Preconditioner: Identity
The identity preconditioner object allows investigation of multigrid methods without smoothers.
Documentation
LFAToolkit.IdentityPC
— TypeIdentityPC()
Identity preconditioner to investigate multigrid without smoother
Returns:
- identity preconditioner object
Example:
# setup
mesh = Mesh2D(1.0, 1.0);
mass = GalleryOperator("mass", 4, 4, mesh);
# preconditioner
identity = IdentityPC(mass);
# verify
println(identity)
# output
identity preconditioner
LFAToolkit.computesymbols
— Methodcomputesymbols(identity, ω, θ)
Compute or retrieve the symbol matrix for a identity preconditioned operator
Arguments:
identity::IdentityPC
: Identity preconditioner to compute symbol matrix forω::Array
: smoothing weighting factor arrayθ::Array
: Fourier mode frequency array (one frequency per dimension)
Returns:
- symbol matrix for the identity preconditioner (I)
Example:
using LinearAlgebra
# setup
mesh = Mesh2D(1.0, 1.0);
mass = GalleryOperator("mass", 4, 4, mesh);
# preconditioner
identity = IdentityPC(mass);
# compute symbols
A = computesymbols(identity, [], []);
# verify
@assert A ≈ I
# output