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Shape Optimization

Defines optimization applicability and derivative ownership for Shape Optimization.

Reference contract

FieldValueDescription
kindShape Optimization
namespaceshape
statusdevelopment
visiblefalse
optimizationContract{"baseStudies":["optimization"],"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contributionBindings":[{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contribution":"boundary-feature:Free Shape Boundary","runtimeOwner":"telion_backend.v2.runtimes.shape.optimize_free_shape"},{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","contribution":"boundary-feature:Fixed Mesh Boundary","runtimeOwner":"telion_backend.v2.runtimes.shape.optimize_free_shape"}],"functionalReductions":[],"geometricModes":{"coordinate":{"applicability":"design-provider","reason":""},"materialTopology":{"applicability":"inapplicable","reason":"Shape Optimization moves coordinates and does not define a material topology field."}},"historyFields":[],"objectiveRules":[],"objectiveSymbols":[],"requiredDerivativeChannels":["coordinate"],"role":"shape-design","runtimeProvider":"telion_backend.v2.runtimes.shape.optimize_free_shape","schemaVersion":"1.0.0","stateFields":["d"]}
governingEquations[{"description":"","differentiability":"analytic","editor":null,"entityDimension":"boundary","latex":"\\left(I+\\left(\\frac{r_f}{h_\\Gamma}\\right)^2L_\\Gamma\\right)\\widetilde{\\mathbf d}_\\Gamma=\\mathbf c_\\Gamma","mathml":"<math display=\"block\"><mrow><mo>(</mo><mi>I</mi><mo>+</mo><msup><mrow><mo>(</mo><mfrac><msub><mi>r</mi><mi>f</mi></msub><msub><mi>h</mi><mi>Γ</mi></msub></mfrac><mo>)</mo></mrow><mn>2</mn></msup><msub><mi>L</mi><mi>Γ</mi></msub><mo>)</mo><msub><mover><mi mathvariant=\"bold\">d</mi><mo>~</mo></mover><mi>Γ</mi></msub><mo>=</mo><msub><mi mathvariant=\"bold\">c</mi><mi>Γ</mi></msub></mrow></math>","name":"Surface control filter","readOnly":true,"section":"definition"},{"description":"","differentiability":"analytic","editor":null,"entityDimension":"domain","latex":"L_{ff}\\mathbf d_f=-L_{fb}\\mathbf d_b","mathml":"<math display=\"block\"><mrow><msub><mi>L</mi><mi>ff</mi></msub><msub><mi mathvariant=\"bold\">d</mi><mi>f</mi></msub><mo>=</mo><mo>−</mo><msub><mi>L</mi><mi>fb</mi></msub><msub><mi mathvariant=\"bold\">d</mi><mi>b</mi></msub></mrow></math>","name":"Harmonic ALE extension","readOnly":true,"section":"governing-equation"},{"description":"","differentiability":"analytic","editor":null,"entityDimension":"domain","latex":"\\mathbf x=\\mathbf X+\\mathbf d_\\Omega","mathml":"<math display=\"block\"><mrow><mi mathvariant=\"bold\">x</mi><mo>=</mo><mi mathvariant=\"bold\">X</mi><mo>+</mo><msub><mi mathvariant=\"bold\">d</mi><mi>Ω</mi></msub></mrow></math>","name":"Deformed coordinates","readOnly":true,"section":"definition"},{"description":"","differentiability":"analytic","editor":null,"entityDimension":"domain","latex":"\\frac{\\partial\\mathbf x}{\\partial\\mathbf c_\\Gamma}=\\mathbf P_{\\mathrm{ALE}}\\mathbf P_{\\mathrm{filter}}","mathml":"<math display=\"block\"><mrow><mfrac><mrow><mo>∂</mo><mi mathvariant=\"bold\">x</mi></mrow><mrow><mo>∂</mo><msub><mi mathvariant=\"bold\">c</mi><mi>Γ</mi></msub></mrow></mfrac><mo>=</mo><msub><mi mathvariant=\"bold\">P</mi><mi>ALE</mi></msub><msub><mi mathvariant=\"bold\">P</mi><mi>filter</mi></msub></mrow></math>","name":"Exact design-to-coordinate derivative","readOnly":true,"section":"definition"},{"description":"","differentiability":"analytic","editor":null,"entityDimension":"boundary","latex":"\\mathbf d_\\Omega=\\mathbf0\\quad\\mathrm{on}\\ \\Gamma_f","mathml":"<math display=\"block\"><mrow><msub><mi mathvariant=\"bold\">d</mi><mi>Ω</mi></msub><mo>=</mo><mn>0</mn><mspace width=\"1em\"/><mtext>on</mtext><mspace width=\".5em\"/><msub><mi>Γ</mi><mi>f</mi></msub></mrow></math>","name":"Fixed mesh boundary","readOnly":true,"section":"constraint"},{"description":"","differentiability":"semismooth","editor":null,"entityDimension":"global","latex":"\\min_{e\\in\\mathcal T}\\frac{\\det J_e(\\mathbf x)}{\\det J_e(\\mathbf X)}>J_{\\min}","mathml":"<math display=\"block\"><mrow><munder><mi>min</mi><mrow><mi>e</mi><mo>∈</mo><mi>𝒯</mi></mrow></munder><mfrac><mrow><mi>det</mi><msub><mi>J</mi><mi>e</mi></msub><mo>(</mo><mi mathvariant=\"bold\">x</mi><mo>)</mo></mrow><mrow><mi>det</mi><msub><mi>J</mi><mi>e</mi></msub><mo>(</mo><mi mathvariant=\"bold\">X</mi><mo>)</mo></mrow></mfrac><mo>&gt;</mo><msub><mi>J</mi><mi>min</mi></msub></mrow></math>","name":"Mesh-quality inequality","readOnly":true,"section":"constraint"}]

The runtime provider, evidence fixture, derivative channels, geometric modes, objective symbols, reductions, contribution bindings, and governing equations are generated from the physics catalog.

Authoritative source

Catalog
telion_backend.v2.catalog.PhysicsCatalog
Identity
PhysicsDeclaration/shape/optimizationContract
Path
src/telion_backend/v2/physics/specs.py
Symbol
DifferentiablePhysicsContract