ABSTRACT
This chapter describes iterative techniques for numerical solutions with nonlinear materials. Calculations for field-dependent dielectrics illustrate some of the stability problems that may arise. The chapter explains how to represent material properties in numerical tables. Good interpolation techniques are essential to achieve solution convergence. The chapter concentrates on the cubic spline method which ensures continuity of the interpolated values and first derivatives of the dependent variable. It shows how to represent anisotropic materials in finite-element electrostatic calculations on a conformal triangular mesh. The only change is a modification of the coupling constants. To illustrate an alternate application of the methods, the chapter describes finite-element solutions for steady-state flow of compressible gases. The variation of gas density introduces a nonlinearity. To illustrate nonlinear solutions to the Poisson equation, the chapter reviews steady-state nonturbulent gas flow. The methods are useful for aerodynamics and pneumatic systems.
