# Manual

## FEM machines

### Acoustics: volume

FinEtoolsAcoustics.FEMMAcoustModule.acousticstiffnessFunction
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:

$$$\mathbf{M}_a \mathbf{\ddot{p}} + \mathbf{K}_a \mathbf{{p}} = \mathbf{{f}}$$$
Note

The bilinear-form function bilform_diffusion from FinEtools.FEMMBaseModule is used to compute the matrix.

acousticstiffness(self::FEMMAcoustNICE, assembler::A, geom::NodalField, P::NodalField{T}) where {T<:Number, A<:AbstractSysmatAssembler}

Compute the acoustic mass matrix.

Arguments

• self = acoustics model
• assembler = matrix assembler
• geom = geometry field
• P = acoustic (perturbation) pressure field

Return a matrix.

FinEtoolsAcoustics.FEMMAcoustModule.acousticmassFunction
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:

$$$\mathbf{M}_a \mathbf{\ddot{p}} + \mathbf{K}_a \mathbf{{p}} = \mathbf{{f}}$$$
Note

The bilinear-form function bilform_dot from FinEtools.FEMMBaseModule is used to compute the matrix.

FinEtoolsAcoustics.FEMMAcoustModule.inspectintegpointsFunction
inspectintegpoints(self::FEMMAcoust,
geom::NodalField{GFT},
P::NodalField{T},
temp::NodalField{FT},
felist::VecOrMat{IntT},
inspector::F,
idat,
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.

### Acoustics: surface

FinEtoolsAcoustics.FEMMAcoustSurfModule.acousticABCFunction
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.acousticrobinFunction
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.pressure2resultantforceFunction
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.pressure2resultanttorqueFunction
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
FinEtoolsAcoustics.FEMMAcoustSurfModule.acousticcouplingpanelsFunction
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
Note
• 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.

## Algorithms

### Acoustics

FinEtoolsAcoustics.AlgoAcoustModule.steadystateFunction
steadystate(modeldata::FDataDict)

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)