A High-Order Discretization Scheme for Surface Integral Equations for Analyzing the Electroencephalography Forward Problem
Abstract
A Nyström-based high-order (HO) discretization scheme for surface integral equations (SIEs) for analyzing the electroencephalography (EEG) forward problem is proposed in this work. We use HO surface elements and interpolation functions for the discretization of the interfaces of the head volume and the unknowns on the elements, respectively. The proposed scheme is more flexible and versatile than the existing isoparametric HO discretization schemes for the following reasons: The interpolation points are different from the mesh nodes, allowing for the flexible manipulation of the order of the basis functions without regenerating the mesh of the interfaces. Moreover, the interpolation points are chosen from the quadrature rules with the same number of points on the elements simplifying the numerical computation of the surface integrals for the far-interaction case. In addition, we extend the implementation of the HO discretization scheme to the double-layer and the adjoint double-layer formulations, as well as to the isolated-skull-approach for the double-layer formulation and to the indirect adjoint double-layer formulation, employed to improve the solution accuracy in case of high conductivity contrast models, which requires the development of different techniques for the singularity treatment. Numerical experiments are presented to demonstrate the accuracy, flexibility, and efficiency of the proposed scheme for the four SIEs for analyzing the EEG forward problem.
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BibTeX
@article{chen2026highorder,
title = {{A High-Order Discretization Scheme for Surface Integral Equations for Analyzing the Electroencephalography Forward Problem}},
author = {Rui Chen and Viviana Giunzioni and Adrien Merlini and Francesco Andriulli},
journal = {IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology},
year = {2026},
month = sep,
doi = {10.1109/jerm.2026.3695986},
eprint = {2512.04845},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05734591v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A High-Order Discretization Scheme for Surface Integral Equations for Analyzing the Electroencephalography Forward Problem
AU - Rui Chen
AU - Viviana Giunzioni
AU - Adrien Merlini
AU - Francesco Andriulli
PY - 2026
DA - 2026/09/03
JO - IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology
DO - 10.1109/jerm.2026.3695986
UR - https://hal.science/hal-05734591v1
AB - A Nyström-based high-order (HO) discretization scheme for surface integral equations (SIEs) for analyzing the electroencephalography (EEG) forward problem is proposed in this work. We use HO surface elements and interpolation functions for the discretization of the interfaces of the head volume and the unknowns on the elements, respectively. The proposed scheme is more flexible and versatile than the existing isoparametric HO discretization schemes for the following reasons: The interpolation points are different from the mesh nodes, allowing for the flexible manipulation of the order of the basis functions without regenerating the mesh of the interfaces. Moreover, the interpolation points are chosen from the quadrature rules with the same number of points on the elements simplifying the numerical computation of the surface integrals for the far-interaction case. In addition, we extend the implementation of the HO discretization scheme to the double-layer and the adjoint double-layer formulations, as well as to the isolated-skull-approach for the double-layer formulation and to the indirect adjoint double-layer formulation, employed to improve the solution accuracy in case of high conductivity contrast models, which requires the development of different techniques for the singularity treatment. Numerical experiments are presented to demonstrate the accuracy, flexibility, and efficiency of the proposed scheme for the four SIEs for analyzing the EEG forward problem.
SN - 2469-7249
ER -