iterpdesolver 0.1.0

Iterative PDE solvers for 2D elliptic equations with finite differences

iterpdesolver

Iterative PDE solvers for 2D elliptic equations with finite differences.

A Python library implementing 11 solver algorithms for second-order elliptic PDEs on uniform rectangular grids, including classical iterative methods, Krylov solvers, and multigrid methods.

Originally based on a Bachelor thesis on iterative methods for the discrete Poisson equation (University of Regensburg), now extended to support multiple equation types.

Installation

pip install iterpdesolver

Or install from source:

git clone https://github.com/michaelwallner/iterpdesolver.git
cd iterpdesolver
pip install -e ".[dev]"

Quick Start

import iterpdesolver as pde

result = pde.solve(
    equation=pde.Poisson(source=lambda x, y: -4.0),
    grid=pde.UniformGrid(nx=63, ny=63),
    boundary=pde.DirichletBC(lambda x, y: x**2 + y**2),
    solver="cg",
    tol=1e-6,
)

print(f"Converged in {result.iterations} iterations ({result.time_seconds:.3f}s)")
print(f"Residual: {result.residual_norm:.2e}")

Supported Equations

Equation	Class	PDE
Poisson	pde.Poisson(source)	$-\nabla^2 u = f$
Helmholtz	pde.Helmholtz(source, k)	$-\nabla^2 u + k^2 u = f$
Convection-Diffusion	pde.ConvectionDiffusion(source, diffusion, velocity)	$-D\nabla^2 u + \mathbf{v} \cdot \nabla u = f$
Heat (implicit Euler)	pde.Heat(source, alpha, dt, u_prev)	$u^{n+1}/\Delta t - \alpha \nabla^2 u^{n+1} = u^n/\Delta t + f$

Available Solvers

Solver	Key	Type
Direct (LU)	"direct"	Direct
Jacobi	"jacobi"	Iterative
Jacobi Relaxation	"jacobi_relaxation"	Iterative
Gauss-Seidel	"gauss_seidel"	Iterative
SOR	"sor"	Iterative
Conjugate Gradient	"cg"	Krylov
PCG (ILU)	"pcg_ilu"	Krylov
PCG (MILU)	"pcg_milu"	Krylov
Two-Grid	"two_grid"	Multigrid
V-Cycle	"v_cycle"	Multigrid
W-Cycle	"w_cycle"	Multigrid

SolveResult

Every solver returns a SolveResult with:

• solution — 1D numpy array of interior point values
• iterations — number of iterations (0 for direct solver)
• time_seconds — wall-clock solve time
• residual_norm — final residual norm
• converged — whether tolerance was met
• residual_history — list of residual norms per iteration
• plot(grid=...) — quick matplotlib surface plot

Examples

python examples/basic_poisson.py
python examples/solver_comparison.py
python examples/helmholtz_example.py

Streamlit App

pip install iterpdesolver[app]
streamlit run examples/streamlit_app/app.py

Testing

pip install -e ".[dev]"
pytest tests/ -v

License

MIT