Solution formulation methods for indirect acoustic analysis (Acoustics BEM)

When you create solutions for indirect acoustic radiation problems using Acoustics BEM, you can choose from three methods:

• Standard Indirect BEM (IBEM)

• H-Matrix for medium-size and medium-/high-frequency problems

• Fast Multipole for large-size and high-frequency problems

Standard IBEM method

The Standard IBEM method is a very efficient method for solving small size (typically 10,000 to 25,000 degrees of freedom) model acoustic problems.

As a general guideline, accurate results typically require at least six boundary elements per wavelength. The size of the model increases exponentially with the frequency. Therefore, an analysis of large-size (typically 100,000 to 1,000,000 degrees of freedom) models with the Standard method is practically limited to low frequency or medium frequency problems.

Medium-size model problems can be solved with the Standard method in a few minutes per frequency and provide full frequency analysis. However, large-size model problems may require several days to solve.

H-Matrix method

The hierarchical matrix method, or H-Matrix, is a recursive matrix storage and compression solution method. The H-Matrix method is very efficient for medium-size (typically 25,000 to 100,000 degrees of freedom) and medium and high-frequency model problems. It efficiently handles large-size boundary element acoustic model problems that are not practical to solve using the Standard method.

This method also allows you to include the convection effect of a uniform mean fluid flow.

Fast Multipole method

The Fast Multipole method efficiently solves large acoustic problems in terms of both speed and memory requirements. The Fast Multipole method allows faster computations and uses less memory to solve large acoustic problems (typically 100,000 to 1,000,000 degrees of freedom) and high-frequency problems. The solver efficiently handles large-size boundary element acoustic model problems that are not practical to solve using the Standard method.

Fast Multipole BEM uses a classical evaluation of the BEM operator in the near field. In the far field, it forms a clustering of boundary elements and evaluates the solution through a multipole expansion and multilevel hierarchical cell sub-structuring. Instead of solving the entire model at one time, the method divides the model into domains, which are then divided again and again. With the Fast multipole method, computation time still grows exponentially, yet at much lower rate compared to the Standard method. The total computation time scales much better with the number of nodes, compared to the Standard method.

This clustering is a function of frequency and switches to the Standard method at low frequencies. The computation becomes more intensive with decreasing frequencies, so the Fast Multipole method is more suitable for medium and high frequency ranges.

This method also allows you to include the convection effect of a uniform mean fluid flow.

Comparison of methods

The graph shows a comparison of the Standard, H-Matrix, and Fast Multipole solution methods relative computation time versus model size.

Comparison of the Standard, H-Matrix and Fast Multipole computation times (vertical axis) relative to model size (horizontal axis).	(1) Standard method(2) H-Matrix method(3) Fast Multipole method(4) Difference in computation time for the H-Matrix method and the Standard method, showing that in general, the H-Matrix method is faster than the Standard method.

Use the summary in the following table to help you decide which method to select.

	Solution methods
Standard	H-Matrix	Fast Multipole
Model type based on frequency	For low-frequency models, for example, full passenger car acoustic scattering up to 1 kHz.	For medium and high-frequency models, for example, full passenger car acoustic scattering up to 3kHz and up to 10kHz respectively.	For high-frequency models, for example, full passenger car acoustic scattering up to 10 kHz.
Model type based on size	For small-size models, such as 10,000 to 25,000 degrees of freedom.	For medium-size models, such as 25,000 to 100,000 degrees of freedom.	For large-size models, such as 100,000 to 1,000,000 degrees of freedom.
Example use cases	Pumps, speakers, and so on	Complete vehicles up to higher frequencies, engines with enclosures, aircraft, ships, submarines, turbines	Exterior acoustics of complete vehicles, large engines, pedestrian warning systems, engines with enclosures, aircraft, ships, submarines, ultra-sonic sensor design

Where do I find it?

Application	Pre/Post
Prerequisites	A Simulation file as the work part and displayed partSimcenter 3D Acoustics BEM as the specified solverIndirect Acoustic as the specified analysis type
Command Finder	Solution
Location in dialog box	Solution dialog box → Indirect Acoustic Model Formulation group → Model Formulation list

Learn more

Using structural results as input to an Acoustics BEM vibro-acoustic solution

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Solution formulation methods for indirect acoustic analysis (Acoustics BEM), Simcenter 3D 2021.1 Series

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