fastfd's Introduction

FastFD

A finite differences simulation library.

This package lets you quickly build simple numerical simulations.

Features

Quickly build finite difference simulations with an arbitrary number of domains, scalars, dimensions and boundary conditions.
Concise, clear syntax.
Build models for CPU or GPU using Scipy or Cupy sparse libraries.
Arbitrary derivative order and approximation accuracy.
Partial model updates minimize overheads in iterative solutions.
Implicit transient simulation.

Installation

pip install fastfd

Usage

# Import fastfd and select the scipy sparse library (or cupy for GPU support)
import fastfd as ffd
ffd.sparse_lib('scipy')

import numpy as np

# Define axes
x = ffd.LinearAxis('x', start = 0, stop = 1, num = 201)
y = ffd.LinearAxis('y', start = 0, stop = 1, num = 201)

# Define scalars
T = ffd.Scalar('T', [x, y], accuracy = 4)

# Define the model
model = ffd.FDModel([T])

# Set model governing equations (thermal diffusion)
model.update_equations({
    'Conductivity': ((T.d('x', 2) + T.d('y', 2)), 0),
})

# Set model boundary conditions
model.update_bocos({
    'Tx=1 adiabatic': (T.i[-1, :], T.d('x')[-1, :], 0),
    'Ty=1 adiabatic': (T.i[:, -1], T.d('y')[:, -1], 0),
    'Tx=0 sinewave': (T.i[0, :], T.i[0, :], 100 * np.sin(x.coords * 2*np.pi)),
    'Ty=0 sinewave': (T.i[:, 0], T.i[:, 0], -100 * np.sin(y.coords * 2*np.pi)),
})

# Solve the model
result = model.solve()

GPU

FastFD can be set to use the Cupyx sparse libraries, though support is still a little rough around the edges. The current version of Cupy (8.5) only supports a least squares solver ('lsqr') which is much slower than the default 'spsolve'. However, spsolve will be implemented in the upcoming release of Cupy 9.0.