Add Dirichlet Boundary Projectors #536

jowezarek · 2025-10-30T14:05:15Z

We implement the class DirichletProjector and MultipatchDirichletProjector and include tests.

DirichletProjector

is a subclass of LinearOperator. Projects coefficients of functions belonging to a fem_space of space_kind $\in$ {"h1", "hcurl", "hdiv", "l2"} to coefficients of functions satisfying the corresponding homogeneous Dirichlet boundary conditions. These projectors respect periodicity, i.e., coefficients corresponding to "periodic boundaries" will not be changed.

Take for example the constant function $f(x, y) = 1$ on an Annulus.

P0, _, _ = derham_h.projectors()
f        = lambda x, y : 1
F        = P0(f)
plot_field_2d(fem_field=F, domain=domain, N_vis=100, cmap='plasma')

Applying the DirichletProjector sets correctly only the DOFs to 0 that belong to basis functions that are different from 0 on the "x1-direction-boundary".

DP0, _ = derham_h.dirichlet_projectors(kind='linop')
F_dp   = FemField(derham_h.V0, DP0 @ F.coeffs)
plot_field_2d(fem_field=F_dp, domain=domain, N_vis=100, cmap='plasma')

Note: Low resolution! ncells = [3, 3]; degree = [1, 1]

Usage

Obtain these projectors in the FEEC context directly from a DiscreteDeRham object

# in 1D
DP0, DP1 = derham_h.dirichlet_projectors(kind='linop')

# in 2D
DP0, DP1, DP2 = derham_h.dirichlet_projectors(kind='linop')

# in 3D
DP0, DP1, DP2, DP3 = derham_h.dirichlet_projectors(kind='linop')

The last projector is simply an IdentityOperator.

When instead working with FEM objects only:

from psydac.fem.projectors import DirichletProjector

# working with a space that has a kind
V   = ScalarFunctionSpace('V', domain, kind='h1')
Vh  = discretize(V, domain_h, degree=degree)
DP  = DirichletProjector(Vh)

# working with a space that has no kind
V   = VectorFunctionSpace('V', domain)
Vh  = discretize(V, domain_h, degree=degree)
DP  = DirichletProjector(Vh, kind='hcurl') # or 'hdiv'

Similarity with `conforming_projectors`

Identical to derham_h.conforming_projectors(kind='linop', hom_bc=True) on a single-patch.
On multi-patch domains, derham_h.conforming_projectors also affect the solution at the interfaces between patches, as required by the broken-FEEC theory. If required, they have the additional ability to preserve moments of the solution.
Unfortunately, the conforming projectors are only implemented in 2D.

codacy-production · 2025-10-30T14:51:47Z

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yguclu · 2025-10-30T15:40:42Z

Good job @jowezarek! I will look into the details shortly.

@FrederikSchnack: How much work do you think is needed to extend this PR to multi-patch domains?

FrederikSchnack · 2025-10-31T09:36:06Z

Good catch! The conforming projectors are not very well tested on single-patch domains. Since the single-patch geometry behaves fundamentally different than in the multi-patch setting, at least when it comes to boundaries, we did not check if the periodicity is enforced by the FEM spaces. There is a very easy fix to this, should I push it to this pull-request?

FrederikSchnack · 2025-10-31T09:45:23Z

I think the extension to multi-patch should not be too difficult, the question is if/ for what this is needed? As I see it, this PR is mainly used for the 3D cases, where we don't have conforming projections (w/ BC) at hand.

Everything else in 2D can be done by conforming projections and other multi-patch examples like a Nitsche method enforce the BC weakly.

FrederikSchnack

My main remark is to integrate the DBP a little better into the feec-api, otherwise the additions look good to me.

psydac/api/feec.py

psydac/fem/projectors.py

yguclu · 2025-11-03T10:27:13Z

@FrederikSchnack On the topic of API consistency between the Dirichlet boundary projectors and the conforming projectors... I have just noticed that the boolean parameter mom_pres is not documented in the docstrings of

DiscreteDeRham.conforming_projectors
ConformingProjectionV0
ConformingProjectionV1

If this is an important parameter, I think it should be included in the docstrings. Or maybe it could be skipped altogether given that the parameter p_moments should contain sufficient information?

yguclu

Good job!

