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Many operations on structured arrays can be formulated as stencil codes, where the update of one array cell depends only on values in its local neighborhood. Stencil codes arise in many different fields, for example in image processing or in computational fluid dynamics by discretizing partial differential equations (PDEs) using finite differences or finite volume schemes.

We present the pystencils package that allows for fast execution of stencil codes on numpy arrays using code generation techniques.
The stencil is formulated in sympy and transformed into an intermediate representation (IR).
pystencils comes with a set of optimizing transformations that can be applied on this IR, for example cache blocking or explicit SIMD vectorization with intrinsics. The intermediate representation is transformed into C or CUDA code and automatically loaded as a C extension module. This approach yields highly efficient implementations, outperforming current acceleration techniques like Cython or numba. Additionally, together with the waLBerla package, the resulting stencil codes can be run on large computing clusters, using MPI parallelization.

pystencils also comes with functions to automatically derive the sympy-based stencil representation from a continuous PDE. Symbolic, continuous differential operators are automatically discretized by finite difference schemes of arbitrary order.

We show two examples of large-scale setups run with pystencils: a phase-field method simulating solidification of alloys and a CFD simulation based on the lattice-Boltzmann method.