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docs/src/guide/boundaries.md

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## Flux boundary
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Flux loop boundary conditions are available for magnetostatic simulations and are specified using the [`"FluxLoop"`](../config/boundaries.md#boundaries%5B%22FluxLoop%22%5D)
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boundary keyword. This boundary condition prescribes magnetic flux through specified holes in conducting surfaces,
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enabling inductance matrix extraction for flux-based excitations. The flux loop boundary condition works by:
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1. **Identifying holes**: Mesh boundary attributes specify holes through which flux is prescribed
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2. **Constraining flux**: The total magnetic flux through each hole is set to the specified value
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3. **Solving surface problem**: A 2D surface curl problem determines the required boundary conditions for the 3D problem
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4. **Computing inductance**: The resulting 3D field solutions enable inductance matrix extraction
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Flux loop boundary conditions are available for magnetostatic simulations and are specified
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using the [`"FluxLoop"`](../config/boundaries.md#boundaries%5B%22FluxLoop%22%5D) boundary
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keyword. This boundary condition prescribes magnetic flux through specified holes in
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conducting surfaces, enabling inductance matrix extraction for flux-based excitations. The
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flux loop boundary condition works by:
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1. **Identifying holes**: Mesh boundary attributes specify holes through which flux is
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prescribed
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2. **Constraining flux**: The total magnetic flux through each hole is set to the specified
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value
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3. **Solving surface problem**: A 2D surface curl problem determines the required boundary
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conditions for the 3D problem
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4. **Computing inductance**: The resulting 3D field solutions enable inductance matrix
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extraction
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!!! note "Flux loop requirements"
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Flux loop boundaries require:
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- Metal surface attributes defining the conducting surface containing the holes
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- Hole attributes specifying the boundaries through which flux is prescribed
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- Flux amounts defining the magnetic flux through each hole
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- Loop normal vector defining the flux orientation
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The mesh must be topologically compatible with the flux loop geometry, with holes properly defined as
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boundary surfaces within the conducting region. Currently, only planar holes are supported.
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- Metal surface attributes defining the conducting surface containing the holes
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- Hole attributes specifying the boundaries through which flux is prescribed
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- Flux amounts defining the magnetic flux through each hole
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- Loop normal vector defining the flux orientation
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The mesh must be topologically compatible with the flux loop geometry, with holes properly
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defined as boundary surfaces within the conducting region. Currently, only planar holes are
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supported.

docs/src/guide/problem.md

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For magnetostatic simulations,
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([`config["Problem"]["Type"]: "Magnetostatic"`](../config/problem.md#config%5B%22Problem%22%5D),
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the user can specify excitations using either source current boundaries or flux loop boundaries.
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the user can specify excitations using either source current boundaries or flux loop
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boundaries.
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### Current source excitation
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For current-based excitations, specify a number of source current boundaries. For each current source, a
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magnetostatic field is computed by applying a unit current to the source index of interest,
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leaving all other sources open with no excitation. Surfaces which are expected to carry
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current should be labeled as perfectly conducting, which prescibes a zero magnetic flux, or
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For current-based excitations, specify a number of source current boundaries. For each
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current source, a magnetostatic field is computed by applying a unit current to the source
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index of interest, leaving all other sources open with no excitation. Surfaces which are
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expected to carry current should be labeled as perfectly conducting, which prescibes a zero
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magnetic flux, or
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[magnetic insulation](https://doc.comsol.com/5.5/doc/com.comsol.help.comsol/comsol_ref_acdc.17.74.html),
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boundary condition.
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### Flux loop excitation
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Alternatively, flux loop boundaries
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([`config["Boundaries"]["FluxLoop"]`](../config/boundaries.md#boundaries%5B%22FluxLoop%22%5D))
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can be used to prescribe magnetic flux through specified holes in conducting surfaces. For each flux loop, a
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magnetostatic field is computed by applying flux through the loop of interest,
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leaving all other flux loops with zero flux. This enables inductance matrix extraction for flux-based excitations.
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can be used to prescribe magnetic flux through specified holes in conducting surfaces. For
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each flux loop, a magnetostatic field is computed by applying flux through the loop of
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interest, leaving all other flux loops with zero flux. This enables inductance matrix
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extraction for flux-based excitations.
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### Mixed current-flux systems
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Both current sources and flux loops can be specified in the same simulation, enabling inductance matrix
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extraction for mixed excitation systems. In this case, *Palace* solves a system of equations to compute
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the exact inductance matrix accounting for coupling between current and flux excitations.
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Both current sources and flux loops can be specified in the same simulation, enabling
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inductance matrix extraction for mixed excitation systems. In this case, *Palace* solves a
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system of equations to compute the exact inductance matrix accounting for coupling between
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current and flux excitations.
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### Output files
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The resulting fields are used to compute the inductance matrix and its
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inverse, which are written to an ASCII file named `terminal-M.csv` and `terminal-Minv.csv`,
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respectively, in the directory specified by
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The resulting fields are used to compute the inductance matrix and its inverse, which are
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written to an ASCII file named `terminal-M.csv` and `terminal-Minv.csv`, respectively, in
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the directory specified by
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[`config["Problem"]["Output"]`](../config/problem.md#config%5B%22Problem%22%5D). A "mutual"
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inductance matrix which has the same form as the mutual capacitance matrix (its entries are
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based on current differences between ports rather than absolute currents) is computed and
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written to `terminal-Mm.csv` in the same directory.
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written to `terminal-Mm.csv` in the same directory.

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