This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of... The equation sequence solver is a stationary solver that analyzes the dependencies among equations and solves smaller blocks ﬁrst. An example would be the thermoelas-ticity problem described below, where the elasticity equa-tion depends on the load given by temperature distribu-tion, but the temperature distribution (Poisson equation) Solving a PDE such as the Poisson equation in FEniCS consists of the following steps Write a Python program which defines the computational domain, the variational problem, the boundary conditions, and source terms, using the corresponding FEniCS abstractions.3.2 Schrödinger-Poisson Solver. The electronic subbands of the conduction band near the zone center of the Brillouin zone and the corresponding envelope functions are determined by solving the Schrödinger equation selfconsistently with the Poisson equation. Poisson’s equation plays a fundamental role in semiconductor device modeling.