ReferenceAlpha
Weak Form PDE
Defines optimization applicability and derivative ownership for Weak Form PDE.
Reference
| Field | Value | Description |
|---|---|---|
| kind | Weak Form PDE | — |
| namespace | w | — |
| status | development | — |
| visible | false | — |
| optimizationContract | {"baseStudies":["stationary"],"baseStudyExclusions":[],"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","constraintRules":[],"contributionBindings":[{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contribution":"domain-feature:Weak Form Domain","runtimeOwner":"WeakFormPDE.supported_scalar_weak_forms"},{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contribution":"boundary-feature:Point Constraint","runtimeOwner":"WeakFormPDE.supported_scalar_weak_forms"},{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contribution":"boundary-feature:Weak Contribution","runtimeOwner":"WeakFormPDE.supported_scalar_weak_forms"},{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contribution":"weak-contribution:w.domain","runtimeOwner":"WeakFormPDE.supported_scalar_weak_forms"}],"functionalReductions":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum","value"],"geometricModes":{"coordinate":{"applicability":"required","reason":""},"materialTopology":{"applicability":"required","reason":""}},"historyFields":[],"objectiveRules":[{"entityDimensions":["global","domain","boundary","point"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supportsSelection":true,"symbols":["w.u"],"valueKind":"field"},{"entityDimensions":["global"],"modes":["stationary"],"operators":["value"],"supportsSelection":false,"symbols":["w.energy"],"valueKind":"scalar-global"},{"entityDimensions":["global"],"modes":["stationary"],"operators":["value"],"supportsSelection":false,"symbols":["w.compliance"],"valueKind":"scalar-global"}],"objectiveSymbols":["w.u","w.energy","w.compliance"],"requiredDerivativeChannels":["parameter","input","coordinate","material"],"role":"spatial-analysis","runtimeProvider":"WeakFormPDE.supported_scalar_weak_forms","schemaVersion":"1.0.0","stateFields":["u"]} | — |
| governingEquations | [{"description":"","differentiability":"exact-ad","editor":null,"entityDimension":"domain","latex":"\\int_{\\Omega} F(u,\\nabla u,\\mathrm{test}(u),\\nabla\\mathrm{test}(u))\\,d\\Omega=0","mathml":"<math display=\"block\"><mrow><mo>∫</mo><mi>F</mi><mo>d</mo><mi>Ω</mi><mo>=</mo><mn>0</mn></mrow></math>","name":"Scalar weak equation","readOnly":true,"section":"governing-equation"}] | — |
The runtime provider, evidence fixture, derivative channels, geometric modes, objective symbols, reductions, contribution bindings, and governing equations are generated from the physics catalog.