[FEM] Introduce higher accuracy quadrature rules by th-skam · Pull Request #6225 · sofa-framework/sofa

th-skam · 2026-08-10T16:12:38Z

For each Element, an option is added to use a higher-accuracy quadrature rule. The default behaviour of existing force fields is preserved. Lower-order rules are also included for completeness.

The purpose of this change is to enable more accurate error-norm computations in the V&V suite using the Method of Manufactured Solutions.

If the accuracy is insufficient, the integration introduces errors in the computed norms. This we observe either as the convergence rate approaching the expected one more slowly or as apparent superconvergence that counters the purpose of the test.

The degrees are:

Element	Up to degree	Default degree
Edge	3	1
Quad	3	2
Tri	2	1
Tetra	2	1
Hex	5	3

[with-all-tests]

By submitting this pull request, I acknowledge that
I have read, understand, and agree SOFA Developer Certificate of Origin (DCO).

Reviewers will merge this pull-request only if

it builds with SUCCESS for all platforms on the CI.
it does not generate new warnings.
it does not generate new unit test failures.
it does not generate new scene test failures.
it does not break API compatibility.
it is more than 1 week old (or has fast-merge label).

alxbilger

I would be curious to know how you use quadratureRule

th-skam · 2026-08-26T11:27:05Z

@alxbilger
It was used like so in my cases: 97581c5

sofabot · 2026-08-27T08:35:11Z

[ci-depends-on] detected during build #4.

To unlock the merge button, you must

Merge or close Bindings for quadrature data and element Jacobian SofaPython3#634
For this build, the following CMake flags will be set
-DSOFAPYTHON3_GIT_REPOSITORY='https://github.com/sofa-framework/SofaPython3'
-DSOFAPYTHON3_GIT_TAG='e094b25a72b3ebfa0bb993670a959c190ca7d642'

sofabot · 2026-09-01T14:24:16Z

[ci-depends-on] detected during build #5.

To unlock the merge button, you must

Merge or close Bindings for quadrature data and element Jacobian SofaPython3#634
For this build, the following CMake flags will be set
-DSOFAPYTHON3_GIT_REPOSITORY='https://github.com/sofa-framework/SofaPython3'
-DSOFAPYTHON3_GIT_TAG='e094b25a72b3ebfa0bb993670a959c190ca7d642'

alxbilger

Could you just add the new quadrature points to the unit tests testSumWeights ? It's not enough, but there are not other tests for now...

sofabot · 2026-09-04T12:20:46Z

[ci-depends-on] detected during build #6.

To unlock the merge button, you must

Merge or close Bindings for quadrature data and element Jacobian SofaPython3#634
For this build, the following CMake flags will be set
-DSOFAPYTHON3_GIT_REPOSITORY='https://github.com/sofa-framework/SofaPython3'
-DSOFAPYTHON3_GIT_TAG='e094b25a72b3ebfa0bb993670a959c190ca7d642'

alxbilger · 2026-09-04T18:15:01Z

I think you can remove the ci-depends-on. It's actually the other PR that needs this one.

th-skam · 2026-09-14T08:22:31Z

Now that we added quadratic elements, I refactored the quadrature rules. Linear or quadratic, the integration is done over the same reference domain. The rules are now re-used, implemented in QuadratureRules.h. AI was used to help with std usage to have compile-time/runtime paths.

The literals were also substituted by std:: variants, wherever possible. This has triggered a unit test failure in ElementMass__test.

New rules can be added in the existing tables. There are two paths:

Compile-time: using the function quadraturePoints<Degree>. It has a default value, and it is the one used by the existing FEM force fields
Runtime: using quadratureRule and requesting a degree. I use this path for the source terms in [FEM] Add component for source term integration based on new FEM framework - constant source terms #6196

Each element has a default and minimum degree, so quadratic elements cannot use 1st order rules.
Will work on populating tests, either here or in subsequent PR.

th-skam · 2026-10-01T14:03:53Z

For the failing tests on ubuntu, we were failing by a small margin (2.27e-13 and 9.0949e-13 against 2.2204e-13 🥹 ).
I turned the comparison to normalize with the value it's compared against. Which should be more fair in general.

