This repository contains the code for reproducing the experiments in the paper Sparse recovery of elliptic solution operators from matrix-vector products, to appear in SISC.
They rely on the (publicly available) custom Julia package CompressingSolvers.jl. The environment
is specified using the files Manifest.toml and Project.toml.
The experiments in Figures 7 and 8 were run using the script fd_poisson.pbs, that calls
julia --threads=24 --project=. ./src/vary_rho_fd_poisson.jl --n $N --d $D --boundary $BOUNDARY --coefficients $COEFFICIENTS --potential $POTENTIAL.
The parameter d is the spatial dimension. n is the number of grid points in each dimension, resulting in a total of n^d grid points.
The parameters boundary, coefficients, potential prescribe the boundary conditions, the conductivity coefficient field, and the zero order,
potential term of the elliptic PDE. The plots in Figure 7 use boundary=periodic, coefficients=constant, and potential=random_mild. Those
in Figure 8 use boundary=periodic, coefficients=periodic_severe, and potential=random_mild.
The experiments in Figure 9 were run using the script fractional_poisson.pbs, which calls
julia --threads=24 --project=. ./src/vary_rho_fractional_poisson.jl --n $N --d $D --s $S.
Here, n and d have the same meaning as before, and s specifies the order of the PDE.
For instance, the Laplace operator corresponds to s=1.
Finally, the results in Figure 11 were run using gridap_poisson.pbs, which calls
julia --threads=24 --project=. ./src/vary_rho_gridap_poisson.jl --model_size $MODEL_SIZE. Here, model_size is an integer between 1 and 3
that specifies the size of the FEM model to be used.