field.hpp

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/// @file field.hpp
/// @brief EM-specific field types and solvers.
///
/// ScalarField3D, VectorField3D, FieldSolver, and MagneticSolver now live in
/// the numerics library (include/spatial/fields.hpp) in the num:: namespace.
/// This file brings them into the physics:: namespace and adds the
/// EM-specific ElectricSolver (variable-conductivity current flow).
#pragma once
 
#include "spatial/fields.hpp"
#include "linalg/solvers/solvers.hpp"
#include <vector>
 
namespace physics {
 
using ScalarField3D  = num::ScalarField3D;
using VectorField3D  = num::VectorField3D;
using FieldSolver    = num::FieldSolver;
using MagneticSolver = num::MagneticSolver;
 
// ============================================================
// ElectrodeBC + ElectricSolver
// ============================================================
 
/// A grid node with a fixed voltage (Dirichlet BC for current flow).
struct ElectrodeBC {
    int   flat_idx;  ///< Flat grid index: k*ny*nx + j*nx + i
    float voltage;   ///< Applied voltage [V]
};
 
class ElectricSolver {
public:
    /// Solve div(σ∇φ) = 0 with Dirichlet BCs at electrode nodes,
    /// Neumann (zero normal flux) on all remaining boundaries.
    ///
    /// Uses symmetric elimination so the system is SPD → CG converges.
    static num::SolverResult solve_potential(ScalarField3D& phi,
                                             const ScalarField3D& sigma,
                                             const std::vector<ElectrodeBC>& bcs,
                                             double tol      = 1e-6,
                                             int    max_iter = 500);
 
    /// Compute Joule heating power density Q = σ|∇φ|² [W/m³].
    static ScalarField3D joule_heating(const ScalarField3D& sigma,
                                       const ScalarField3D& phi);
};
 
} // namespace physics