毕业设计&课设-Numba在Python、Julia和Matlab中加速了MPDATA的Python实现.zip

# PyMPDATA [](https://www.python.org/) [](https://www.numba.org) [](https://en.wikipedia.org/wiki/Linux) [](https://en.wikipedia.org/wiki/macOS) [](https://en.wikipedia.org/wiki/Windows) [](https://jupyter.org/) [](https://github.com/open-atmos/PyMPDATA/graphs/commit-activity) [](https://www.openhub.net/p/atmos-cloud-sim-uj-PyMPDATA) [](https://joss.theoj.org/papers/10e7361e43785dbb1b3d659c5b01757a) [](https://zenodo.org/badge/latestdoi/225610671) [](https://www.fnp.org.pl/en/) [](https://www.ncn.gov.pl/?language=en) [](https://www.gnu.org/licenses/gpl-3.0.html) [](https://github.com/open-atmos/PyMPDATA/actions) [](https://ci.appveyor.com/project/slayoo/pympdata/branch/main) [](https://app.codecov.io/gh/open-atmos/PyMPDATA) [](https://pypi.org/project/PyMPDATA) [](https://open-atmos.github.io/PyMPDATA/) PyMPDATA is a high-performance Numba-accelerated Pythonic implementation of the MPDATA algorithm of Smolarkiewicz et al. used in geophysical fluid dynamics and beyond. MPDATA numerically solves generalised transport equations - partial differential equations used to model conservation/balance laws, scalar-transport problems, convection-diffusion phenomena. As of the current version, PyMPDATA supports homogeneous transport in 1D, 2D and 3D using structured meshes, optionally generalised by employment of a Jacobian of coordinate transformation. PyMPDATA includes implementation of a set of MPDATA variants including the non-oscillatory option, infinite-gauge, divergent-flow, double-pass donor cell (DPDC) and third-order-terms options. It also features support for integration of Fickian-terms in advection-diffusion problems using the pseudo-transport velocity approach. In 2D and 3D simulations, domain-decomposition is used for multi-threaded parallelism. PyMPDATA is engineered purely in Python targeting both performance and usability, the latter encompassing research users', developers' and maintainers' perspectives. From researcher's perspective, PyMPDATA offers hassle-free installation on multitude of platforms including Linux, OSX and Windows, and eliminates compilation stage from the perspective of the user. From developers' and maintainers' perspective, PyMPDATA offers a suite of unit tests, multi-platform continuous integration setup, seamless integration with Python development aids including debuggers and profilers. PyMPDATA design features a custom-built multi-dimensional Arakawa-C grid layer allowing to concisely represent multi-dimensional stencil operations on both scalar and vector fields. The grid layer is built on top of NumPy's ndarrays (using "C" ordering) using the Numba's ``@njit`` functionality for high-performance array traversals. It enables one to code once for multiple dimensions, and automatically handles (and hides from the user) any halo-filling logic related with boundary conditions. Numba ``prange()`` functionality is used for implementing multi-threading (it offers analogous functionality to OpenMP parallel loop execution directives). The Numba's deviation from Python semantics rendering [closure variables as compile-time constants](https://numba.pydata.org/numba-doc/dev/reference/pysemantics.html#global-and-closure-variables) is extensively exploited within ``PyMPDATA`` code base enabling the just-in-time compilation to benefit from information on domain extents, algorithm variant used and problem characteristics (e.g., coordinate transformation used, or lack thereof). A separate project called [``PyMPDATA-MPI``](https://github.com/open-atmos/PyMPDATA-MPI) depicts how [``numba-mpi``](https://pypi.org/project/numba-mpi) can be used to enable distributed memory parallelism in PyMPDATA. The [``PyMPDATA-examples``](https://pypi.org/project/PyMPDATA-examples/) package covers a set of examples presented in the form of Jupyer notebooks offering single-click deployment in the cloud using [mybinder.org](https://mybinder.org) or using [colab.research.google.com](https://colab.research.google.com/). The examples reproduce results from several published works on MPDATA and its applications, and provide a validation of the implementation and its performance. ## Dependencies and installation To install PyMPDATA, one may use: ``pip install PyMPDATA`` (or ``pip install git+https://github.com/open-atmos/PyMPDATA.git`` to get updates beyond the latest release). PyMPDATA dep