Standard FEM meshes are globally coupled. CRT decomposes boundary conditions into 6 independent channels. Each channel solves a tiny heat equation (mod 8, 9, 25, 49, 11, 13). No inter-channel sync. CRT reconstruct gives the global temperature field. The ring IS the domain decomposition.
How It Works
CRT Domain Decomposition
A 2D heat equation with boundary condition T_bc in Z/12612600 decomposes into 6 independent heat equations, one per CRT channel. Channel i solves on Z/m_i with boundary T_bc mod m_i. After convergence, CRT reconstruct gives the global solution. Block-diagonal stiffness: 36x fewer entries than coupled. 490 split: DEAD={D,E,b} = temperature data. ALIVE={K,L,G} = solution integrity.
6 solvers
Zero coupling
Each channel converges independently. No global stiffness matrix.
36x fewer ops
Block-diagonal
Coupled: (sum m_i)^2 entries. CRT: sum(m_i^2) entries. Ratio = 36x.
GPU mapping
6 workgroups
Each PDE solver = 1 GPU workgroup. Zero inter-workgroup sync.
L=11 verify
Free check
L channel verifies solution integrity. Corruption = instant flag.
Heat Equation Demo
Boundary temp (0-12612599):
Sets boundary condition on 8x8 grid. Runs 4 diffusion steps per channel. CRT reconstructs center temperature.
Heat Map (Canvas)
6 panels: one per CRT channel. 32x32 grid, 4 diffusion steps. Colors: D(red), K(green), E(blue), b(yellow), L(magenta), G(cyan).
GPU Parallel Solve (WebGPU)
WebGPU not available. Use Chrome 113+ for real GPU PDE solving benchmarks.