Good topic - Following

I discuss the strengths and weaknesses of these approaches in my book on CFD, which will be free on 9/1 and also Differential Equations, which will be free on 8/18. Both come with examples and software that's always free. Just Google my name. There's a free software link and also one to the books, which lists when each is free. One method works better for some applications while another method works better for different applications so that there's no simple answer to this question like: always use this or that approach for everything.

Dear Prof. Dudley J Benton, Thank you for your contribution and your reference

Concerning acoustic scattering I think that Boundary Element Methods (BEM) are more appropriate and convenient because the mesh involved in the discretization is a boundary mesh (i.e. a 2D mesh for a 3D scattering problem). The acoustic scattering problem under a FEM or FDTD approach usually involves a 3D mesh and some kind of absorbing layer far away the scatterer to simulate a proper decay for the fields and to avoid spurious bounces of the field back to the scatterer.

Edmundo Lavia , Thank you for your reply.

In the acoustic scattering and in the case of the 3D complex structure , the Boundary Element Methods (BEM) remains appropriate and better than FEM or other methods?

All methods has its advantages and drawbacks depending the particular situation. For acoustic 2D scattering based in the Helmholtz equation (with constant wavenumber k) the collocation method developed by Kress (10.1016/0377-0427(94)00073-7) is between the most fast and accurate. A similar approach for 3D, regarding precision and generality, is (IMHO) lacking. The BEM is capable to tackle scattering by complex structures (10.1016/j.jsv.2020.115609) but in the asumption that each domain involved has a constant wavenumber. In this respect FEM is more general because can consider a k(x) situation more easily that BEM but with the extra cost of a full 3D mesh.

Dear Edmundo Lavia , I agree with you, each method has its advantages and disadvantages and the used method depends on the type of studied structure.

It is also true that FEM is more general and it is limited neither by the situation of k (x) nor by the complexity of the studied structure.

Certainly, FEM is more expensive compared to the other methods. This difficulty can be overcome with the use of super powerful computers or techniques such as:

• the refinement of the mesh only in the places where it is necessary
• the use of domain decomposition method
• The use of the suitable langage such as: C++, Python
• ....

Best

Dear Sirs,

Anyone know about the FDTD simulation ? I need some help regarding the simulation in FDTD. Please help me. Edmundo Lavia sir, please help me.

Regards,

Subrat Sahu

Subrat Sahu , you want apply FDTD to what kind of equations (Maxwell, elasticity, Navier-Stokes, ...) ?

Hi Subrat,

Years ago I implemented the FDTD, restricted to 2D acoustic scattering, following a work of S. Wang published in the Journal of Acoustic Society of America (Article Finite-difference time-domain approach to underwater acousti...

In the electromagnetic case (not my field of research) surely there are other seminal references.

Regards,

E.L.

Dear Sir,

I want to simulate optical fiber structure. And, I want to calculate the coupling efficiency of nanoparticle with the optical fiber using LUMERICAL FDTD software.