Taiga.FastDiagonalization(model::PotentialFlow{Dim, T}; method::Type{<:DataApproximationMethod} = Wachspress, kwargs)

Potential flow fast diagonalization preconditioner.

LinearOperator{Dim, T, B <: KroneckerProduct{T}, M <: AbstractMatrix{T}, V <: AbstractVector{T}}

Linear operator for PotentialFlow model.

Fields:

• C::B: Kronecker product extraction operator
• K::M: sparse stiffness matrix
• b::V: forcing vector
• cache₁::Vector{T}: mul! cache
• cache₂::Vector{T}: mul! cache

PotentialFlow{Dim, T, M <: GeometricMapping{Dim}, V <: ScalarSplineSpace{Dim, T}, W <: Field{Dim}}

Galerkin formulation of potential flow. The solution field can be either velocity potential or stream function.

Fields:

• F::M: geometric mapping
• S::V: constrained solution space
• Δ::Partition{Dim, T}: partition
• uʰ::W: solution field
• ūʰ::W: function satisfying Dirichlet boundary conditions
• t::Function: traction vector

Pressure{Dim, T1, T2 <: Velocity{Dim}}

Pressure mapping for uniform far field flow.

Fields:

• ρ::T1: density
• p::T1: far field pressure
• U::T1: far field velocity magnitude
• velocity::T2: velocity field

PullbackBody{Dim, T <: GeometricMapping{Dim}}

Pullback of bilinear form.

Fields:

• mapping::T: geometric mapping

PullbackBoundary{Dim, T <: GeometricMapping{Dim}}

Pullback of linear form.

Fields:

• mapping::T: geometric mapping
• traction::Function: traction vector
• side::Int: side restriction (side <= 2Dim)

Velocity{Dim, T1 <: GeometricMapping{Dim}, T2 <: Field{Dim}}

Velocity mapping.

Fields:

• mapping::T1: geometric mapping
• potential::T2: potential field

assemble_body(acc::ElementAccessor{Dim}, partition::Partition{Dim}, pullback::PullbackBody{Dim})

Assemble unconstrained stiffness matrix.

Arguments:

• acc: element accessor
• partition: partition
• pullback: bilinear form pullback

assemble_boundary(acc::ElementAccessor{Dim}, partition::Partition{Dim, T}, pullbacks_boundary::NTuple{N, PullbackBoundary{M}})

Assemble right hand side vector.

Arguments:

• acc: element accessor
• partition: partition
• pullbacks_boundary: tuple of 2Dim linear form pullbacks restricted to each boundary

Taiga.apply_particular_solution(L::LinearOperator, model::PotentialFlow, x₀::V)

Return particular solution.

Arguments:

• L: linear operator
• model: model
• x₀: homogeneous solution

Taiga.forcing!(b::AbstractVector, L::LinearOperator, model::PotentialFlow)

Update forcing vector.

Arguments:

• b: cache vector
• L: linear operator
• model: model

Taiga.forcing(L::LinearOperator, model::PotentialFlow)

Return forcing vector.

Taiga.linear_operator(model::PotentialFlow)

Construct linear operator.