parivp: Parallel IVP in Python using multiprocessing

This module allows for parallel integration of initial value problems (IVP) using Python's multiprocessing features. Syntax follows those of scipy.integrate.solve_ivp(), hence enabling parallelization with minimal changes.

See here for scipy's documentation on solve_ivp().

Dependencies

• multiprocessing, numpy, scipy

Basic usage

When solving a single IVP, solve_ivp() takes in as basic arguments the ODE function, the time-span, the initial condition, and optionally additional arguments passed to the ODE function.

The parallelized version of this function, parivp.parsolve_ivp(), takes in as arguments lists of these basic arguments.

Example

We start by importing relevant modules (matplotlib is for plotting the results later), and defining the ODE; here, we are using the restricyed twobody problem:

import numpy as np
import matplotlib.pyplot as plt  # optional, for plotting results later
from parivp import parsolve_ivp

def twobody(t,state,mu):
    """Two-body equation of motion"""
    dstate = np.zeros(6,)
    dstate[0:3] = state[3:6]
    dstate[3:6] = -mu/np.linalg.norm(state[0:3])**3 * state[0:3]
    return dstate

We now prepare lists of the time-span, initial conditions, and additional arguments; in this case, we are only varying the initial conditition, and we keep the time-spans and arguments the same.

# number of integrations to perform
n = 50

# create list of final times
t0 = 0.0
tf = 10.0
t_spans = [(t0,tf) for el in range(n)]

# create list of initial conditions
ics = []
state0 = np.array([1.0, 0.0, 0.2, 0.0, 1.0, -0.02])
sigR, sigV = 0.02, 0.01
for idx in range(n):
    ics.append(state0 + np.concatenate((sigR*np.random.rand(3),sigV*np.random.rand(3))))

# create list of argument to EOM
ps = [(1.0,) for el in range(n)]

We can now call the parallel integrator function

# integrate in parallel
n_cpu = 4
t_eval = np.linspace(t0,tf,1000)
respar = parsolve_ivp(fun=twobody, t_spans=t_spans, ics=ics, ps=ps, n_cpu=n_cpu, t_eval=t_eval)

We can visualize the results

# plot result
fig = plt.figure(figsize=(6,6))
ax = fig.add_subplot()
for sol in respar:
    ax.plot(sol.y[0,:], sol.y[1,:], linewidth=0.5)
ax.axis('equal')
ax.set(xlabel="x", ylabel="y")
plt.show()

More Examples

For examples, see scripts in ./tests.