129 research outputs found
High performance Python for direct numerical simulations of turbulent flows
Direct Numerical Simulations (DNS) of the Navier Stokes equations is an
invaluable research tool in fluid dynamics. Still, there are few publicly
available research codes and, due to the heavy number crunching implied,
available codes are usually written in low-level languages such as C/C++ or
Fortran. In this paper we describe a pure scientific Python pseudo-spectral DNS
code that nearly matches the performance of C++ for thousands of processors and
billions of unknowns. We also describe a version optimized through Cython, that
is found to match the speed of C++. The solvers are written from scratch in
Python, both the mesh, the MPI domain decomposition, and the temporal
integrators. The solvers have been verified and benchmarked on the Shaheen
supercomputer at the KAUST supercomputing laboratory, and we are able to show
very good scaling up to several thousand cores.
A very important part of the implementation is the mesh decomposition (we
implement both slab and pencil decompositions) and 3D parallel Fast Fourier
Transforms (FFT). The mesh decomposition and FFT routines have been implemented
in Python using serial FFT routines (either NumPy, pyFFTW or any other serial
FFT module), NumPy array manipulations and with MPI communications handled by
MPI for Python (mpi4py). We show how we are able to execute a 3D parallel FFT
in Python for a slab mesh decomposition using 4 lines of compact Python code,
for which the parallel performance on Shaheen is found to be slightly better
than similar routines provided through the FFTW library. For a pencil mesh
decomposition 7 lines of code is required to execute a transform
Finite Difference Computing with Exponential Decay Models
Computational Science and Engineering; software Engineering; Programming Technique
Programming for Computations - Python: A Gentle Introduction to Numerical Simulations with Python
Numerical simulations; programming; Pytho
Solving PDEs in Python
This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license
Finite Difference Computing with PDEs: A Modern Software Approach
finite difference methods; programming; python; verification; numerical methods; differential equation
Solving PDEs in Python
This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license
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