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.
@article{arxiv.2204.06857,
title = {A New Refinement-Free Preconditioner for the Symmetric Formulation in Electroencephalography},
author = {Viviana Giunzioni and John E. Ortiz G. and Adrien Merlini and Simon B. Adrian and Francesco P. Andriulli},
journal= {arXiv preprint arXiv:2204.06857},
year = {2022}
}