Currently, we use an LU factorization for the BBMBBMEquations1D and BBMBBMVariableEquations1D although the matrix is spd, which means we could use a Cholesky decomposition. We did this because ldiv! was not supported for sparse Cholesky factorizations, see the discussion in #108 (comment). For the SvaerdKalischEquations1D we use a sparse Cholesky decomposition, but use \ instead of ldiv!, again, because ldiv! was not implemented for sparse Cholesky decompositions.
Once JuliaSparse/SparseArrays.jl#547 (thanks for the PR @ranocha!) is available, it should be possible to use a sparse Cholesky decomposition together with ldiv! for all equations. This will be with Julia v1.12.
Currently, we use an LU factorization for the
BBMBBMEquations1DandBBMBBMVariableEquations1Dalthough the matrix is spd, which means we could use a Cholesky decomposition. We did this becauseldiv!was not supported for sparse Cholesky factorizations, see the discussion in #108 (comment). For theSvaerdKalischEquations1Dwe use a sparse Cholesky decomposition, but use\instead ofldiv!, again, becauseldiv!was not implemented for sparse Cholesky decompositions.Once JuliaSparse/SparseArrays.jl#547 (thanks for the PR @ranocha!) is available, it should be possible to use a sparse Cholesky decomposition together with
ldiv!for all equations. This will be with Julia v1.12.