Non-orthogonal mesh improvements #166

bendudson · 2023-01-27T02:28:44Z

I think this is now ready for others to try out.

This PR adds a new way to optimise meshes, to generate non-orthogonal meshes that align to the walls of the domain and have other "nice" properties. The idea is to start with an orthogonal mesh, then generate meshes by shifting points along flux surfaces. To use it first an orthogonal mesh is generated:

from hypnotoad.cases import tokamak
from hypnotoad.core.mesh import BoutMesh

with open("geqdsk", "r") as fh:
    eq = tokamak.read_geqdsk(fh, {})

mesh = BoutMesh(eq, {})  # Default settings

Then we define a measure to optimise. In this case we combine distance to the boundary with orthogonality:

from hypnotoad.core.mesh import BoundaryDistance, Orthogonality
measure = BoundaryDistance(mesh) + Orthogonality()

These are classes that inherit from MeshMeasure, that can be added together and multipled by constant weighting factors. The argument to BoundaryDistance ensures that the boundary intersections with the underlying FineContours are found. We then optimise the mesh using this measure:

opt_mesh = measure.optimise(mesh)

The original mesh isn't modified; this returns a new BoutMesh.

This is implemented in the hypnotoad-geqdsk script: Setting optimise: true in the input YAML file will run the optimiser on the initial grid. Other options control the weights applied to the mesh metrics.

Closes #xxxx
Tests added
Udated manual
Updated doc/whats-new.md with a summary of the changes

If both upper_wall and lower_wall are True, `len(contour) // 2` rather than `len(contour // 2)` should be used.

If a contour starts outside the wall then it can be that no intersection is found. Handle that case, leaving original contour.

Method to plot single points, for interactive debugging

Attempting to handle cases where no intersection is found

Plots cell corners joined together, and cell centers as points. Perhaps could use xlow, ylow points to provide a quadratic cell shape?

The idea is to first extend FineContour to the wall, then distort PsiContour's points along the FineContour curve. A divide-and-conquer algorithm is used to make finding intersections with a large number of points efficient.

Move plotting to MeshRegion so individual regions can be plotted. Mesh plotting methods iterate over and call MeshRegions.

Broke test case TestContour.test_append

FineContour.getPoint is the inverse of getDistance: It returns a Point2D if given a distance along the FineContour PsiContour.map takes a function that returns a distance shift, and returns a new PsiContour that shares the FineContour with the original. This will be used to perform mesh deformations.

If given, MeshRegion doesn't need to follow radial coordinate lines and create PsiContours.

Enables mapping of the mesh points using shift functions.

Plots straight-sided cells connecting cell corners. Added script plotting options to possible options list, so that an exception isn't raised when they're used.

- Ensure that psi is passed to get_fine_contour - Handle rounding errors near FineContour edges

Mesh.map() now creates an instance of self.__class__, so subclasses including BoutMesh can be mapped.

Ensure that final index has ypos=1, to be consistent with upper_shift. Prevent crossing lines from going off end of FineContour

MeshRegion.setWallIntersections(Equilibrium) calls FineContour.setWallIntersections to calculate where contours intsersect walls. MeshRegion.wallAlignShiftFunction() creates a lambda function that shifts a MeshRegion to align to the wall. That can map cells to have zero size, but PsiContour.map prevents cells from crossing.

Change `axis` keyword to `ax` for consistency, return axis.

Use a polynomial basis to represent mesh point shifts within each MeshRegion. MeshRegionMapper generates new MeshRegion objects given a list of polynomial coefficients. The order of the polynomials in X and Y is set in the constructor. MeshMapper uses MeshRegionMapper to generate new Mesh objects, using a combined list of polynomial coefficients.

PsiContours that are shared between MeshRegions will in general not be mapped in the same way. These PsiContours are averaged in MeshMapper.generate to produce a consistent boundary between regions.

Optimises meshes by varying the distortion parameters to minimise a MeshMeasure. For now only one MeshMeasure: BoundaryDistance combines distances between the mesh and the wall.

Enables the optimiser to take into account the orthogonality of the mesh, by minimising tan(Beta) over the mesh, where Beta is the angle between coordinate lines.

Can be used to disable some parts of Mesh construction in optimiser loop.

