Comments (6)
In testing if S is unitary (i.e. S \dot adjoint(S) = Identity matrix OR det(S)det(adjoint(S))=1), which it isn't, it appears that det(S)det(adjoint(S))=1/(2k)^2 hinting at a problem with the scaling of the incident field, most likely.
from acoustics.
Next steps:
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Research LU factorization and understand it.
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Alter computation of scattering matrix. Don't compute Z for each harmonic. Compute once, store LU factors, then generate all RHSs and apply LU factorization to each to get the J vectors. Then stitch together V and J matrices. Alternative: compute V and J matrices straight from Z's LU factors and a matrix of RHSs (e.g. V^T LU V).
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Compute S for max l = 8. Compute determinant. determinant of S (which is a submatrix of full S) for l = 7 should be nearly the same.
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Try to find a scale factor on VJ, not S
from acoustics.
to solve Ax=b
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Call A_factors = factorize(A) or A_lu = lu(A). This may or may not use LU factorization, but it will do a check to see the type of matrix A is and choose a method accordingly (https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.factorize). Directly calling lu(A) might be best since I know A isn't going to have any special properties (unless the mesh has some order to it), but in general A will just be a "general square" matrix. Can probably save (negligible) computation time by using lu(A).
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A_factors \ b = x will solve the equation for x using the factors of A.
from acoustics.
Determinant is doing weird stuff for max_l = 8. As I truncate S, every two truncations, the determinant flips sign but remains unchanged in magnitude. Not sure about that. Currently I am trying to find a scale factor on VJ
from acoustics.
SCALE FACTOR MIGHT BE THE FACT THAT I AM NOT SCALING INCIDENT FIELD BY K
from acoustics.
All looks good. Awaiting thoughts from Eric before merging
from acoustics.
Related Issues (20)
- add run file HOT 1
- Could solve at WS modes using other integral equations HOT 7
- Use ACA in Wigner Smith routines HOT 3
- update readme to describe how to run the code HOT 1
- use Js and Vs_trans from calculating S in dS/dk
- add function to plot WS time delays
- ability to select LU or GMRES
- add timers for each major segment of the code
- Save Js matrix after first calculation HOT 1
- investigate why CFIE doesnt agree well with IE HOT 30
- verify WS CFIE solver HOT 3
- add normal check HOT 1
- Check CFIE new error versus old
- use soft IE for open geometries and WS HOT 6
- add ability to run at multiple WS modes HOT 2
- output and input function for WS matrix HOT 2
- parallelize scattering matrix loops HOT 3
- add multithreading to ACA Z matrix fill HOT 2
- RHS fill taking obscene amount of time HOT 5
- fix unnecessary calls of sphericalHarmonics in scattering matrix calculation
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from acoustics.