All of the math you are trying to do here could be simplified by using Grassmann.jl multivectors instead of matrices. It encodes both rotational algebras as well as spacetime geometry, so that matrices are no longer needed for that.

Perhaps you could demo a rewrite of the existing code in Grassmann so we can see it in action?

Sure, I’m writing a few papers to explain how to use groups in Grassmann and doing some other work but I don’t currently have time for blog-post style things. I have my own specific problems right now to deal with. When I’m ready publish it, there will be a much longer paper explaining how to work w…

I don’t necessarily disagree, lacking familiarity with geometric algebra, but the snippets above are part of a coupled-dipole method which at its core consists of solving a linear system of, unsurprisingly, coupled-dipole equations. So I think some use of matrices is warranted, though I imagine that…

The standard reference for that would be http://www.mrao.cam.ac.uk/~cjld1/pages/book.htm

Offtopic, but my recollection is that Grassman-algebra formulations of electromagnetism are mainly useful in vacuum. Once you have matter, e.g. for scattering problems, the matter sets a preferred reference frame and wedge-product-type formulations (while possible) become extremely cumbersome. As…

Scattering type problems are actually related to what I study, which is acoustic and microwave scattering and soliton particles. If you use projections and spin groups from a higher dimensional Grassmann cone, it actually gets less cumbersome to linearize geometrically, at least for multi-layer opti…

Grassman algebras for electromagnetic scattering

Specific Domains Modelling & Simulations

kristoffer.carlsson August 18, 2019, 9:06am 4

I just meant a direct translation of these 20 lines of code (which might be shorter with the extra simplicity from Grassmann), not a big blog post. But I understand if you are busy with other things.

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Grassman algebras for electromagnetic scattering

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