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Optimal Use of Infinite Element Domain
Posted 13.03.2023, 14:19 GMT-4 Electromagnetics, Geometry, Physics Interfaces Version 6.1 1 Reply
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Let's say I am trying to model the potential in the region around a source using the Electrostatics interface. Ideally, I would set V = 0 at infinity as one of my boundary conditions. I can approximate this in COMSOL by creating a spherical domain around the region of interest. I can either assign V = 0 to its outer surface directly or treat it as an infinite element domain. How should I decide which method to use? For my applications, I don't care about the very far field. I just want an accurate representation of the potential around the source.
If going with the first, I've heard that ~10x the scale of the core geometry will generally provide an accurate solution. Is there a similar scale factor required for modelling with infinite elements? What are the respective roles of the inner and outer layers in an infinte element geometry? Perhaps most importantly, if I want a V = 0 condition at infinity, is there any reason not to use infinite elements?
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Dear Aryan,
I understand that you are trying to model the potential in the region around a source using the Electrostatics interface in COMSOL Multiphysics, and you would like to approximate the V = 0 at infinity boundary condition. You are correct that the main issue with defining boundary conditions on the outside of a domain is that they can affect the solution around the source. The farther away the boundary is from the source, the smaller the effect will be.
There are two options to address this issue:
Creating a very large physical domain: As you mentioned, you can create a spherical domain around the region of interest and assign V = 0 to its outer surface. A size of 10 times the scale of the core geometry might be a good value, but the required size depends on your specific situation. It is recommended to test different sizes to ensure accurate results.
Using infinite elements: This approach stretches the domain in the equations rather than in the geometry. Infinite elements can be advantageous in some cases, but they can also be computationally more expensive compared to a small domain. However, you should be aware of some known issues when modeling with infinite elements, such as poor element quality, slow convergence for iterative solvers, and increased time for assembly stages. To overcome these issues, it is recommended to use swept meshing in the infinite element domains and avoid using objects with different material parameters or boundary conditions inside an infinite element region. The required distance of the infinite elements to the source depends on the specific scenario, and it is recommended to test different distances to ensure an accurate solution.
Regarding the roles of the inner and outer layers in an infinite element geometry, the inner layer is where the transition between the domain of interest and the scaling domain happens, while the outer layer represents the "infinity" boundary condition. As you mentioned, if your primary concern is the V = 0 condition at infinity, infinite elements can be a viable option. In summary, both methods have their merits, and the choice depends on your specific application and requirements. To determine the most appropriate method for your situation, I recommend testing different geometries and distances to ensure an accurate representation of the potential around the source.
Regards, Andreas