I have a few comments, mostly on the unit tests.
Further, I would like to see some tests run in parallel, could this be done?

psydac/linalg/tests/test_solvers.py

psydac/fem/projectors.py

FrederikSchnack · 2025-11-03T11:43:51Z

@FrederikSchnack On the topic of API consistency between the Dirichlet boundary projectors and the conforming projectors... I have just noticed that the boolean parameter mom_pres is not documented in the docstrings of

If this is an important parameter, I think it should be included in the docstrings. Or maybe it could be skipped altogether given that the parameter p_moments should contain sufficient information?

Good catch! The parameter mom_pres was introduced for simplicity to set the projectors to the maximal order of moment preservation. This is probably the parameter a user should set, so I think we should document it in the doc strings.

Together with your other comments on the conforming projections, should we do the changes here or as a separate PR?

yguclu · 2025-11-03T12:53:26Z

@FrederikSchnack On the topic of API consistency between the Dirichlet boundary projectors and the conforming projectors... I have just noticed that the boolean parameter mom_pres is not documented in the docstrings of

If this is an important parameter, I think it should be included in the docstrings. Or maybe it could be skipped altogether given that the parameter p_moments should contain sufficient information?

Good catch! The parameter mom_pres was introduced for simplicity to set the projectors to the maximal order of moment preservation. This is probably the parameter a user should set, so I think we should document it in the doc strings.

Together with your other comments on the conforming projections, should we do the changes here or as a separate PR?

This should be a small change, so we could include it here directly

…ity proj

codacy-production · 2025-11-03T16:35:21Z

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yguclu

Thanks for the changes! I have some other remarks

psydac/fem/projectors.py

psydac/linalg/tests/test_solvers.py

psydac/fem/projectors.py

yguclu

Thanks for addressing (most of) my comments! I have a few more 😄

psydac/fem/projectors.py

…atch to MultipatchDiscreteDeRham

yguclu · 2025-11-10T17:54:47Z

Good job for addressing my comments!

The one (important) thing which is still missing is parallel tests. I asked this in a previous review last week 😉

jowezarek · 2025-11-11T08:35:26Z

Good job for addressing my comments!

The one (important) thing which is still missing is parallel tests. I asked this in a previous review last week 😉

Out of the three new tests

@pytest.mark.parametrize('dim', [1, 2, 3])
def test_function_space_boundary_projector(dim)

@pytest.mark.parametrize('dim', [1, 2, 3])
def test_discrete_derham_boundary_projector_parallel(dim)

def test_discrete_derham_boundary_projector_multipatch()

the first two are rather slow (in particular the 3D parts).
I propose the following change: Let's perform the first test for dims 1 & 2, and the second in parallel for dims 1 & 3.

@pytest.mark.parametrize('dim', [1, 2])
def test_function_space_boundary_projector(dim)

@pytest.mark.parametrize('dim', [1, 3])
@pytest.mark.parallel
def test_discrete_derham_boundary_projector_parallel(dim) # here now passing comm=MPI.COMM_WORLD instead of None

def test_discrete_derham_boundary_projector_multipatch()

This way, we still test all dimensions, the tests run faster, and we have a parallel test. What do you think @yguclu ?

yguclu

Here are my last comments!

psydac/fem/tests/test_dirichlet_projectors.py

yguclu

Looks good to me! Good job!

