Support Floquet periodic boundary conditions #314

simlapointe · 2024-12-13T16:16:15Z

Add support for Floquet periodic boundary conditions and improve flexibility of periodic boundary conditions specifications.

Support Floquet boundary conditions by incorporating the phase delay into Maxwell's equations and solving the modified PDE with periodic boundary conditions.
Automatically detect periodic boundary transformations.
Support both translation and rotation transformations.

…tions

…single operator

hughcars

Looking pretty good, I think there are a few larger changes to take care of first

FP should be part of K, given it has no omega dependence in its construction unlike A2. This will simplify loads of things
The muinv kx should be in the MaterialOperator, (doing this neatly will mean adding the ability to use transpose coefficients in the ceed context)
The geodata.cpp can be shortened and simplified some, I have some initial work on doing this in hughcars/periodic-bc, but I'm sure once you get started you'll probably see even more things to do. The basic thing is a mixing assumptions on sdim and no assumptions on sdim.

docs/src/config/boundaries.md

docs/src/config/solver.md

hughcars · 2025-01-08T15:43:19Z

docs/src/examples/cylinder.md

+distance between them is given by the `"Translation"` vector in mesh units. In `floquet.json`,
+an additional `"FloquetWaveVector"` specifies the phase delay between the donor and receiver
+boundaries in the X/Y/Z directions.


Given the relative simplicity of this example, it would be great if we can derive the expected modes analytically. I suspect it'll be possible to map them to an equivalent set of modes on a full length cylinder without phase shift, at which point analytic results can be compared against like for the waveguide case.

I compared the cylindrical waveguide modes (as well as a rectangular waveguide and a nail/pillar) against Comsol and they all matched so I feel confident about it, but I'll see if I can derive analytical modes for the Floquet case.

hughcars · 2025-01-08T15:59:00Z

docs/src/guide/boundaries.md

@@ -74,7 +74,7 @@ Periodic boundary conditions on an existing mesh can be specified using the
 ["Periodic"](../config/boundaries.md#boundaries%5B%22Periodic%22%5D) boundary keyword. This
 boundary condition enforces that the solution on the specified boundaries be exactly equal,
 and requires that the surface meshes on the donor and receiver boundaries be identical up to
-translation. Periodicity in *Palace* is also supported through meshes generated
+translation or rotation. Periodicity in *Palace* is also supported through meshes generated


How have you tested the rotational case? Might make for a cool example, thinking plausibly the waveguide cylinder could be split into wedges maybe and analyzed.

I tested the pure rotation with an annulus wedge and the rotation + translation case with a helical case.

palace/fem/libceed/operator.hpp

palace/utils/configfile.cpp

palace/utils/configfile.hpp

palace/utils/geodata.cpp

palace/drivers/drivensolver.cpp

palace/linalg/floquetcorrection.cpp

hughcars

Some minor typos, and one further simplification of the coefficient handling for the floquet hermitian term then we're good to go.

hughcars · 2025-02-07T22:30:33Z

palace/drivers/eigensolver.cpp

+      // B = -1/(iω) ∇ x E + 1/ω kp x E.
+      floquet_corr->AddMult(E, B, 1.0 / omega);


Why is the sign of the correction here different to that in the driven case?

Curl.Mult(E.Real(), B.Real()); Curl.Mult(E.Imag(), B.Imag()); B *= -1.0 / (1i * omega); if (space_op.GetMaterialOp().HasWaveVector()) { // Calculate B field correction for Floquet BCs. // B = -1/(iω) ∇ x E - 1/ω kp x E floquet_corr->AddMult(E, B, -1.0 / omega); }

Should be the same (+) everywhere, forgot to change one of the driven ones.

palace/fem/integrator.hpp

palace/models/spaceoperator.cpp

hughcars · 2025-02-07T22:50:59Z

palace/models/materialoperator.cpp

+  if (has_wave_attr && local_wave_vector.Norml2() > tol)
+  {
+    mfem::Vector diff(sdim);
+    diff = wave_vector;
+    diff -= local_wave_vector;
+    MFEM_VERIFY(diff.Norml2() < tol,
+                "Conflicting definitions of the Floquet wave vector in the "
+                "configuration file.");
+    wave_vector = local_wave_vector;
+  }


This implies a weird non-additive effect:

{ bdr_a : {Floquet: 1,0,0}, bdr_b : {Floquet: 0,1,0}, Floquet: {0,0,1}

A user might intend to mean {1,1,1}, but this would error. I'm inclined to say either they add, or only one can be specified. I'm biased towards allowing the sum because this implies a non-present value is equivalent to {0,0,0}.

I'm good with allowing the sum.

hughcars · 2025-02-07T22:57:47Z

palace/utils/geodata.cpp

@@ -1721,6 +1706,350 @@ double RebalanceMesh(const IoData &iodata, std::unique_ptr<mfem::ParMesh> &mesh)
 namespace
 {

+// Compute the centroid of a container of vertices.
+template <typename T>


Might no longer need these templates, I had only put them in whilst I was playing with going to general containers and was moving back and forth.

