Multigrid Configuration

PMultigridConfiguration{TC<:AbstractCoarseningStrategy}

This struct represents the configuration for the polynomial multigrid method.

pmultigrid_config(;coarse_strategy = Galerkin())

This function is the main api to instantiate PMultigridConfiguration.

GMultigridConfiguration{TC}

Configuration for the geometric multigrid method (analogous to PMultigridConfiguration).

gmultigrid_config(; coarse_strategy = Galerkin())

Create a GMultigridConfiguration.

Galerkin <: AbstractCoarseningStrategy

Galerkin coarsening operator can be defined as follows:

\[A_{h,p-1} = \mathcal{I}_{p}^{p-1} A_{h,p} \mathcal{I}_{p-1}^p\]

and according to Tielen et al. [2] $\mathcal{I}_{p-1}^p$ is the interpolation operator from the coarse space to the fine space and is defined as follows:

\[\mathcal{I}_{p-1}^p (\mathbf{v}_{p-1}) = (\mathbf{M}_p)^{-1} \mathbf{P}_{p-1}^p \, \mathbf{v}_{p-1}\]

Rediscretization{TI, TS} <: AbstractCoarseningStrategy

Coarsening strategy that re-assembles the operator on the coarse grid using FerriteOperators.

Fields

• integrator::TI – an AbstractBilinearIntegrator (e.g. DiffusionMultigrid)
• strategy::TS – an AbstractAssemblyStrategy (default: SequentialAssemblyStrategy(SequentialCPUDevice()))
• is_sym::Bool – whether the operator is symmetric (determines R = Pᵀ vs separate assembly)