Finite Element Method Adaptive Order (FEMAO) solutions

The Finite Element Method Adaptive Order (FEMAO) method is a higher-order polynomial technique that provides more accurate and faster solutions for acoustic and vibro-acoustic analyses than previous methods.

You can use the FEMAO method for one-way coupling vibro-acoustic analysis, two-way coupling vibro-acoustic analysis, and uncoupled acoustic analysis.

The FEMAO method is supported in SOL 108 Direct Frequency Response and SOL 111 Modal Frequency Response. You can use the FEMAO method for prediction of acoustic transfer functions for pass-by noise, prediction of engine intake noise for aero-engine, perfection of transmission loss for an industrial muffler, and so on.

Benefits of FEMAO over standard FEM

• Improved accuracy. FEMAO adjusts the element order (shape functions) automatically, which provides greater accuracy. In standard FEM, you typically use a single mesh for the full frequency range of the analysis, which results in an over-discretized model at lower frequencies and therefore higher solve times. At higher frequencies, the standard FEM model becomes under-discretized and less accurate. It may even miss the targeted accuracy because no automatic correction is in place.FEMAO automatically adapts the order, and the model is represented each time with the correct number of degrees of freedom to reach the desired accuracy.

• Improved performance through adaptability. The order adaptation for each frequency ensures optimal model size and, consequently, optimal solving time for each frequency. This yields much faster computation times compared with the fixed number of degrees of freedom approach that standard FEM uses.

• Improved performance through shape function efficiency. The higher-order shape function basis is more efficient in capturing the acoustic pressure field within each element compared to a standard first-order or second-order elements-based FEM approach.For example, if you fill a volume with large elements using higher-order shape functions, which results in more degrees of freedom and shape functions in a single element, and then fill the same volume with small elements using first-order or second-order shape functions (as in standard FEM), the total number of degrees of freedom to reach the same accuracy is higher for the standard FEM than for the FEMAO method. Thus, FEMAO becomes more efficient as the frequency increases.

• Improved performance in pre-processing. FEMAO allows you to use large elements in the acoustic domain. This results in a lean FEMAO model that contains fewer elements than an equivalent standard FEM model. This also means that the model can be meshed faster in Pre/Post, and a model with fewer elements has better graphics performance.

Following are examples of standard FEM and FEMAO meshes.

FEM mesh	FEMAO mesh	FEMAO mesh with local refinement

Acoustic shape functions

When solutions use the FEMAO method, the computational effort adapts to the complexity of the problem. The FEMAO method uses higher-order interpolation (acoustic shape functions for orders 4 through 10) at high frequencies and/or for large elements (mesh contains around 4 elements per wavelength), and use lower-order interpolation (acoustic shape functions for orders 1 through 3) at low frequencies (20 Hz to 200 Hz) and/or for small elements (mesh contains around 8 to 20 elements per wavelength). The large elements use a quadratic interpolation, and small elements use a linear interpolation.

The shape functions used in an element can go up to polynomial order 10. At order 1, an element using linear shape functions can span only 1/6 to 1/8 of a wavelength; you need at least 6 to 8 elements per wavelength. In FEMAO, when using higher-order shape functions up to order 10, an element can span more than 2 acoustic wavelengths, and therefore, the same mesh can be used to compute frequencies more than 10 times higher than in standard FEM. Therefore, you can use coarser meshes to solve high-frequency problems without compromising accuracy.

To ensure accuracy, the FEMAO solution method chooses the optimal order of shape functions per element. The order adaptation is based on the following parameters:

• Mesh size (element size)Pre/Post local mesh size. You can create smaller elements to capture accurately the geometric boundaries of the acoustic domain (for example, engine and engine surface), or where local variations of the fluid properties exist.Solver adaptivity. The FEMAO solver chooses the order per element automatically, taking into account the element size.

• FrequencyPre/Post element frequency accuracy. You should ensure that the maximum frequency of interest can be represented by the mesh. The solver will return the maximum frequency as a quality result.Solver adaptivity. Automatically lowers element order (low number of degrees of freedom per element) at low frequencies, and increases element order (higher number of degrees of freedom per element) at high frequencies.

