Workshop: Beyond Finite Element Method:
Fast Multipole Method for High-Resolution Brain Stimulation, Brain Recordings, and Cellular-Scale Modeling

Overview

This workshop introduces a modern fast multipole method (FMM) – based computational framework for high-resolution brain stimulation, recording, and cellular-scale modeling. Rather than positioning FMM as a replacement for the finite element method (FEM), we will discuss it as a complementary and, in some regimes, highly advantageous alternative – particularly for problems requiring extreme geometric detail, long-range field interactions, or multiscale coupling from millimeter anatomy down to neuronal membranes.

The workshop will begin with an intuitive introduction to the underlying principles of the FMM and its integration with boundary-element formulations for electric and magnetic field modeling. We will then focus on practical application examples spanning transcranial stimulation, M/EEG modeling, and microscopic neuron–field interactions, highlighting accuracy, scalability, and performance considerations relative to FEM. Common modeling challenges – such as complex tissue interfaces, large problem sizes, convoluted cell membranes and realistic cell networks in microscopic brain modeling– will be discussed.

The workshop will conclude with a hands-on overview of a simple, end-to-end software pipeline, demonstrating how FMM-based solvers can be used in practice through a Python interface.

Program

Part I: FMM Primer & Mesoscale Modeling

9:00 - 9:10 AM	Sergey Makaroff & Aapo Nummenmaa Introduction: Brain Modeling Problems Where BEM-FMM May Unlock New Science
9:10 - 9:30 AM	Leslie Greengard The Fast Multipole Method: What Every Modeler Should Know.
9:30 - 9:50 AM	Gregory Noetscher, Esra Neufeld, Antonino Cassara, Bryn Lloid, Hanbing Lu, Zhi-De Deng Accurate Deep-Brain Field Prediction for ECT/TES: Why BEM-FMM Matters.
9:50 - 10:10 AM	Guillermo Nuñez Ponasso, Derek Drumm, Alexander Linke, Thomas Knoesche, Burkhard Maess, Jens Haueisen, Tommi Raij High-Definition M/EEG Forward Modeling with BEM-FMM: The Other Side of Reciprocity.
10:10 - 10:30 AM	Coffee Break

Part II. Microscale and Nanoscale Modeling & Tools

10:30 - 10:50 AM	Gregory Noetscher, Konstantin Weise, Bethanny Danskin, Bruce Rosen, Marom Bikson Gray Matter Is Not Homogeneous: 50-µm Conductivity Structure from Data and Models.
10:50 - 11:10 AM	Luis Gomez Bidomain neuron modeling for predicting cellular responses to electromagnetic fields.
11:10 - 11:30 AM	Sergey Makaroff, Dexuan Tang, Schelley Fried, Jake Lee, Padma Sundaram, Gustav Bizik, Marom Bikson, Aapo Nummenmaa Inside Neurons During Brain Stimulation: What Actually Happens?
11:30 - 11:40 AM	Derek Drumm, Verit Lee, Manas Rachh BEM-FMM in Python: Up and Running in 10 Minutes.
11:40 - 11:50 AM	General Discussion