greatly speeds up the convergence towards the desired time-harmonic solution when compared to simply running the time-marching code until the time-harmonic regime is eventually reached.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03250886
Contributor : Théophile Chaumont-Frelet Connect in order to contact the contributor
Submitted on : Saturday, June 5, 2021 - 12:13:43 PM
Last modification on : Wednesday, March 16, 2022 - 3:46:30 AM
Long-term archiving on: : Monday, September 6, 2021 - 6:03:22 PM

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  • HAL Id : hal-03250886, version 1
  • ARXIV : 2106.02858

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Théophile Chaumont-Frelet, Marcus Grote, Stephane Lanteri, Jet Hoe Tang. A controllability method for Maxwell's equations. 2021. ⟨hal-03250886⟩

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