Spectral analysis on triangular meshes

shalabhks · March 20, 2020, 06:44

Is there any existing literature on spectral analysis of numerical schemes on triangular meshes?

Eifoehn4 · March 20, 2020, 11:46

Dear shalabhks,

you may apply your spectral analysis after swapping your data from the triangle to a cartesian background mesh via interpolation or projection. If your solution is smooth enough this should work.

Generally a spectral analysis also depends on your solution representation. What numerics do you use for your results?

FMDenaro · March 20, 2020, 13:47

If you google in internet there are references. Interpolation of data on equidistant nodes is a rude way on high wavenumber components and can produce large error. I suggest also to search on this site for some hints

https://people.maths.ox.ac.uk/trefethen/

praveen · March 21, 2020, 01:16

"spectral analysis of numerical schemes" seems to imply von-neumann analysis to study stability and dispersion/dissipation properties of the numerical scheme. Is this what you are asking ? If yes, then I think there is not much option that I am aware of, since this type of analysis requires cartesian grids.

shalabhks · March 21, 2020, 22:59

Thank you. I am using JST scheme.

March 20, 2020, 06:44	Spectral analysis on triangular meshes	#1
shalabhks New Member Join Date: Sep 2018 Location: Bangalore Posts: 6 Rep Power: 8	Is there any existing literature on spectral analysis of numerical schemes on triangular meshes?

March 20, 2020, 11:46		#2
Eifoehn4 Senior Member - Join Date: Jul 2012 Location: Germany Posts: 184 Rep Power: 14	Dear shalabhks, you may apply your spectral analysis after swapping your data from the triangle to a cartesian background mesh via interpolation or projection. If your solution is smooth enough this should work. Generally a spectral analysis also depends on your solution representation. What numerics do you use for your results? __________________ Check out my side project: A multiphysics discontinuous Galerkin framework: Youtube, Gitlab.

March 21, 2020, 01:16		#4
praveen Super Moderator Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 342 Blog Entries: 6 Rep Power: 18	"spectral analysis of numerical schemes" seems to imply von-neumann analysis to study stability and dispersion/dissipation properties of the numerical scheme. Is this what you are asking ? If yes, then I think there is not much option that I am aware of, since this type of analysis requires cartesian grids. __________________ http://cpraveen.github.io http://twitter.com/cfdlab http://github.com/cpraveen

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March 20, 2020, 13:47		#3
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,842 Rep Power: 73	If you google in internet there are references. Interpolation of data on equidistant nodes is a rude way on high wavenumber components and can produce large error. I suggest also to search on this site for some hints https://people.maths.ox.ac.uk/trefethen/

March 21, 2020, 22:59		#5
shalabhks New Member Join Date: Sep 2018 Location: Bangalore Posts: 6 Rep Power: 8	Thank you. I am using JST scheme.