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Support Chebyshev Grids for collision operator and other weak form operations #220

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mrhardman opened this issue May 29, 2024 · 0 comments

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@mrhardman
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Currently the collision operator is only implemented for Gauss Legendre grids. This could be overcome if the setup for the various underlying matrices involving integrals of produces of lagrange polynomials was added for the Chebyshev grid. This take could be completed relatively straightforwardly if we can provide and option to compute these matrices using the explicit interpolation formula for the Lagrange polynomials and their derivatives, in terms of arbitrary grid locations. (I believe @johnomotani already started work on this some time ago).

Currently the reason for avoiding this approach in the Gauss Legendre grids and instead using a formulation in terms of Legendre polynomials was to gain understanding of the weak-form method with definite testable results provided by http://dx.doi.org/10.1016/j.jcp.2014.12.012.

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