• Local speed of soundPre/Post acoustic fluid. You can define the speed of sound when defining a Fluid type of material in the Material dialog box (corresponds to the Simcenter Nastran material bulk entries (MAT10, MAT10C, and MATF10C).Solver speed of sound. FEMAO automatically incorporates of the speed of sound per element to determine the element order (shape functions).

• Adaptation rulePre/Post settings. You can define the adaptation rule by editing the solution and selecting Enable Adaptive Order for Acoustic Elements. Then, you set the Adaptation Rule (ACADAPT) to Coarse, Standard, or Fine.Solver settings. A finer adaptation rule results in more higher-order elements being used at lower frequencies compared to a coarse adaption rule for the same mesh.

• Polynomial orderPre/Post settings. You can control the lowest and highest allowed polynomial order by editing the solution and selecting Enable Adaptive Order for Acoustic Elements. Then, you set the Order Limit (ACORDER) to Minimum, Maximum, or Minimum and Maximum, or use the Default.Note: The default value for the minimum order number is 2 instead of 1 for the following reasons:Some acoustic analyses require a pressure gradient (spatial derivative of the pressure) next to pressure computation. On the surface of a first-order element mesh, where the mesh represents a set of combined elements, only the computed pressure field is continuous. The pressure gradient field, which is associated with acoustic particle velocity, is piecewise constant with abrupt changes between the element faces. However, for a surface with free second-order element faces, the pressure gradient is continuous. Thus, the use of second-order element faces results in increased computational accuracy.Incident acoustic pressure from, for example, acoustic monopole sources outside of the FEM domain, is also more accurately captured with second-order elements.You can override the software default value with a number from 1 through 10.Solver settings. High-order polynomials result in higher computed frequencies compared to low-order polynomials for the same mesh.

Order adaptivity

The following image shows a 3D example of FEMAO order adaptivity on the elements of a mesh at a low and high frequency.

In this example, the FEMAO method uses orders 1, 2, and 3 at a low frequency, and orders 8, 9, and 10 at a high frequency.

FEMAO order adaptivity on elements of a mesh at a low frequency (100 Hz)	FEMAO order adaptivity on elements of a mesh at a high frequency (2200 Hz)

The following image shows a 2D example of frequency dependency of the element order adaptivity on a mesh at a low and high frequency.

In this example, the FEMAO method used orders 1 through 3 at a low frequency, and orders 3 through 10 at a high frequency.

Frequency dependency of element order adaptivity on a mesh at a low frequency (100 Hz)	Frequency dependency of element order adaptivity on a mesh at a high frequency (1000 Hz)

Quality checks for FEMAO solution

You can validate the FEMAO mesh quality before you proceed with the computation-intensive part of the solution. When you submit an acoustic or vibro-acoustic solution with the Solve Model Quality Results in the Solve dialog box, the software:

1. Outputs the maximum valid frequency and element order information.

2. Exits the solution before the computation-intensive frequency response computation.

A typical application is to:

1. Submit a FEMAO solution that contains a model with acoustic fluid elements with the Solve Model Quality Results option.

2. Wait until the following message appears in the Solution Monitor:^^^  *** CHECK MODE DETECTED *** ^^^ ENCOUNTERED USER REQUEST ACORDCHK= STOP ^^^ SOLUTION WILL BE TERMINATED NOW

3. Use the acoustics post-processing scenario Quality Metrics to assess the maximum frequency and element order information that is stored in the partial result file.

4. If you do not need to adjust the FEMAO options, proceed to the next step.Adjust the FEMAO options in the FEM Adaptive Order - FEMAO group in the Bulk Data page in the Solution dialog box to affect the maximum frequency and element order information and proceed to step 1.

5. Submit the solution for a final solve.Note: For a vibro-acoustic solution using FEMAO and distributed memory parallel (DMP) processing, there may not be enough memory assigned to Simcenter Nastran by default. This can result in an error, and an incorrect error message that does not indicate memory shortage. A workaround may be to increase the memory using the memorydefault keyword. You can set this additional keyword in the nastran Command Keywords group in the Solver Parameters dialog box.For information on memorydefault, see Managing Memory in the Simcenter Nastran Installation and Operations Guide.

