Field Examples

Field types provide grid storage for PDE and vector-calculus examples.

Scalar Field

const int nx = 64;
const int ny = 64;
const int nz = 64;
const float dx = 1.0f / 63.0f;
 
num::ScalarField3D rho(nx, ny, nz, dx);
rho.fill([&](int i, int j, int k) {
    const double x = i * dx;
    const double y = j * dx;
    const double z = k * dx;
    return std::exp(-40.0 * ((x - 0.5) * (x - 0.5)
                           + (y - 0.5) * (y - 0.5)
                           + (z - 0.5) * (z - 0.5)));
});

Vector Field

num::VectorField3D v(nx, ny, nz, dx);
v.x.fill(0.0);
v.y.fill(0.0);
v.z.fill(1.0);

Poisson Utility

num::ScalarField3D phi(nx, ny, nz, dx);
 
num::SolverResult info =
    num::FieldSolver::solve_poisson(phi, rho, 1e-8, 1000);

Internally this wraps the finite-difference operator with num::operators::make_op and solves with conjugate gradients.

Magnetic Field Utility

num::VectorField3D J(nx, ny, nz, dx);
load_current_density(J);
 
num::VectorField3D B = num::MagneticSolver::solve_magnetic_field(J);

This computes vector potential components from Poisson solves and returns \(\mathbf{B}=\nabla\times\mathbf{A}\).