Finite Volume Discretizations for Python

Creating finite volume equation systems with ease.

PyFVM provides everything that is needed for setting up finite volume equation systems. The user needs to specify the finite volume formulation in a configuration file, and PyFVM will create the matrix/right-hand side or the nonlinear system for it. This package is for everyone who wants to quickly construct FVM systems.

## Examples

### Linear equation systems

PyFVM works by specifying the residuals, so for solving Poisson’s equation with Dirichlet boundary conditions, simply do

import pyfvm from pyfvm.form_language import * import meshzoo from scipy.sparse import linalg import voropy class Poisson(object): def apply(self, u): return integrate(lambda x: -n_dot_grad(u(x)), dS) \ - integrate(lambda x: 1.0, dV) def dirichlet(self, u): return [(lambda x: u(x) - 0.0, Boundary())] # Create mesh using meshzoo vertices, cells = meshzoo.rectangle(0.0, 2.0, 0.0, 1.0, 401, 201) mesh = voropy.mesh_tri.MeshTri(vertices, cells) matrix, rhs = pyfvm.discretize_linear(Poisson(), mesh) u = linalg.spsolve(matrix, rhs) mesh.write('out.vtu', point_data={'u': u})

This example uses meshzoo for creating a simple mesh, but anything else that provides vertices and cells works as well. For example, reading from a wide variety of mesh files is supported (via meshio):

mesh, _, _ = pyfvm.reader.read('pacman.e')

Likewise, PyAMG is a much faster solver for this problem

import pyamg ml = pyamg.smoothed_aggregation_solver(linear_system.matrix) u = ml.solve(linear_system.rhs, tol=1e-10)

More examples are contained in the examples directory.

### Nonlinear equation systems

Nonlinear systems are treated almost equally; only the discretization and obviously the solver call is different. For Bratu’s problem:

import pyfvm from pyfvm.form_language import * import meshzoo import numpy from sympy import exp import voropy class Bratu(object): def apply(self, u): return integrate(lambda x: -n_dot_grad(u(x)), dS) \ - integrate(lambda x: 2.0 * exp(u(x)), dV) def dirichlet(self, u): return [(u, Boundary())] vertices, cells = meshzoo.rectangle(0.0, 2.0, 0.0, 1.0, 101, 51) mesh = voropy.mesh_tri.MeshTri(vertices, cells) f, jacobian = pyfvm.discretize(Bratu(), mesh) def jacobian_solver(u0, rhs): from scipy.sparse import linalg jac = jacobian.get_linear_operator(u0) return linalg.spsolve(jac, rhs) u0 = numpy.zeros(len(vertices)) u = pyfvm.newton(f.eval, jacobian_solver, u0) mesh.write('out.vtu', point_data={'u': u})

Note that the Jacobian is computed symbolically from the `Bratu`
class.

Instead of `pyfvm.newton`, you can use any solver that accepts the
residual computation `f.eval`, e.g.,

import scipy.optimize u = scipy.optimize.newton_krylov(f.eval, u0)

## Installation

PyFVM is available from the Python Package Index, so simply type

pip install -U pyfvm

to install or upgrade.

## Testing

To run the tests, check out this repository and type

pytest

## Distribution

To create a new release

bump the

`__version__`number,publish to PyPi and GitHub:

make publish

## License

PyFVM is published under the MIT license.

## Download Files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

File Name & Checksum SHA256 Checksum Help | Version | File Type | Upload Date |
---|---|---|---|

PyFVM-0.2.3-py2.py3-none-any.whl (17.5 kB) Copy SHA256 Checksum SHA256 | py2.py3 | Wheel | May 29, 2017 |