Note:

In a FEMAO vibro-acoustic solution, when you request a debug file with coupling information, regardless of Solve Model Quality Results, the software still writes the coupling quality information to the OP2 file before exiting the solution. You can request the coupling information by setting Coupling Information (SKINOUT) to STOP in the Fluid-Structure Interaction Control Parameters modeling object.

Summary of feature support

	Simcenter 3D FEM and FEMAO
Feature	Standard FEM SOL 108 and SOL 111	FEMAO SOL 108	FEMAO SOL 111
Monopole (ACSCRE)	Available	*	*
Monopole (ACPOLE1)	Available	Available	Available
Dipole (ACPOLE2)	Available	Available	Available
Acoustic Plane Wave	Available	Available	Available
Panel Normal Velocity	Available	Available	Available
Damping and Stiffness Absorber	Available	*	*
Admittance / Impedance Absorber	Available	Available	Available
Transfer Admittance	Available	Available	Available
Gluing	Available	*	*
Acoustic Continuity		Available	Available
Enforced Pressure	Available	*	*
Enforced Acoustic Pressure	Available	Available	Available
ATV	Available
FRF Set	Available
Mode Set	Available
VATV		Available	Available
Surface Dipole		Available	Available
Fan Noise		Available	Available
Duct Modes		Available
Anechoic End Duct Property		Available
Gridcon	Available
Pancon / Modcon	Available	Available	Available
Overall Fluid Damping (GFL)	Available	Available	Available
Pyramid transition elements	Available	Available	Available
Constrained elements at fluid-structure coupling surface	Available	Available
Output maximum valid frequency and element order information		Available (also during VATV computation)	Available (also during VATV computation)
Coupling information	Available (only in vibro-acoustic)	Available (only in vibro-acoustic)	Available (only in vibro-acoustic)
* Replaced by new functionality.

Vibro-acoustic output requests

Available outputs with fluid-structure coupling are:

• Pressure, velocity, intensity, acoustic power, transmission loss.

• Panel Contribution, Modal Contribution, and Grid Contribution as listed in the table.

Vibro-acoustic output requests computed by standard FEM and FEMAO
				Panel Contribution	Modal Contribution	Grid Contribution
Solution	Method	Representation	Fluid-structure Interaction	Pressure	Power	Pressure	Power	Pressure
SOL 108	Standard	FEM	Strong	Yes	Yes	*	*	Yes
SOL 108	Standard	FEM	Weak	Yes	Yes	*	*	Yes
SOL 108	Standard	ATV	Weak	Yes	Yes	*	*	Yes
SOL 108	Standard	VATV	Strong	Yes		*	*	Yes
SOL 108	FEMAO	FEM	Strong			*	*
SOL 108	FEMAO	FEM	Weak	Yes	Yes	*	*
SOL 111	Standard	FEM	Strong	Yes	Yes	Yes	Yes	Yes
SOL 111	Standard	FEM	Weak	Yes	Yes	Yes	Yes	Yes
SOL 111	Standard	ATV	Weak	Yes	Yes	Yes	Yes	Yes
SOL 111	FEMAO	FEM	Strong	Yes	Yes	Yes	Yes
SOL 111	FEMAO	FEM	Weak	Yes	Yes	Yes	Yes
* SOL 108 does not use mode shapes to compute a response. It computes structural response at discrete excitation frequencies by solving a set of coupled matrix equations using complex algebra. Thus, SOL 108 cannot compute any modal contributions.

Where do I find it?

Application	Pre/Post
Prerequisites	A simulation file as the work part and displayed partSimcenter Nastran as the specified solverAcoustic or Vibro-Acoustic as the specified analysis typeOne of the following as the specified solution type:SOL 108 Direct Frequency ResponseSOL 108 Direct Frequency Response FunctionsSOL 111 Modal Frequency Response****SOL 111 Modal Frequency Response Functions
Simulation Navigator	Right-click an active acoustic or vibro-acoustic solution → Edit
Location in dialog box	Solution dialog box→Bulk Data page→FEM Adaptive Order - FEMAO group

Learn more

Solution stabilization options

FEMAO convected flow workflow

Steady state fluid velocity in an acoustic solution workflow

Using viscoelastic materials in FEMAO solutions

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Finite Element Method Adaptive Order (FEMAO) solutions, Simcenter 3D 2021.1 Series

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