Integrators

SimpleIntegrator(fun::Function, val; domains=nothing)

Calculate the integrals

\[\int_\Omega f(u, \nabla u, s)\, \mathrm{d}\Omega \int_\Gamma f(u, \nabla u, n)\, \mathrm{d}\Gamma \]

for cell and facet domains respectively. For single-field problems, u is the current function value, ∇u the current function gradient. For multi-field problem, u and ∇u are NamedTuples, where the keys in u and ∇u are the fieldnames.

For cell domains, qp_state the current state in the current quadrature point. This assumes that cell_state::AbstractVector, otherwise, qp_state = cell_state. For facet domains, n is the facet normal vector.

It is the user's responsibility that fun(args...)::typeof(val). Additionally, the type of val must support

• val + val
• val * x (where x::Real)
• zero(val)

One exception to these requirements; val::Tuple, if the elements of the tuple fulfills those requirements.

Specify domains to only integrate over a part of the grid. It should contain a subset of the keys provided to setup_domainbuffers. Single, String, or collections; Set{String}, AbstractVector{String}, or NTuple{N,String} inputs are supported. If domains=nothing, all domains are integrated.

Example: Calculate the average value and gradient
We assume that we have done the setup: buffer = setup_domainbuffer(...),
assembled K and r, and solved a=K\r

integrator = SimpleIntegrator((u, ∇u, state)->(1.0, u, ∇u), (0.0, 0.0, zero(Vec{dim})))
work!(integrator, buffer; a=a)
area = integrator.val[1]
u_avg = integrator.val[2]/area 
∇u_avg = integrator.val[3]/area

If the buffer is setup to be threaded, this calculation will also be threaded.

Integrator(val::V; domains=nothing)

Integrate over the domain by modifying the value val for each cell in the function integrate_cell, which should be overloaded for the specific combination of val::V and the material for that cell. V must be a mutable type.

Specify domains to only integrate over a part of the grid. It should contain the names of the domains to integrate over. Single, String, or collections; Set{String}, AbstractVector{String}, or NTuple{N,String} inputs are supported. If domains=nothing, all domains are integrated.

Note: This integrator will currently only run sequentially even if a threaded assembly is setup with setup_domainbuffer

integrate_cell!(val, cell_state, ae, material, cv, cellbuffer)

Function to be overloaded for val (potentially in combination with material), and will be called when using Integrator. Mutate val to add to the result.

The order of the inputs is chosen to follow the element routines

integrate_facet!(val, ae, material, fv, facetbuffer)

Function to be overloaded for val (potentially in combination with material), and will be called when using Integrator. Mutate val to add to the result.

The order of the inputs is chosen to follow the element routines