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Charge Based Boundary Element Method with Residual Driven Adaptive Mesh Refinement for High Resolution Electrical
Derek A Drumm1, Gregory M Noetscher1, Hannes Oppermann2
1Dept. of Electrical & Computer Engineering, Worcester Polytechnic Institute, Worcester, MA, USA.
Biorxiv : the Preprint Server for Biology
|April 10, 2026
Summary
Accurate modeling for transcranial electrical stimulation (TES), electroconvulsive therapy (ECT), and electroencephalography (EEG) is improved with adaptive mesh refinement. This method enhances numerical stability for charge-based boundary element methods in realistic head models.
Area of Science:
- Computational neuroscience
- Biomedical engineering
- Numerical methods
Background:
- Accurate forward modeling for transcranial electrical stimulation (TES), electroconvulsive therapy (ECT), and electroencephalography (EEG) is crucial.
- Numerical singularities near electrodes and tissue interfaces pose a challenge for existing methods.
- The charge-based boundary element method (BEM) accelerated by the fast multiple method (BEM-FMM) is a common approach.
Purpose of the Study:
- To present an adaptive mesh refinement (AMR) strategy for BEM-FMM that addresses singularities.
- To develop a novel error estimator incorporating local and nonlocal contributions.
- To evaluate the AMR strategy on spherical and subject-specific head models.
Main Methods:
- Developed an AMR strategy for charge-based BEM-FMM.
- Derived a new error estimator for single-layer potential operators.
- Constructed a refinement criterion based on charge solution differences.
- Validated on 5-layer sphere and SimNIBS/Sim4Life head models with different electrode formulations.
Main Results:
- Achieved relative residual errors below 0.1% for SimNIBS and 1% for Sim4Life models.
- Demonstrated numerical stability for TES and EEG forward solutions.
- Showed effective handling of electrode and interface singularities.
Conclusions:
- The proposed residual-based AMR strategy significantly improves the accuracy and stability of BEM-FMM for TES and EEG forward modeling.
- This method is effective even with complex, subject-specific head geometries.
- Enables more reliable computational models for brain stimulation and recording techniques.