It's still used in two places with different inputs (array and unordered_set) so I kept the template.

palace/utils/geodata.cpp

palace/fem/integrator.hpp

hughcars · 2025-02-07T23:08:53Z

palace/models/spaceoperator.cpp

+void SpaceOperator::AddPeriodicCoefficients(double coeff, MaterialPropertyCoefficient &fm,
+                                            MaterialPropertyCoefficient &fwc,
+                                            MaterialPropertyCoefficient &fc)


The only reason there needs to be two coefficients here, is because they are being added in with +1 and -1 coefficients. If you change the MixedVectorWeakCurlIntegrator to a(u, v) = - (Q u, curl v) similar to how MixedVectorWeakDivergenceIntegrator uses the negative Q, then there only needs to be one coefficient and the hermitian nature of the operators is really apparent. This would mean adding the -1 coefficent to the PopulateCoefficientContext call similar to MixedVectorWeakDivergenceIntegrator. This would mean changing some of the unit tests against mfem most likely too, but will reduce the LOC further.

I'm good with that, made the changes.

simlapointe added 30 commits October 25, 2024 17:39

Try different ways to compute the affine transformation matrix

86d6055

Add periodic boundary operator class for periodic/floquet BCs

31a4a9b

Improve Bloch wave vector specification and fix some bugs

6420322

Initial implementation of floquet periodicity terms in governing equa…

707b32b

…tions

Update surface normal calculation and add planar boundary check

82d1d61

Fix some with floquet operators and their use in eigensolver

1de268d

Remove some prints

95502e2

Add a new matrix for the mass periodic term

6021e8f

Ensure enough mesh elements in the periodic direction

0301a71

Debugging tests

63096b3

Debugging tests

974da2a

Allow non-symmetric material properties and merge floquet terms in a …

3f6bef0

…single operator

Merge floquet periodic terms into one operator

975a274

Remove print

57e6d3a

Use CEED Symmetric operator

c45ef21

Merge branch 'main' into simlapointe/periodic-bc

ff552d2

Disable divergence-free projection when using Floquet BCs

5a4f614

Define vector indices in SetOperator

447df80

Constrain Floquet wave vector components

e2d6e46

Update comments since quadrature data is no longer symmetric

49b29e4

Add floquet periodic mass term to auxiliary operator

e8b0d95

Merge main

3b2700c

Fix formatting

951d70f

Merge branch 'main' into simlapointe/periodic-bc

1557829

Warn against using div-free projection and Floquet BCs

7dfcccc

Combine periodic terms in a single helper functions

e687ab9

Test term to help aux space smoother

967c6e6

Test Floquet terms in divergence free projection

12ab759

Clean and reorganize automated periodic boundary matching

e713a6f

Remove print

b5ef9bd

simlapointe added 7 commits December 30, 2024 10:17

Fix formatting

494a51a

Update docs

d31c929

Use FP for Floquet periodic term

5ae3cf3

Fix formatting

a4ea4f1

Add comments

c14cb5b

Update docs

d21f1e7

Update docs

81a8fec

simlapointe marked this pull request as ready for review December 31, 2024 01:55

simlapointe requested a review from hughcars December 31, 2024 01:55

simlapointe and others added 8 commits December 30, 2024 17:57

Update docs

a029c60

Merge branch 'main' into simlapointe/periodic-bc

47bb7ef

Refactor to simplify

24fd936

Further refactor

b2c483c

Remove FindUniquePoints

b5abb11

Fix address bug

67af1db

Rfeactor CreatePeriodicVertexMapping

042d5f5

style

7a70b56

hughcars requested changes Jan 30, 2025

View reviewed changes

simlapointe and others added 10 commits January 30, 2025 15:42

Resolve conflicts

302e031

Merge branch 'hughcars/periodic-bc' into simlapointe/periodic-bc

59d9440

Address PR feedback

946eca9

Remove print

103ee0a

Use vector instead of set

d5385e0

Remove unused code

2ba584c

Remove unused mesh tolerance

9239c20

Fix formatting

e03d52a

Fix incorrect arguments order

eb747a6

Merge branch 'main' into simlapointe/periodic-bc

371e044

hughcars requested changes Feb 7, 2025

View reviewed changes

Address PR feedback

3dd27b1

Provide feedback

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Support Floquet periodic boundary conditions #314

Support Floquet periodic boundary conditions #314

simlapointe commented Dec 13, 2024 •

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simlapointe Feb 10, 2025

		// B = -1/(iω) ∇ x E + 1/ω kp x E.
		floquet_corr->AddMult(E, B, 1.0 / omega);

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simlapointe commented Dec 13, 2024 •

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