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arXiv · 2204.06857

A New Refinement-Free Preconditioner for the Symmetric Formulation in Electroencephalography

Viviana Giunzioni·John E. Ortiz G.·Adrien Merlini·Simon B. Adrian·Francesco P. Andriulli
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Abstract

Widely employed for the accurate solution of the electroencephalography forward problem, the symmetric formulation gives rise to a first kind, ill-conditioned operator ill-suited for complex modelling scenarios. This work presents a novel preconditioning strategy based on an accurate spectral analysis of the operators involved which, differently from other Calder\'on-based approaches, does not necessitate the barycentric refinement of the primal mesh (i.e., no dual matrix is required). The discretization of the new formulation gives rise to a well-conditioned, symmetric, positive-definite system matrix, which can be efficiently solved via fast iterative techniques. Numerical results for both canonical and realistic head models validate the effectiveness of the proposed formulation.

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Viviana Giunzioni, John E. Ortiz G., Adrien Merlini, Simon B. Adrian, Francesco P. Andriulli. 2022-04-14. A New Refinement-Free Preconditioner for the Symmetric Formulation in Electroencephalography. https://arxiv.org/abs/2204.06857

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