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Numerical improvements - #232

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better-integrals
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Numerical improvements#232
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better-integrals

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@daanboer daanboer commented Aug 12, 2025 •
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This patch aims to implement a multitude of numerical improvements. I have opened this draft PR to track the progress, I might split the PR into multiple smaller PRs later down the line.

  • Analytical evaluation of the collision integrals
    • by assuming logarithmic decay of the EEDF between cells (similar to the strategy of BOLSIG+),
    • by assuming linear decay of the EEDF between cells (in theory less potent than the previous strategy, with the upside that it does not require iteration).
    • These strategies should be less sensitive to alignment of the threshold region of inelastic processes to the grid, but this is still to be tested thoroughly.
  • Scharfetter-Gummel discretization for the flux terms.
  • A total flux boundary condition (there is also some experimentation with a logarithmic decay boundary condition).
  • A Newton-Raphson based solving procedure for the nonlinear growth + ee terms.
  • The implementation supports nonuniform discretization.

Resolves #197
Relates to #205

@daanboer daanboer added the enhancement New feature or request label Aug 12, 2025
@daanboer daanboer mentioned this pull request Aug 12, 2025
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@daanboer daanboer mentioned this pull request Oct 1, 2025
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@daanboer
daanboer force-pushed the better-integrals branch 3 times, most recently from 9adb19d to f54e8a1 Compare December 5, 2025 12:53
janvdijk
janvdijk reviewed Feb 7, 2026
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Comment thread LoKI-B/Integrators.h Outdated
janvdijk
janvdijk reviewed Feb 7, 2026
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Comment thread LoKI-B/Iterators.h Outdated
janvdijk
janvdijk reviewed Feb 7, 2026
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Comment thread LoKI-B/OperatorsNew.h
@daanboer
daanboer force-pushed the better-integrals branch 5 times, most recently from 3728dcc to a72102a Compare February 16, 2026 08:25
daanboer added 14 commits March 18, 2026 08:51
@daanboer
Add a function to more accurately compute inelastic collision integrals
93c916d 
The function computes an analytic solution to the u*sig*f collision integrals,
assuming sig to be locally linearly dependent on u, and f to the locally
exponentially dependent on u.
@daanboer
Add sink and source function for inelastic integrals
83ed341 
Adds functions `collision_integral_sink` and `collision_integral_source` that
do the piecewise integration of the inelastic source terms.
@daanboer
Add temporary invertLinearMatrixNew function
942cf73 
This function uses the new method of computing the inelastic
collision integrals. The solution now requires iteration, hence
the new function. The nonconservative terms have been temporarily
disabled in `invertLinearMatrix`, to allow for comparison between
the two functions.
@daanboer
Remove unused import
ab11351
@daanboer
Initialize u_f_start to the first cell energy
2c2ae39
@daanboer
Add operator classes that provide separate drift and diff coeffs
6b63dc3
@daanboer
Add advanced inelastic sink and source functions
d579d41 
These functions directly interpolate the given cross section
from the raw data (skipping an interpolation onto the grid
faces). These functions are a bit more involved, as the
cross section grid needs to be taken into account when
splitting up the energy domain for integration.
@daanboer
Disable not yet supported sections of code
0a2710c 
Done to compare the original solution to the solution
proposed on this branch. This currently includes growth
schemes, ionization, attachment and e-e collisions.
@daanboer
Use a Scharfetter-Gummel discretization for the drift-diffusion typ…
94dea57 
…e operators
@daanboer
Add alternative inelastic integration functions
499a45c
@daanboer
Fix drift and diffusion coefficients of the elastic operator
c701a31
@daanboer
Correctly increment cell iterator at cell boundaries
0fa5ed1
@daanboer
Skip processes that have thresholds above the maximum grid energy
53bde28
@daanboer
Only normalize the EEDF after the final iteration
1fd2f0b
daanboer added 12 commits March 18, 2026 08:51
@daanboer
Add skeleton for spatial growth operator
7580f95 
Currently it only computes the mobility in two different ways.
@daanboer
Add integration iterator and integrator machinery
69e08ba 
The idea is that using this machinery we can easily build expressions that
fold the EEDF with other quantities, while also easily being able to switch
between the different interpolating expressions for the EEDF.
@daanboer
Add new collision integral integration functions
900ad0c 
These functions use the new iterator/integrator machinery.
@daanboer
Fix GridIterator not advancing when it should
a6bfe2f 
The grid iterator sometimes got stuck when integrating the superelastic
source on (very) large grids. This is fixed by adding a small epsilon
in the lhs of the predicate.
@daanboer
Use the new integration procedures in the inelastic operators
911036d 
The procedures now use a linear integrator.
@daanboer
Add missing break statements in switch
716b3f4
@daanboer
Use user-defined ionization operator type
69cf6dd
@daanboer
[TMP] Patch N2 cross sections
fc886c9 
The new `InterpolatingIterator` machinery only work for cross
sections that start their energy domain at zero energy for now.
@daanboer
Remove deprecated collision integration routines
af6a1ad
@daanboer
Compute spatial growth operator terms
bf45057
@daanboer
Add Newton-Raphson and Picard routines for spatial growth
579c2e2
@daanboer
Fix include guards
325c6f7 
Resolves comments by @janvdijk.
@daanboer
daanboer force-pushed the better-integrals branch 3 times, most recently from 2b64312 to d11b667 Compare March 18, 2026 08:25
daanboer added 2 commits March 18, 2026 19:59
@daanboer
Use the new ConvectionDiffusionOperator
98c94c9 
Scale new collisional operators by cell widths

This is required as the convection diffussion terms are also
divided by the cell width.
@daanboer
Implement equal sharing source term
ea3e4a8
@daanboer daanboer mentioned this pull request Jun 2, 2026
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Implement a single flux-boundary condition

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