Computational limits to solving ultrasound wave scattering in Elmer

Numerical methods and mathematical models of Elmer
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francisco_b
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Computational limits to solving ultrasound wave scattering in Elmer

Post by francisco_b »

Hello,

I'm trying to solve ultrasound wave scattering in parametric CAD models using a FEM pipeline and HPC. I'm not proficient in acoustics or FEM but I am trying to learn what I need to solve the problem as I go.

To learn how to use Elmer effectively for my problem, I've been running simulations based on what I read from Elmer documentation, Crocoducks's excellent Computational Acoustics' tutorials, and also a few Elmer forum posts that are close to my application domain, e.g. :

Simple Pipe Acoustics - the very basics
Acoustics Simulation (from Comsol to Elmer)?
2d simulation of acoustic wave propagation
Acoustics – Basic Postprocessing With ElmerSolver & Paraview

I was hoping to better understand the limits of what I can do with Elmer and perhaps get some ball park figures. I picked up in the forum some of the assumptions ingrained in Elmer.

E.g. " to describe a sinusoidal wave with polynomial basis functions we need between 10-12 elements for each wave."

Also found a rough estimate by raback here which I don't fully understand:

"Ultrasound is <2cm and hence if you want to study surroundings of cars you need at least 20 m which means at least 1000 waves. For each wave you need 10 elements. Make this 3D and you suddenly have 10^12 elements which cannot be done."

So I have a few questions:

a) I don't fully understand how does one arrive to 10^12 elements for that 3D model with the given constraints. Can you provide further clarification?

b) I am working with ultrasound up to 40kHz and sub-wavelength (λ<8.6 mm) structures with a complex 3D geometry. I am considering a linear wave number of 116. The computational domain that I am considering is 20cm * 20cm * 20cm (20cm^3). Would this be feasible to solve Helmholtz in Elmer with reliable accuracy (i.e. not sure what would be a meaningful error but perhaps <0.1% )?

Thank you,
Francisco
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Re: Computational limits to solving ultrasound wave scattering in Elmer

Post by raback »

Hi Francesco,

So I guess you need ~(10*20/0.86)^3 or ~12.5 M elements. This can be done if you have decent computer and find a preconditioner that works reasonably well. The thing is that you need the same ~10 elements for wavelength in each direction. You might perhaps cheat if you know a priori the direction of the wavefront but generally this is not possible hence you need rather uniform and isotropic mesh.

You can search for current research on "preconditioner helmholtz equation" and see that it is still an active area of research. Elmer would benefit from some tailored preconditioning technique.

There are also better formulations for wave problems that the standard Galerkin method. You may use multipole accelerated BEM or some FEM version where the basis functions have been enriched with plane waves. With such basis you can probably reduce the number of elements by an order of magnitude in each direction. Elmer does not have these implemented.

-Peter
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