API Reference: PDE

The Python surface exposes PDE solvers at top level (from pysicrs import ...). See also Algorithms: PDE Solvers.

import pysicrs

Quantum

schrodinger_split_step_1d

schrodinger_split_step_1d(psi0_real, psi0_imag, v, dx, dt, n_steps,
                          mass=1.0, hbar=1.0)
    -> (real: list[float], imag: list[float])

Split-step Fourier time evolution of the 1D TDSE. psi0_real, psi0_imag, v are equal-length arrays on the spatial grid.

schrodinger_eigen_1d

schrodinger_eigen_1d(v, dx, n_states, mass=1.0, hbar=1.0)
    -> (energies: list[float], states: list[list[float]])

Imaginary-time propagation to bound-state energies/eigenstates.

dirac_split_step_1d

dirac_split_step_1d(psi0_real, psi0_imag, v, dx, dt, n_steps,
                    c_speed=1.0, mass=1.0, hbar=1.0)
    -> (real: list[float], imag: list[float])

Split-step Fourier 1D Dirac equation with scalar potential.

Parabolic / hyperbolic / elliptic

heat_crank_nicolson_1d / heat_crank_nicolson_2d

heat_crank_nicolson_1d(u0, dx, dt, alpha, n_steps) -> list[float]
heat_crank_nicolson_2d(u0, nx, ny, dx, dy, dt, alpha, n_steps) -> list[list[float]]

A-stable Crank–Nicolson (1D) / ADI (2D).

wave_fdtd_1d / wave_fdtd_2d

wave_fdtd_1d(u0, v0, dx, dt, v, n_steps) -> list[float]
wave_fdtd_2d(u0, v0, nx, ny, dx, dy, dt, v, n_steps) -> list[list[float]]

Leapfrog FDTD. Respect the CFL ratio \(\frac{v\Delta t}{\Delta x} \le 1\).

poisson_fft_2d

poisson_fft_2d(f, nx, ny) -> list[list[float]]

Spectral (FFT) Poisson solve on a periodic \(nx\times ny\) grid.

Rust-only (not yet bound)

function	purpose
poisson_sor_2d	SOR Poisson solve
maxwell_step_3d / maxwell_max_dt	3D Yee-grid FDTD