kernelpack-python/examples/diffusion_solver_example.py at main · VarShankar/kernelpack-python · GitHub

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"""Advance the same manufactured diffusion problem with FD and PU solvers."""

import numpy as np

from kernelpack import solvers

from _common import build_square_domain, exact_solution, unit_dirichlet, zero_neumann


def run_solver(solver, domain) -> np.ndarray:
    dt = 0.02
    diffusivity = 0.25
    points = domain.get_int_bdry_nodes()
    forcing = lambda nu, time, x: (
        -np.exp(-time) * (x[:, 0] ** 2 + x[:, 1] ** 2)
        - 4.0 * nu * np.exp(-time)
    )
    boundary = lambda alpha, beta, normals, time, xb: exact_solution(time, xb)
    solver.init(domain, 3, dt, diffusivity)
    solver.set_initial_state(exact_solution(0.0, points))
    solver.bdf1_step(dt, forcing, zero_neumann, unit_dirichlet, boundary)
    solver.bdf2_step(2.0 * dt, forcing, zero_neumann, unit_dirichlet, boundary)
    return solver.bdf3_step(3.0 * dt, forcing, zero_neumann, unit_dirichlet, boundary)


def main() -> None:
    domain = build_square_domain()
    points = domain.get_int_bdry_nodes()
    fd_solution = run_solver(
        solvers.DiffusionSolver(
            lap_assembler="fd",
            bc_assembler="fd",
            lap_stencil="wls",
            bc_stencil="wls",
        ),
        domain,
    )
    pu_solution = run_solver(solvers.PUDiffusionSolver(), domain)
    truth = exact_solution(0.06, points)
    print(f"FD relative l2 error: {np.linalg.norm(fd_solution - truth) / np.linalg.norm(truth):.6e}")
    print(f"PU relative l2 error: {np.linalg.norm(pu_solution - truth) / np.linalg.norm(truth):.6e}")


if __name__ == "__main__":
    main()