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JuliaApproximation / CompactBases.jl

Julia library for function approximation with compact basis functions
MIT License
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Alternate BandedMatrix/BandedBlockBandedMatrix storage for FE-DVR operators #25

Open jagot opened 3 years ago

jagot commented 3 years ago

b = A*x is not particularly fast for A isa BlockSkylineMatrix, at least not for the block sizes that commonly arise in FE-DVR. Maybe representing A as a BandedMatrix (thus explicitly storing structural zeros) could improve arithmetic performance due to cache-friendliness? When we get to distributed computing, we could similarly use a BandedBlockBandedMatrix, where each node essentially has a banded matrix with some number of finite elements stored in it, and the only communication between nodes would be the bridge function between two finite elements, i.e. a single scalar. I assume an incomplete factorization could be formed by factorizing each banded matrix, and this could be used as e.g. a preconditioner.

dlfivefifty commented 3 years ago

You could even wrap the banded matrix in a PseudoBlockArray to preserve the block structure