# Functions

## FEM machines

### Acoustics

`FinEtoolsAcoustics.FEMMAcoustModule.acousticmass`

— Method```
acousticmass(self::FEMMAcoust, assembler::A,
geom::NodalField,
Pddot::NodalField{T}) where {T<:Number,
A<:AbstractSysmatAssembler}
```

Compute the acoustic mass matrix.

**Arguments**

`self`

= acoustics model`assembler`

= matrix assembler`geom`

= geometry field`Pddot`

= second order rate of the acoustic (perturbation) pressure field

The acoustic "mass" matrix is by convention called mass, however its mechanical meaning is quite different. (It has to do with potential energy.) It is the matrix $\mathbf{M}_a$ in this matrix ODE system for the acoustic pressure:

\[\mathbf{M}_a \mathbf{\ddot{p}} + \mathbf{K}_a \mathbf{{p}} = \mathbf{{f}}\]

The bilinear-form function `bilform_dot`

is used to compute the matrix.

`FinEtoolsAcoustics.FEMMAcoustModule.acousticstiffness`

— Method`acousticstiffness(self::FEMMAcoust, assembler::A, geom::NodalField, P::NodalField{T}) where {T<:Number, A<:AbstractSysmatAssembler}`

Compute the acoustic "stiffness" matrix.

**Arguments**

`self`

= acoustics model`assembler`

= matrix assembler`geom`

= geometry field`P`

= acoustic (perturbation) pressure field

Return a matrix.

The acoustic "stiffness" matrix is by convention called stiffness, however its mechanical meaning is quite different. (It has to do with kinetic energy.) It is the matrix $\mathbf{K}_a$ in this matrix ODE system for the acoustic pressure:

\[\mathbf{M}_a \mathbf{\ddot{p}} + \mathbf{K}_a \mathbf{{p}} = \mathbf{{f}}\]

The bilinear-form function `bilform_diffusion`

is used to compute the matrix.

`FinEtoolsAcoustics.FEMMAcoustModule.inspectintegpoints`

— Method```
inspectintegpoints(self::FEMMAcoust,
geom::NodalField{GFT},
P::NodalField{T},
temp::NodalField{FT},
felist::VecOrMat{IntT},
inspector::F,
idat,
quantity = :gradient;
context...) where {T <: Number, GFT, FT, IntT, F <: Function}
```

Inspect integration point quantities.

**Arguments**

`geom`

- reference geometry field`P`

- pressure field`temp`

- temperature field (ignored)`felist`

- indexes of the finite elements that are to be inspected: The fes to be included are:`fes[felist]`

.`context`

- struct: see the update!() method of the material.`inspector`

- function with the signature`idat = inspector(idat, j, conn, x, out, loc);`

where`idat`

- a structure or an array that the inspector may use to maintain some state, for instance gradient,`j`

is the element number,`conn`

is the element connectivity,`out`

is the output of the`update!()`

method,`loc`

is the location of the integration point in the*reference*configuration.

**Output**

The updated inspector data is returned.

`FinEtoolsAcoustics.FEMMAcoustSurfModule.acousticABC`

— Method```
acousticABC(self::FEMMAcoustSurf, assembler::A,
geom::NodalField,
Pdot::NodalField{T}) where {T<:Number, A<:AbstractSysmatAssembler}
```

Compute the acoustic ABC (Absorbing Boundary Condition) matrix.

**Arguments**

`self`

= acoustics model`assembler`

= matrix assembler; must be able to assemble unsymmetric matrix`geom`

= geometry field`Pdot`

= rate of the acoustic (perturbation) pressure field

We assume here that the impedance of this boundary is $ho c$.

`FinEtoolsAcoustics.FEMMAcoustSurfModule.acousticcouplingpanels`

— Method`acousticcouplingpanels(self::FEMMAcoustSurf, geom::NodalField, u::NodalField{T}) where {T}`

Compute the acoustic pressure-structure coupling matrix.

The acoustic pressure-nodal force matrix transforms the pressure distributed along the surface to forces acting on the nodes of the finite element model. Its transpose transforms displacements (or velocities, or accelerations) into the normal component of the displacement (or velocity, or acceleration) along the surface.

**Arguments**

`geom`

=geometry field`u`

= displacement field

`n`

= outer normal (pointing into the acoustic medium).- The pressures along the surface are assumed constant (uniform) along each finite element –- panel. The panel pressures are assumed to be given the same numbers as the serial numbers of the finite elements in the set.

`FinEtoolsAcoustics.FEMMAcoustSurfModule.acousticrobin`

— Method```
acousticrobin(
self::FEMMAcoustSurf,
assembler::A,
geom::NodalField,
Pdot::NodalField{T},
impedance
) where {T<:Number,A<:AbstractSysmatAssembler}
```

