A stabilized diffuse-interface electroporation model with a semi-analytical spectral electrolyte solver

We develop a diffuse-interface continuum model for membrane electroporation that couples a phase field for pore geometry to a quasi-static electrolyte potential and a spatially varying leaky-dielectric model for the transmembrane voltage. The main contribution is a stabilized time-integration strategy for transmembrane voltage V m : the stiff leakage term is treated implicitly while the electrolyte-to-membrane ionic current is lagged, yielding a closed-form update that removes the restriction imposed by the fast dielectric relaxation time. The electrolyte potential is computed efficiently using a semi-analytical spectral Laplace solver: a 2D discrete cosine transform (DCT) in the membrane plane reduces the 3D problem to independent 1D ODEs in z , solved in closed form and reconstructed by an inverse transform. The coupled method is robust under grid refinement, recovers the sharp-interface critical-radius bifurcation, and qualitatively reproduces electric-field focusing through conductive pores. We also demonstrate stochastic pore nucleation by adding thermal noise to the phase-field dynamics, enabling fully emergent electroporation events without prescribing initial defects.