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Metis package extension for fill-reducing renumbering
This patch adds new DoF renumbering possibilities using "package
extensions" which is available from Julia 1.10. These extensions hook
into the new `DofOrder.Ext{T}` type, where `T` is the external package
module providing the new ordering capability.
Currently only the fill-reducing renumbering algorithm from Metis.jl is
provided, ie.. `DofOrder.Ext{Metis}()`.
Closes #393.- Loading branch information
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,83 @@ | ||
| module MetisExt | ||
|
|
||
| using Ferrite | ||
| using Ferrite: AbstractDofHandler | ||
| using Metis.LibMetis: idx_t | ||
| using Metis: Metis | ||
| using SparseArrays: sparse | ||
|
|
||
| struct MetisOrder <: DofOrder.Ext{Metis} | ||
| coupling::Union{Matrix{Bool},Nothing} | ||
| end | ||
|
|
||
| """ | ||
| DofOrder.Ext{Metis}(; coupling) | ||
| Fill-reducing permutation order from [Metis.jl](https://github.com/JuliaSparse/Metis.jl). | ||
| Since computing the permutation involves constructing the structural couplings between all | ||
| DoFs the field/component coupling can be provided; see [`create_sparsity_pattern`](@ref) for | ||
| details. | ||
| """ | ||
| function DofOrder.Ext{Metis}(; | ||
| coupling::Union{AbstractMatrix{Bool},Nothing}=nothing, | ||
| ) | ||
| return MetisOrder(coupling) | ||
| end | ||
|
|
||
| function Ferrite.compute_renumber_permutation( | ||
| dh::AbstractDofHandler, | ||
| ch::Union{ConstraintHandler,Nothing}, | ||
| order::DofOrder.Ext{Metis} | ||
| ) | ||
|
|
||
| # Expand the coupling matrix to size ndofs_per_cell × ndofs_per_cell | ||
| coupling = order.coupling | ||
| if coupling === nothing | ||
| n = ndofs_per_cell(dh) | ||
| entries_per_cell = n * (n - 1) | ||
| else # coupling !== nothing | ||
| # Set sym = true since Metis.permutation requires a symmetric graph. | ||
| # TODO: Perhaps just symmetrize it: coupling = coupling' .| coupling | ||
| coupling = Ferrite._coupling_to_local_dof_coupling(dh, coupling, #= sym =# true) | ||
| # Compute entries per cell, subtract diagonal elements | ||
| entries_per_cell = | ||
| count(coupling[i, j] for i in axes(coupling, 1), j in axes(coupling, 2) if i != j) | ||
| end | ||
|
|
||
| # Create the CSR (CSC, but pattern is symmetric so equivalent) using | ||
| # Metis.idx_t as the integer type | ||
| L = entries_per_cell * getncells(dh.grid) | ||
| I = Vector{idx_t}(undef, L) | ||
| J = Vector{idx_t}(undef, L) | ||
| idx = 0 | ||
| @inbounds for cc in CellIterator(dh) | ||
| dofs = celldofs(cc) | ||
| for (i, dofi) in pairs(dofs), (j, dofj) in pairs(dofs) | ||
| dofi == dofj && continue # Metis doesn't want the diagonal | ||
| coupling === nothing || coupling[i, j] || continue | ||
| idx += 1 | ||
| I[idx] = dofi | ||
| J[idx] = dofj | ||
| end | ||
| end | ||
| @assert idx == L | ||
| N = ndofs(dh) | ||
| # TODO: Use spzeros! in Julia 1.10. | ||
| S = sparse(I, J, zeros(Float32, length(I)), N, N) | ||
|
|
||
| # Add entries from affine constraints | ||
| if ch !== nothing | ||
| error("TODO: Use constraints.") | ||
| end | ||
|
|
||
| # Construct a Metis.Graph | ||
| G = Metis.Graph(idx_t(N), S.colptr, S.rowval) | ||
|
|
||
| # Compute the permutation | ||
| _, perm = Metis.permutation(G) | ||
|
|
||
| return perm | ||
| end | ||
|
|
||
| end # module MetisExt |
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