Compute the acoustic "Robin boundary condition" (damping) matrix.

**Arguments**

`self`

= acoustics model`assembler`

= matrix assembler; must be able to assemble unsymmetric matrix`geom`

= geometry field`Pdot`

= rate of the acoustic (perturbation) pressure field`impedance`

= acoustic impedance of the boundary

We assume here that the impedance of this boundary is $ho c$.

`FinEtoolsAcoustics.FEMMAcoustSurfModule.pressure2resultantforce`

— Method```
pressure2resultantforce(self::FEMMAcoustSurf, assembler::A,
geom::NodalField,
P::NodalField{T},
Force::Field) where {T<:Number, A<:AbstractSysmatAssembler}
```

Compute the rectangular coupling matrix that transcribes given pressure on the surface into the resultant force acting on the surface.

**Arguments**

`self`

= acoustics model`assembler`

= matrix assembler; must be able to assemble unsymmetric matrix`geom`

= geometry field`P`

= acoustic (perturbation) pressure field`Force`

= field for the force resultant

`FinEtoolsAcoustics.FEMMAcoustSurfModule.pressure2resultanttorque`

— Method```
pressure2resultanttorque(self::FEMMAcoustSurf, assembler::A,
geom::NodalField,
P::NodalField{T},
Torque::GeneralField, CG::FFltVec) where {T<:Number, A<:AbstractSysmatAssembler}
```

Compute the rectangular coupling matrix that transcribes given pressure on the surface into the resultant torque acting on the surface with respect to the CG.

**Arguments**

`self`

= acoustics model`assembler`

= matrix assembler; must be able to assemble unsymmetric matrix`geom`

= geometry field`P`

= acoustic (perturbation) pressure field`Torque`

= field for the torque resultant

## Algorithms

### Acoustics

`FinEtoolsAcoustics.AlgoAcoustModule.steadystate`

— Method`steadystate(modeldata::FDataDict)`

Steady-state acoustics solver.

`modeldata`

= dictionary with string keys

`"fens"`

= finite element node set`"regions"`

= array of region dictionaries`"essential_bcs"`

= array of essential boundary condition dictionaries`"ABCs"`

= array of absorbing boundary condition dictionaries`"flux_bcs"`

= array of flux boundary condition dictionaries

For each region (connected piece of the domain made of a particular material), mandatory, the region dictionary contains items:

`"femm"`

= finite element mmodel machine (mandatory);

For essential boundary conditions (optional) each dictionary would hold

`"pressure"`

= fixed (prescribed) pressure (scalar), or a function with signature function T = f(x) If not given, zero pressure assumed.`"node_list"`

= list of nodes on the boundary to which the condition applies (mandatory)

For absorbing boundary conditions (optional) each dictionary may hold

`"femm"`

= finite element mmodel machine (mandatory).

For flux boundary conditions (optional) each dictionary would hold

`"femm"`

= finite element mmodel machine (mandatory);`"normal_flux"`

= normal component of the flux through the boundary (scalar), which is the normal derivative of the pressure.

**Output**

`modeldata`

= the dictionary is augmented with

`"geom"`

= the nodal field that is the geometry`"P"`

= the nodal field that is the computed pressure (in the general a complex-number field)

## Material models

### Material models for acoustics

`FinEtoolsAcoustics.MatAcoustFluidModule.bulkmodulus`

— Method`bulkmodulus(self::MatAcoustFluid)`

Return the bulk modulus.