SFEPY FREE DOWNLOAD

Let us clamp the left edge , and shift the right edge in the direction a bit, depending on the coordinate. This example shows how to use SfePy interactively, but also how to make a custom simulation script. For a test variable, the last item is the name of the corresponding unknown variable. The declarative API involves almost no programming besides using basic Python data types dicts, lists, tuples, strings, etc. So that is it — using the code a black-box PDE solver shields the user from having to create the Problem instance by hand. What is Going on Under the Hood. The imperative API allows immediate evaluation of expressions, and thus supports interactive exploration or inspection of the FE data.

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Nearly incompressible hyperelastic material model with active fibres.

Let us show the displacements by shifting the mesh. Regions serve as domains of integration and allow defining boundary and initial conditions.

SfePy: Simple Finite Elements in Python — SfePy documentation

We wish to solve a heat conduction problem, that can be written in the weak form as follows: Because the code relies on vectorization provided by NumPy, the code tries to work on all cells in a region in each operation: We employ the separation of concerns strategy with respect to parallelism: It allows both fast exploration of various ideas and efficient implementation, thanks to many high-performance solvers with a Python interface, and numerical tools and libraries available among open source packages.

Besides external solvers, several solvers are implemented directly in SfePyfor example:. Laplace equation using the short syntax of keywords. A term is the smallest unit that can be used to build equations.

The problems defined using the imperative API usually have a main function and can be run directly using the Python interpreter. Wfepy finite element problems require the definition of material parameters. In addition to the above elements, two structural elements are implemented using SfePy terms: SfePy relies on a number of packages of the scientific Python software stack, namely: Diffusion Laplace equation eg: Linear elasticity with nodal linear combination constraints.

Acoustic pressure distribution in sfdpy. Multiscale modelling of compact bone based on homogenization of double porous medium. Stokes equations for incompressible fluid flow.

Tutorial — SfePy +gitedec0aaf07e28b0b17d8a documentation

This abstraction allows adding various discretization methods. In this section we briefly outline the approach to solving multiscale problems based on the theory of homogenization Allaire ; Cioranescu and Donato In this section we briefly outline the package implementation, structure and general features. Let us clamp the left edgeand shift the right edge in the direction a bit, depending on the coordinate.

Before we can define the terms to build the equation of linear elasticity, we have to create also the materials, i. For speed in general, it relies on fast vectorized operations provided by NumPy arrays Oliphantwith significant use of advanced features such as broadcasting.

Two Laplace equations with multiple linear combination constraints. Next we define the actual finite element approximation using the Field class.

Multiscale finite element calculations in Python using SfePy

Invoking SfePy from the Command Line. Multiscale finite element calculations in Python using SfePy R. Thermo-elasticity with a given temperature distribution.

The volume forces will be defined also as a material as a constant column vector.

Laplace equation with zfepy field-dependent material parameter. The local microscopic responses of the piezoelectric structure are given by the following sub-problems which are solved within the periodic reference cell Ysee Fig. It corresponds to a weak formulation integral over a sub domain and takes usually several arguments: Navier Stokes Navier-Stokes equations for incompressible fluid flow.

Scepy can be specified in a variety of ways, including by element or by node. This places a restriction on a practically usable order of the basis function polynomials, especially for 3D hexahedrons, where orders greater than 4 are not practically usable.