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OptiXDE OptiXDE is a fast optical-inspired solver for differential equations.

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One-line pitch¶

A matrix-free spectral propagation-operator approach (FFT → propagate → iFFT) for rapid PDE solves on uniform grids, with support for embedded domains and penalty-based boundary handling.

Tip: Keep this page “light” and visual—put deeper explanations into the Method/Benchmarks pages.

Highlights¶

Matrix-free: no stiffness-matrix assembly; GPU-friendly building blocks.
Fast: FFT-based operators with typical complexity O(N log N).
Unified: diffusion / Poisson / wave share a consistent operator view.
Embedded geometry: work with irregular domains via mask + penalty.
Reproducible: clean benchmarks, fixed seeds, and documented configs.

The big picture¶

pipeline

A minimal diffusion solving using 20 Lines¶

import numpy as np
import matplotlib.pyplot as plt
from optixde.solvers.base.diffusion import diffusion2d_solve
Lx=Ly=np.pi
N=128
D=1.0
dt=0.5 
T=2.0
steps=int(round(T/dt))
dx=Lx/(N+1)
dy=Ly/(N+1)
x=np.linspace(dx,Lx-dx,N)
y=np.linspace(dy,Ly-dy,N)
X,Y=np.meshgrid(x,y,indexing="xy")
u=np.zeros((N+2,N+2))
u[1:-1,1:-1]=10*np.sin(X)*np.sin(Y)
for _ in range(steps): u = diffusion2d_solve(u, D, Lx, Ly, dt, bc="dirichlet")
plt.imshow(u, cmap="jet", origin="lower", extent=[0,Lx,0,Ly])
plt.colorbar()
plt.show()

Results snapshot¶

Add a few representative figures: - error vs resolution - runtime vs resolution - a complex geometry demo (L-shape, hole, union/intersection)

Create these images from your private repo results and copy only the exported figures into docs/assets/figures/.