Extensions: Improving the Poisson Solver

Abstract

The FEniCS programs we have written so far have been designed as flat Python scripts. This works well for solving simple demo problems. However, when you build a solver for an advanced application, you will quickly find the need for more structured programming. In particular, you may want to reuse your solver to solve a large number of problems where you vary the boundary conditions, the domain, and coefficients such as material parameters. In this chapter, we will see how to write general solver functions to improve the usability of FEniCS programs. We will also discuss how to utilize iterative solvers with preconditioners for solving linear systems, how to compute derived quantities, such as, e.g., the flux on a part of the boundary, and how to compute errors and convergence rates.

Keywords

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