Abstract
Chapter 5 constructs finite-difference models for scalar transport in two space dimensions. The focus is on steady-state, equilibrium problems. Some analytical properties and solutions of the Laplace and Poisson equations are developed, and are used for comparison with computational results. Methods for solving sparse systems of linear equations are analyzed, and their rates of convergence are compared. The conjugate gradient and multigrid methods are developed in detail, and applied to sequential and parallel computing. The complications arising from curvilinear boundaries are examined, and certain techniques are presented for implementing boundary node computations.
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