Cartesian 3D PDE operators factor exactly into 1D line kernels via Kronecker algebra, yielding O(N) cost and O(Nx+Ny+Nz) storage for any fixed stencil or polynomial degree.
The 2DECOMP&FFT library: an update with new CPU/GPU capabilities
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No 3D Matrices: A Unified Tensor-Product View of Matrix-Free Cartesian PDE Solvers
Cartesian 3D PDE operators factor exactly into 1D line kernels via Kronecker algebra, yielding O(N) cost and O(Nx+Ny+Nz) storage for any fixed stencil or polynomial degree.