We implement the class `DirichletProjector` and `MultipatchDirichletProjector` and include tests. DirichletProjector --------------------------- is a subclass of `LinearOperator`. Projects coefficients of functions belonging to a `fem_space` of `space_kind` $\in$ `{"h1", "hcurl", "hdiv", "l2"}` to coefficients of functions satisfying the corresponding homogeneous Dirichlet boundary conditions. These projectors **respect periodicity**, i.e., coefficients corresponding to "periodic boundaries" **will not be changed**. Take for example the constant function $f(x, y) = 1$ on an Annulus. ```python P0, _, _ = derham_h.projectors() f = lambda x, y : 1 F = P0(f) plot_field_2d(fem_field=F, domain=domain, N_vis=100, cmap='plasma') ``` See [image](https://github.com/user-attachments/assets/83dc42c6-5ecc-46ae-a0a0-6ceae85526fe). Applying the `DirichletProjector` sets correctly only the DOFs to 0 that belong to basis functions that are different from 0 on the "x1-direction-boundary". ```python DP0, _ = derham_h.dirichlet_projectors(kind='linop') F_dp = FemField(derham_h.V0, DP0 @ F.coeffs) plot_field_2d(fem_field=F_dp, domain=domain, N_vis=100, cmap='plasma') ``` See [image](https://github.com/user-attachments/assets/a117c5c6-8379-4bcf-b8a8-71e59d2d0eeb). Usage --------- Obtain these projectors in the **FEEC context** directly from a `DiscreteDeRham` object ```python DP0, DP1 = derham_h.dirichlet_projectors(kind='linop') # in 1D DP0, DP1, DP2 = derham_h.dirichlet_projectors(kind='linop') # in 2D DP0, DP1, DP2, DP3 = derham_h.dirichlet_projectors(kind='linop') # in 3D ``` The last projector is simply an `IdentityOperator`. When instead working with **FEM** objects only: ```python from psydac.fem.projectors import DirichletProjector # working with a space that has a kind V = ScalarFunctionSpace('V', domain, kind='h1') Vh = discretize(V, domain_h, degree=degree) DP = DirichletProjector(Vh) # working with a space that has no kind V = VectorFunctionSpace('V', domain) Vh = discretize(V, domain_h, degree=degree) DP = DirichletProjector(Vh, kind='hcurl') # or 'hdiv' ``` Similarity with `conforming_projectors` -------------------------------------------------------- Identical to `derham_h.conforming_projectors(kind='linop', hom_bc=True)` **on a single-patch**. On **multi-patch** domains, `derham_h.conforming_projectors` also affect the solution at the **interfaces** between patches, as required by the broken-FEEC theory. If required, they have the additional ability to preserve moments of the solution. Unfortunately, the conforming projectors are only implemented in 2D. --------- Co-authored-by: Frederik Schnack <frederik.schnack@ipp.mpg.de>

add dirichlet projectors and tests

fe9b0d0

jowezarek marked this pull request as ready for review October 30, 2025 15:20

jowezarek requested a review from yguclu October 30, 2025 15:20

jowezarek mentioned this pull request Oct 30, 2025

Add diagonal() to KroneckerStencilMatrix #537

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FrederikSchnack added 2 commits October 31, 2025 14:12

fix periodic BC in conforming projectors and add test

a898cae

add preliminary DirichletMultipatchBoundaryProjector

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jowezarek mentioned this pull request Oct 31, 2025

Add LST preconditioner #538

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jowezarek added 2 commits October 31, 2025 15:48

Merge branch 'devel' into dirichlet

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move Dirichlet projectors to fem.projectors

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move import, add dirichlet_proj as attribute, return tuple, add ident…

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…ity proj

remove periodic from _get_bcs in multipatch case

8bbb6b6

change tolerance in _test_LO_equality...

08f5525

make dim a parameter, add sqrts, compute errs better

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add empty lines

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include type checks

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bug fix

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add docstrings

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jowezarek added 2 commits November 4, 2025 13:41

addressing comments

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Codacity fix

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addressing comments pt. 2

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add docstrings to conforming projections, change DiscreteDeRhamMultip…

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add toarray, tosparse, and tests

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Add Dirichlet Boundary Projectors #536

Add Dirichlet Boundary Projectors #536

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DirichletProjector

Usage

Similarity with conforming_projectors

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jowezarek commented Oct 30, 2025 •

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