MagTetris+ : A fast simulator for magnetic field and force calculation for ferromagnetic materials and permanent magnets.

Permanent magnet array (PMA) is a popular option for low-field portable magnetic resonance imaging (MRI) to generate the main magnetic field for polarization because it does not require large power supply nor a cooling system. A typical PMA consists of permanent magnets and ferromagnetic components, such as shims and yokes. The conventional simulation of PMA uses Finite-Element-Method (FEM). Although widely accepted as the standard for simulation accuracy, FEM is time-consuming and memory intensive, hindering research and development progress. A rapid and memory-efficient simulator for PMA consisting of ferromagnetic materials and permanent magnets is proposed. The calculation uses physics-based formulation with heuristics and stabilization term. Its field-map agreement is assessed against FEM simulations for selected benchmark cases. The results show that MagTetris+ can provide rapid preliminary field estimation with substantially reduced computation time and memory usage, while FEM remains necessary for high-fidelity validation.