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A Calderon regularized symmetric formulation for the electroencephalography forward problem

John E. Ortiz G., Axelle Pillain, Lyes Rahmouni, Francesco P. Andriulli
2018 Journal of Computational Physics  
The symmetric formulation of the electroencephalography (EEG) forward problem is a well-known and widespread equation thanks to the high level of accuracy that it delivers.  ...  The new scheme is obtained by leveraging on Calderon identities which allow to introduce a dual symmetric equation that, combined with the standard one, results in a second kind operator which is both  ...  Conclusion In this work, leveraging on Calderon identities, we have proposed a Calderon preconditioned symmetric formulation for the EEG forward problem.  ... 
doi:10.1016/ fatcat:3dd6jwmrgncitikpr2k62w5lt4

On a Low-Frequency and Contrast Stabilized Full-Wave Volume Integral Equation Solver for Lossy Media [article]

Clément Henry, Adrien Merlini, Lyes Rahmouni, Francesco P. Andriulli
2021 arXiv   pre-print
This new formulation is particularly suitable for modeling biological tissues at low frequencies, as it is required by brain epileptogenic area imaging, but also at higher ones, as it is required by several  ...  In this work we address these shortcomings by leveraging a new set of volume quasi-Helmholtz projectors.  ...  equation [18] by leveraging the Calderón identities while the low-frequency breakdown of the PMCHWT was tackled by its preconditioning with quasi-Helmholtz projectors [22] .  ... 
arXiv:2108.10690v1 fatcat:k4rfm4sqlzgo5e7ohbclcuyxyy