Comparison of Algebraic Multigrid Preconditioners for Solving Helmholtz Equations

Algorithm 1

SA_setup (𝑛_ℓ,𝐴_ℓ,ℓ).

(1) 𝑡_ℓ=𝑆^𝜈1_ℓ(ones(𝑛,1),0)

(2) While ℓ≤𝐿

(3) [neighbour, hoods] = aggregate (𝑛_ℓ,𝐴_ℓ);

(4) [𝑃,𝑡_ℓ+1] = qr(𝑛_ℓ,𝑡_ℓ,hoods);

(5) 𝑆_ℓ= smoother (𝑛_ℓ,𝐴_ℓ,𝜔,neighbour);

(6) 𝐼^ℓ_ℓ+1=𝑆_ℓ𝑃;

(7) 𝐴_ℓ+1=(𝐼^ℓ_ℓ+1)^𝑇𝐴_ℓ𝐼^ℓ_ℓ+1;

(8) ℓ=ℓ+1;

(9) Endwhile