gbmsc-pde 0.1.0

PDE solvers using the Grid-Based Multinode Shepard Collocation method.

gbmsc-pde

gbmsc-pde is a Python package for solving linear PDEs on two-dimensional rectangular domains with the Grid-Based Multinode Shepard Collocation Method (GBMSC).

Version: 0.1.0

Method

GBMSC uses a structured source grid, samples local multinode tensor-product subgrids, builds local Lagrange interpolants on those subgrids, and blends the local interpolants with Shepard weights. PDE equations are enforced by collocation at source nodes, with sparse differential operators assembled from the blended approximation.

Features

• Structured 2D source-grid generation.
• Local multinode Lagrange interpolation on sliding subgrids.
• Shepard blending of local approximants.
• Sparse first- and second-derivative operators.
• Linear PDE assembly with diffusion, convection, reaction, and source terms.
• Dirichlet, Neumann, and Robin boundary-condition helpers.
• Direct, CG, and GMRES sparse linear solvers.
• Exact-nodal interpolation mode for source-node reconstruction.

Installation

Install from a local checkout:

pip install .

For development:

pip install -e ".[dev]"

For documentation tooling:

pip install -e ".[docs]"

For plotting support:

pip install ".[plot]"

Quick Start

import numpy as np

from gbmsc_pde import (
    BoundaryConditions,
    GBMSCApproximation,
    LinearPDE,
    LinearSolver,
    SourceGrid,
)

grid = SourceGrid(grid_shape=(21, 21), subgrid_shape=(5, 5))
approximation = GBMSCApproximation(grid, step=(4, 4), support_mode="nodal_limit")

pde = LinearPDE(approximation)
pde.add_diffusion_term(-1.0)
pde.add_source_term(lambda x, y: np.ones_like(x))

bcs = BoundaryConditions(grid)
bcs.add_dirichlet(grid.boundary_indices()["all"], 0.0)

u = LinearSolver(pde, bcs).solve()
solution_grid = u.reshape(grid.grid_shape)

grid.plot(solution_grid, view="2d")

The step must align with the local subgrid size:

N_x = step_x * k_x + n_x
N_y = step_y * k_y + n_y

for integer k_x and k_y.

Public API

Preferred names:

from gbmsc_pde import (
    SourceGrid,
    GBMSCApproximation,
    BoundaryConditions,
    LinearPDE,
    LinearSolver,
)

New code should use these names consistently: SourceGrid, GBMSCApproximation, BoundaryConditions, LinearPDE, and LinearSolver.

Project Layout

src/
  gbmsc_pde/
    approximation/   GBMSC approximation and interpolation routines
    boundary/        Boundary-condition containers and appliers
    source_grid/     Structured source-grid utilities
    operators/       Sparse differential-operator builders
    pde/             Linear PDE terms and assembly
    solvers/         Linear solvers

Development

Run tests:

pytest

Run lightweight lint checks:

ruff check src tests examples/gbmsc_pde/*.py

Build source and wheel distributions:

python -m build

Check package metadata before uploading:

twine check dist/*

Build the documentation site:

mkdocs build

See CONTRIBUTING.md for the full release checklist.

Contribution Policy

This project is currently not accepting external contributions. Issues and pull requests may be used by the maintainer for project tracking, but there is no expectation that external contributions will be reviewed or merged.

Versioning

This project uses semantic versioning. The first public release is 0.1.0.

Citation

If this package supports academic work, please cite it using the metadata in CITATION.cff. If you also use the underlying numerical method, cite the method preprint as described in the documentation citation page.

License

Distributed under the Apache License 2.0. See LICENSE.