hugtalbot · 2026-10-01T20:59:48Z

+            // 4-point rule
+            constexpr Real sqrt5 = static_cast<Real>(2.23606797749978969640917366873); // sqrt(5)
+            constexpr Real a = (static_cast<Real>(5) - sqrt5) / static_cast<Real>(20);
+            constexpr Real b = (static_cast<Real>(5) + static_cast<Real>(3) * sqrt5) / static_cast<Real>(20);
+            constexpr Real w = static_cast<Real>(1) / static_cast<Real>(24); // 1/24
+
+            return std::array<PointAndWeight, 4>{
+                std::make_pair(Point(a, a, a), w),
+                std::make_pair(Point(b, a, a), w),
+                std::make_pair(Point(a, b, a), w),
+                std::make_pair(Point(a, a, b), w)


This code appears to be a custom 4-point quadrature rule for a tetrahedron. Is this on purpose?
Yet still valid ✔️

Not a custom one. It's the one from FiniteElement[QuadraticTetrahedron] and literals were replaced with a computation involving sqrt(5) etc.
Online I find it as the T3P2 Hammer-Stroud rule, degree 2, 4 points.
Quick example here: https://www.cfd-online.com/Wiki/Code:_Quadrature_on_Tetrahedra

I could catalogue the available rules at some point with references & doc but better not in this PR.

th-skam added pr: status to review To notify reviewers to review this pull-request pr: new feature Implement a new feature labels Aug 10, 2026

th-skam force-pushed the quadrature-rules branch from ec846d2 to 5ad33f1 Compare August 10, 2026 16:14

th-skam added the pr: AI-aided Label notifying the reviewers that part or all of the PR has been generated with the help of an AI label Aug 10, 2026

alxbilger reviewed Aug 26, 2026

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th-skam mentioned this pull request Aug 26, 2026

[FEM] Add component for source term integration based on new FEM framework - constant source terms #6196

Open

th-skam force-pushed the quadrature-rules branch from b8c7deb to 9c42dbf Compare September 1, 2026 14:23

alxbilger reviewed Sep 3, 2026

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th-skam force-pushed the quadrature-rules branch from 9bdcbf1 to 9de02d8 Compare September 14, 2026 08:09

th-skam mentioned this pull request Sep 14, 2026

Bindings for quadrature data and element Jacobian sofa-framework/SofaPython3#634

Open

fredroy force-pushed the quadrature-rules branch from fd61524 to 95a7d95 Compare September 15, 2026 02:30

th-skam requested a review from alxbilger September 17, 2026 08:14

th-skam added 12 commits September 23, 2026 10:29

[FEM] Introduce higher order quadrature rule switch for Triangle

f70bd97

Edge

542d147

Tetrahedra

2f86678

Quad

e0a5955

Hexa

39d2942

Use uint for degree

4abd0a2

Adopt quadratureRule in prism and pyramid

85b9f79

Include quadratureRule in FE test

f6b83fc

Add polynomial order to linear elements

b6569cd

[FEM] Add QuadratureRules.h

fe026d9

Add the ElementQuadrature class

1681cc5

[FEM] Bridge reference domain for quadratic/linear edges

2f3c194

th-skam added 3 commits September 23, 2026 10:29

[FEM] Adopt Quadrature rule dispatch

8b83e4e

Remove is-a and go for has-a

d461e81

remove comments

e8d49f6

fredroy force-pushed the quadrature-rules branch from 95a7d95 to e8d49f6 Compare September 23, 2026 01:29

alxbilger approved these changes Oct 1, 2026

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th-skam added 2 commits October 1, 2026 15:56

Use normalized difference for evaluating error in test

53f50bf

Stricten errorMax as is affordable

b159486

Remove useless include

f15663f

hugtalbot approved these changes Oct 1, 2026

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Merge branch 'master' into quadrature-rules

8915c6c

hugtalbot added pr: status ready Approved a pull-request, ready to be squashed and removed pr: status to review To notify reviewers to review this pull-request labels Oct 8, 2026

hugtalbot merged commit 538e91d into sofa-framework:master Oct 8, 2026
13 of 14 checks passed

th-skam deleted the quadrature-rules branch October 9, 2026 08:57

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[FEM] Introduce higher accuracy quadrature rules - #6225

[FEM] Introduce higher accuracy quadrature rules#6225
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