This means that all statements in the main program that are not insideįunctions should appear within a test if _name_ = That such a file can be imported (and hence reused) in other programs. The refactored code is put in a file ft13_poisson_solver.py. The solution can now be computed, plotted, and saved to file by "Run solver to compute and post-process solution" # Set up problem parameters and call solver Since it is so trivial to use higher-order finite elementįunctions by changing the third argument to FunctionSpace, weĪlso add the polynomial degree of the finite element function space We parameterize solver by \( f \), \( \ub \), and the resolution of the Plotting and comparing the solution with the exact solutionĪre considered to be problem-specific activities to be performed The solver function to just compute the numerical Our special test problem will then just beĪn application of solver with some additional statements. Let us collect the general, reusable code inĪ function called solver. \) with \( u=\ub \) on the boundary, while other statements arise from Is needed to solve any Poisson problem \( -\nabla^2 u=f \) on \( \times We consider the flat program developed in the section FEniCS implementation. Tends to give a blurred understanding of the problem at hand. ![]() In a flat program, generalĪnd specialized code (and mathematics) are often mixed together, which Hand (what is general, what is special?). Specialized code is a key issue when refactoring code, and thisĪbility depends on a good mathematical understanding of the problem at Being able to distinguish reusable code from We will alsoĮncapsulate statements specific to a certain problem into During refactoring, we also try make the functions weĬreate as reusable as possible in other contexts. For a start, this means splitting the code intoįunctions, but this is just a reordering of the existing Therefore look at how to refactor the Poisson solver from the chapter Fundamentals: Solving the Poisson equation. Software, but not well suited for serious problem solving. Such flat programs are useful for quickly testing out some Systems and how to compute derived quantities, such as, e.g., the flux on a part of the boundary.Īll programs created in this book so far are "flat" that is, theyĪre not organized into logical, reusable units in terms of Pythonįunctions. Utilize iterative solvers with preconditioners for solving linear We will see how to write general solver functions to improve the In particular, you may want to reuse your solver to solveĪ large number of problems where you vary the boundary conditions, theĭomain, and coefficients such as material parameters. However, when you build a solver for an advancedĪpplication, you will quickly find the need for more structured The FEniCS programs we have written so far have been designed as flat Computing finite difference approximations.Taking advantage of structured mesh data.Linear variational problem and solver objects.List of linear solver methods and preconditioners.Choosing a linear solver and preconditioner.Exercise 5: Refactor the code for membrane deflection.Parameterizing the number of space dimensions.Extensions: Improving the Poisson solver.Setting multiple Dirichlet, Neumann, and Robin conditions.Exercise 3: Efficiency of Python vs C expressions.Using C code snippets to define subdomains.Vectorized version of subdomain definitions.Using mesh functions to define subdomains.Defining subdomains for different materials.Combining Dirichlet and Neumann conditions.Setting boundary conditions for mixed systems.Setting initial conditions for mixed systems.A system of advection-diffusion-reaction equations.Exercise 2: Simulate channel flow in a 3D geometry.Exercise 1: Visualize a solution in a cube.Examining degrees of freedom and vertex values. ![]()
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