Linear-in-Complexity Computational Strategies for Modeling and Dosimetry at TeraHertz

This work presents a fast direct solver strategy allowing full-wave modeling and dosimetry at terahertz (THz) frequencies. The novel scheme leverages a preconditioned combined field integral equation together with a regularizer for its elliptic spectrum to enable its compression into a non-hierarchical skeleton, invertible in quasi-linear complexity. Numerical results will show the effectiveness of the new scheme in a realistic skin modeling scenario

Linear-in-Complexity Computational Strategies for Modeling and Dosimetry at TeraHertz

This work presents a fast direct solver strategy allowing full-wave modeling and dosimetry at terahertz (THz) frequencies. The novel scheme leverages a preconditioned combined field integral equation together with a regularizer for its elliptic spectrum to enable its compression into a non-hierarchical skeleton, invertible in quasi-linear complexity. Numerical results will show the effectiveness of the new scheme in a realistic skin modeling scenario

On a Calder\'on preconditioner for the symmetric formulation of the electroencephalography forward problem without barycentric refinements

We present a Calder\'on preconditioning scheme for the symmetric formulation of the forward electroencephalographic (EEG) problem that cures both the dense discretization and the high-contrast breakdown. Unlike existing Calder\'on schemes presented for the EEG problem, it is refinement-free, that is, the electrostatic integral operators are not discretized with basis functions defined on the barycentrically-refined dual mesh. In fact, in the preconditioner, we reuse the original system matrix thus reducing computational burden. Moreover, the proposed formulation gives rise to a symmetric, positive-definite system of linear equations, which allows the application of the conjugate gradient method, an iterative method that exhibits a smaller computational cost compared to other Krylov subspace methods applicable to non-symmetric problems. Numerical results corroborate the theoretical analysis and attest of the efficacy of the proposed preconditioning technique on both canonical and realistic scenarios

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

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