ReferenceAvailable
Electrostatics
Electrostatic potential and Poisson equation reference implementation.
Reference
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.coupled_fields","adjoint_vjp_owner":"ElectrostaticsCoupledAdapter","certification":"Quasistatic Poisson block with exact sparse state Jacobian and terminal reaction-charge outputs.","checkpointing":true,"dynamic_state_schema":false,"execution_backend":"telion-v2-shared-execution","gradient_channels":["electrostatics.materials","electrostatics.coordinates","electrostatics.terminals"],"history_depth":1,"history_jacobian_owner":"ElectrostaticsCoupledAdapter","jacobian_owner":"ElectrostaticsCoupledAdapter","nonlinear_solver":"CoupledNewtonSession","output_vjp_owner":"ElectrostaticsCoupledAdapter","requires_spatial_mesh":true,"residual_owner":"ElectrostaticsCoupledAdapter","runtime":"telion-coupled-graph","state_fields":["es.V"],"supported_integrators":["BDF1","BDF2"]} | — |
| differentiable_runtime | {"certification":"ElectrostaticsScalarEllipticRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["permittivity"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["es.V"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["stationary","transient"],"operators":["value"],"supports_selection":false,"symbols":["es.energy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["es.compliance"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["transient"],"operators":["value"],"supports_selection":false,"symbols":["es.terminal.*"],"value_kind":"scalar-global"}],"residual_owner":"Electrostatics.element_residual","state_fields":["V"],"supported_objective_symbols":{"coordinate":["es.V","es.energy","es.compliance"],"material":["es.V","es.energy","es.compliance"],"topology":["es.V","es.energy","es.compliance"]},"topology_expression_gradient":true} | — |
| dynamic_outputs | [] | — |
| equation_summary | -div(epsilon*grad(V)) = rho | — |
| frequency_domain_runtime | null | — |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Available.","selectable":true}} | — |
| preferred_material | null | — |
| schema_version | 0.1.0 | — |
| stateVariables | [{"adjointDescription":"Scalar elliptic adjoint solve supports electric-potential expression objectives and permittivity sensitivities.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"es.V","complexValued":false,"componentDescriptions":["Electric potential"],"componentNames":["V"],"componentSymbols":["es.V"],"components":1,"description":"Electrostatic scalar potential.","differentiability":"exact-ad","displayName":"Electric potential","finiteElementSpace":"H1-P1","initialValue":"0","location":"node","name":"V","namingPolicy":"fixed","quantityId":"es.V","rank":"scalar","role":"state","runtimeEvidence":{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","provider":"Electrostatics.element_residual"},"symbolPattern":null,"unit":"V"}] | — |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: exact affine potential field on a tetrahedral block"},{"certified":false,"differentiability":"exact-ad","kind":"transient","reason":"Standalone Electrostatics has no time-evolution operator."},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Sensitivity is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"optimization","reason":"Optimization is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"eigenvalue","reason":"Eigenvalue is unavailable for this physics interface."}] | — |
| transient_runtime | {"capacity_properties":[],"certification":"ElectrostaticsCoupledAdapter","checkpointing":true,"design_properties":["permittivity"],"design_property_conditions":{},"design_vjp_owner":"ElectrostaticsCoupledAdapter","expression_objectives":true,"gradient_channels":["coordinates","electrostatics.coordinates","electrostatics.materials","electrostatics.terminals","parameter","material","input"],"gradient_vjp_owner":"ElectrostaticsCoupledAdapter","history_depth":1,"input_gradient":true,"input_vjp_owner":"ElectrostaticsCoupledAdapter","observation_vjp_owner":"ElectrostaticsCoupledAdapter","residual_linearization_owner":"ElectrostaticsCoupledAdapter","runtime":"coupled-quasistatic-electrostatics","state_fields":["V"],"state_reconstruction_owner":"ElectrostaticsCoupledAdapter","supported_integrators":["BDF1","BDF2"],"supported_observation_symbols":["es.V","es.energy","es.terminal.*"],"time_derivative_orders":{"V":0},"topology_gradient":true,"transpose_solve_owner":"CoupledNewtonSession"} | — |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(es.V)), permittivity*grad(es.V)) - test(es.V)*chargeDensity","name":"es.poisson","test_field":"es.V"}] | — |
| category | AC/DC | — |
| description | Electrostatic potential and Poisson equation reference implementation. | — |
| dimensions | [3] | — |
| display_name | Electrostatics | — |
| kind | Electrostatics | — |
| namespace | es | — |
| status | certified | — |
| visible | true | — |
Electrostatic potential and Poisson equation reference implementation.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.coupled_fields","adjoint_vjp_owner":"ElectrostaticsCoupledAdapter","certification":"Quasistatic Poisson block with exact sparse state Jacobian and terminal reaction-charge outputs.","checkpointing":true,"dynamic_state_schema":false,"execution_backend":"telion-v2-shared-execution","gradient_channels":["electrostatics.materials","electrostatics.coordinates","electrostatics.terminals"],"history_depth":1,"history_jacobian_owner":"ElectrostaticsCoupled... |
| differentiable_runtime | {"certification":"ElectrostaticsScalarEllipticRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["permittivity"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","sm... |
| dynamic_outputs | [] |
| equation_summary | -div(epsilon*grad(V)) = rho |
| frequency_domain_runtime | null |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Available.","selectable":true}} |
| preferred_material | null |
| schema_version | 0.1.0 |
| stateVariables | [{"adjointDescription":"Scalar elliptic adjoint solve supports electric-potential expression objectives and permittivity sensitivities.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"es.V","complexValued":false,"componentDescriptions":["Electric potential"],"componentNames":["V"],"componentSymbols":["es.V"],"components":1,"description":"Electrostatic scalar potential.","differentiability":"exact-ad","displayName":"Electric potential","finiteElementSpace":"H1... |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: exact affine potential field on a tetrahedral block"},{"certified":false,"differentiability":"exact-ad","kind":"transient","reason":"Standalone Electrostatics has no time-evolution operator."},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Sensitivity is unavailable for this physics interface."},{"certified":false,"differentiability":"ex... |
| transient_runtime | {"capacity_properties":[],"certification":"ElectrostaticsCoupledAdapter","checkpointing":true,"design_properties":["permittivity"],"design_property_conditions":{},"design_vjp_owner":"ElectrostaticsCoupledAdapter","expression_objectives":true,"gradient_channels":["coordinates","electrostatics.coordinates","electrostatics.materials","electrostatics.terminals","parameter","material","input"],"gradient_vjp_owner":"ElectrostaticsCoupledAdapter","history_depth":1,"input_gradient":true,"input_vjp_ow... |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(es.V)), permittivity*grad(es.V)) - test(es.V)*chargeDensity","name":"es.poisson","test_field":"es.V"}] |
| category | AC/DC |
| description | Electrostatic potential and Poisson equation reference implementation. |
| dimensions | [3] |
| display_name | Electrostatics |
| kind | Electrostatics |
| namespace | es |
| status | certified |
| visible | true |