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

Viviana Giunzioni, John E. Ortiz G., Adrien Merlini, Simon B. Adrian, Francesco P. Andriulli
2022 arXiv   pre-print
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
more » ... etization 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.
arXiv:2204.06857v1 fatcat:rfolyrgze5bj3jpb77klbyldqq