Widely employed for the accurate solution of the electroencephalography forward problem, the symmetric formulation gives rise to a first kind, ill-conditioned operator illsuited 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 Calderón-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.

A New Refinement-Free Preconditioner for the Symmetric Formulation in Electroencephalography / Giunzioni, V.; Ortiz, J. E. G.; Merlini, A.; Adrian, S. B.; Andriulli, F. P.. - ELETTRONICO. - (2022), pp. 513-514. ((Intervento presentato al convegno IEEE AP-S international symposium 2022 tenutosi a Denver, CO, USA nel 10-15 July 2022 [10.1109/AP-S/USNC-URSI47032.2022.9887114].

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

Giunzioni V.;Merlini A.;Adrian S. B.;Andriulli F. P.
2022

Abstract

Widely employed for the accurate solution of the electroencephalography forward problem, the symmetric formulation gives rise to a first kind, ill-conditioned operator illsuited 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 Calderón-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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2973287