From sLLG to Fokker-Planck: Accurate WER Modeling for Non-Axisymmetric MRAM Devices

The Fokker--Planck (FP) equation is essential for predicting write error rates (WER) in STT and SOT-MRAM devices, but traditional 1D projections fail when symmetry is broken by in-plane fields, field-like torques, or anisotropic barriers. We develop a 2D finite-volume (FVM) solver on the unit sphere and validate it against $10^6$-trajectory stochastic Landau--Lifshitz--Gilbert (sLLG) simulations. The solver supports four discretization schemes---central, Scharfetter--Gummel (SG), upwind, and hybrid adaptive blending---each with different P\'eclet-dependent accuracy and monotonicity properties. We demonstrate that central differencing recovers ground-truth WER for STT and SOT geometries where 2D effects dominate, and show that the choice of discretization scheme directly affects predicted WER. For magnetic simulations, we recommend hybrid adaptive blending as the optimal balance of accuracy and stability across variable P\'eclet regimes. These results establish that customizable discretization is critical for accurate, unbiased predictions of switching dynamics in next-generation magnetic memory.