ReferenceAlpha
Coefficient Form PDE
Defines optimization applicability and derivative ownership for Coefficient Form PDE.
Reference
| Field | Value | Description |
|---|---|---|
| kind | Coefficient Form PDE | — |
| namespace | cfpde | — |
| 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:Coefficient Form Equation","runtimeOwner":"CoefficientFormPDE.element_residual"},{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contribution":"boundary-feature:Dirichlet Boundary Condition","runtimeOwner":"CoefficientFormPDE.element_residual"},{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contribution":"boundary-feature:Flux Boundary Condition","runtimeOwner":"CoefficientFormPDE.element_residual"},{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contribution":"weak-contribution:cfpde.coefficient","runtimeOwner":"CoefficientFormPDE.element_residual"}],"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":["cfpde.u"],"valueKind":"field"},{"entityDimensions":["global"],"modes":["stationary"],"operators":["value"],"supportsSelection":false,"symbols":["cfpde.energy"],"valueKind":"scalar-global"},{"entityDimensions":["global"],"modes":["stationary"],"operators":["value"],"supportsSelection":false,"symbols":["cfpde.compliance"],"valueKind":"scalar-global"}],"objectiveSymbols":["cfpde.u","cfpde.energy","cfpde.compliance"],"requiredDerivativeChannels":["parameter","input","coordinate","material"],"role":"spatial-analysis","runtimeProvider":"CoefficientFormPDE.element_residual","schemaVersion":"1.0.0","stateFields":["u"]} | — |
| governingEquations | [{"description":"","differentiability":"exact-ad","editor":null,"entityDimension":"domain","latex":"-\\nabla\\!\\cdot\\!\\left(c\\nabla u\\right)=f","mathml":"<math display=\"block\"><mrow><mo>-</mo><mo>∇</mo><mo>⋅</mo><mo>(</mo><mi>c</mi><mo>∇</mo><mi>u</mi><mo>)</mo><mo>=</mo><mi>f</mi></mrow></math>","name":"Coefficient form elliptic 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.