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Charge based boundary element fast multipole method
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<p>The charge-based formulation of the <a href="/facts/Boundary_element_method/FMIb4mLs">boundary element method</a> (BEM) is a <a href="/facts/Dimensionality_reduction/XoRpcrB0">dimensionality reduction</a> <a href="/facts/Numerical_analysis/QT9cYa9z">numerical technique</a> that is used to model quasistatic electromagnetic phenomena in highly complex conducting media (targeting, e.g., the <a href="/facts/Human_brain/qfSwSB8K">human brain</a>) with a very large (up to approximately 1 billion) number of unknowns. The charge-based BEM solves an <a href="/facts/Integral_equation/LCu4Imfq">integral equation</a> of the <a href="/facts/Potential_theory/3sXGIcDA">potential theory</a> written in terms of the induced <a href="/facts/Surface_charge_density/xFDPXUDM">surface charge density</a>. This formulation is naturally combined with <a href="/facts/Fast_multipole_method/fpUr8vsp">fast multipole method</a> (FMM) acceleration, and the entire method is known as charge-based BEM-FMM. The combination of BEM and FMM is a common technique in different areas of <a href="/facts/Computational_electromagnetics/uJKnwCar">computational electromagnetics</a> and, in the context of bioelectromagnetism, it provides improvements over the <a href="/facts/Finite_element_method/eUcfP1vn">finite element method</a>. </p>