A fast ADI algorithm for nonlinear Poisson equation in heterogeneous dielectric media

A nonlinear Poisson equation (NPE) has been introduced to model and nonlocal hyperpolarisation effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due a strong nonlinearity associated with the heterogeneous dielectric media, NPE is difficult solve numerically large protein systems. new pseudo-transient continuation approach proposed this paper efficiently stably. An alternating direction implicit (ADI) method developed solving pseudo-time dependent equation. The scheme validated by considering benchmark examples exact solutions analysis of real biomolecules various sizes. Numerical results are good agreement theoretical prediction, experimental measurements, those obtained from boundary value problem approach. Since time stability ADI can be maintained even using very increments, it efficient involving effects.