Repeatedly creating regions and meshes, so reduce the amount of text printed each iteration

- PoloidalSpacing measures the ratio of the poloidal size of neighbouring cells, penalising variations - When PsiContours are merged on region boundaries, re-use the FineContour and distances that have already been calculated. - Add __str__ methods to the MeshMeasure subclasses - Add automatic optimisation to the `hypnotoad-geqdsk` script

- In optimisation loop only print every 20th iteration - In hypnotoad-geqdsk script save the plotted cells to file

Changes some spacing, line breaks

bendudson added 30 commits January 26, 2023 16:24

Small bugfix in find_intersection

55cb29e

If both upper_wall and lower_wall are True, `len(contour) // 2` rather than `len(contour // 2)` should be used.

MeshRegion.addPointAtWallToContours handle no intersection

0fc5357

If a contour starts outside the wall then it can be that no intersection is found. Handle that case, leaving original contour.

Add Point2D,plot()

f63a8a9

Method to plot single points, for interactive debugging

Improve robustness of non-orthogonal mesh generation

3e019b6

Attempting to handle cases where no intersection is found

Add Mesh.plotCells method

d5530b0

Plots cell corners joined together, and cell centers as points. Perhaps could use xlow, ylow points to provide a quadratic cell shape?

Add wall intersection finding to FineContour

f55a69b

The idea is to first extend FineContour to the wall, then distort PsiContour's points along the FineContour curve. A divide-and-conquer algorithm is used to make finding intersections with a large number of points efficient.

Black formatting

94cd821

MeshRegion add plotGridLines and plotCells

9291e5d

Move plotting to MeshRegion so individual regions can be plotted. Mesh plotting methods iterate over and call MeshRegions.

Revert change to PsiContour.get_distance

c616500

Broke test case TestContour.test_append

Fixing PsiContour.get_distance for tests

0607d52

Merge branch 'master' into non-orthogonal

b6cb785

flake8 fixes

22d8d60

Enable MeshRegion to be passed contours

f4c7f85

If given, MeshRegion doesn't need to follow radial coordinate lines and create PsiContours.

Add MeshRegion.map and Mesh.map

5c2468e

Enables mapping of the mesh points using shift functions.

Add plot_cells option to hypnotoad-geqdsk script

c302eeb

Plots straight-sided cells connecting cell corners. Added script plotting options to possible options list, so that an exception isn't raised when they're used.

Small fixes in FineContour and PsiContour

661902a

- Ensure that psi is passed to get_fine_contour - Handle rounding errors near FineContour edges

flake8 fix (line too long)

e647736

Enable BoutMesh.map() method

ddb59e5

Mesh.map() now creates an instance of self.__class__, so subclasses including BoutMesh can be mapped.

PsiContour.map small improvements, fix

cb8a2f4

Ensure that final index has ypos=1, to be consistent with upper_shift. Prevent crossing lines from going off end of FineContour

Simplify Equilibrium.plotWall()

e9d4468

Change `axis` keyword to `ax` for consistency, return axis.

MeshMapper combine shared PsiContours

8c0e0e8

PsiContours that are shared between MeshRegions will in general not be mapped in the same way. These PsiContours are averaged in MeshMapper.generate to produce a consistent boundary between regions.

MeshMeasure and BoundaryDistance optimiser

494eda2

Optimises meshes by varying the distortion parameters to minimise a MeshMeasure. For now only one MeshMeasure: BoundaryDistance combines distances between the mesh and the wall.

Add Orthogonality mesh measure

e5a1d1e

Enables the optimiser to take into account the orthogonality of the mesh, by minimising tan(Beta) over the mesh, where Beta is the angle between coordinate lines.

Mesh user_options and versioning arguments

7362778

Can be used to disable some parts of Mesh construction in optimiser loop.

Reduce printed output when optimising

abe7cbe

Repeatedly creating regions and meshes, so reduce the amount of text printed each iteration

Output printing and plotting in script

1128299

- In optimisation loop only print every 20th iteration - In hypnotoad-geqdsk script save the plotted cells to file

bendudson changed the title ~~WIP: non-orthogonal mesh improvements~~ Non-orthogonal mesh improvements Feb 2, 2023

bendudson requested a review from johnomotani February 2, 2023 00:45

bendudson added 2 commits February 1, 2023 16:51

Black v23.1.0

7e2bd16

Changes some spacing, line breaks

Updates, more options to control optimisation

a317cba

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Non-orthogonal mesh improvements #166

Non-orthogonal mesh improvements #166

bendudson commented Jan 27, 2023 •

edited

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Non-orthogonal mesh improvements #166

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bendudson commented Jan 27, 2023 • edited Loading

bendudson commented Jan 27, 2023 •

edited

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