Field Solvers

PyPIC3D supports two production runtime modes selected from simulation_parameters.

Runtime Modes

Electrostatic mode

Set:

solver = "electrostatic"

Per step, PyPIC3D:

1. Pushes particles.

2. Deposits rho.

3. Solves Poisson’s equation for phi.

4. Computes E = -grad(phi).

The electrostatic path uses the finite-difference Yee method:

• conjugate-gradient Poisson solve for phi

• centered finite-difference gradient for E = -grad(phi)

Electrodynamic mode

Set:

solver = "electrodynamic_yee"

Per step, PyPIC3D:

1. Pushes particles.

2. Deposits current J.

3. Updates E.

4. Updates B.

The electrodynamic update uses first-order Yee-style kernels in PyPIC3D.solvers.first_order_yee.

Electrodynamic Update Equations

\[\mathbf{E}^{n+1} = \mathbf{E}^{n} + \Delta t \left(c^2 \nabla \times \mathbf{B}^{n} - \frac{\mathbf{J}^{n}}{\epsilon_0}\right)\]

\[\mathbf{B}^{n+1} = \mathbf{B}^{n} - \Delta t \left(\nabla \times \mathbf{E}^{n+1}\right)\]

PyPIC3D additionally applies a digital filter controlled by constants.alpha to field components each update.

Boundary Conditions

Field boundary conditions are defined by:

• simulation_parameters.x_bc

• simulation_parameters.y_bc

• simulation_parameters.z_bc

Supported values:

• periodic

• conducting

For conducting boundaries, tangential electric-field components are zeroed on boundary faces during the E update.

Current Deposition Selection

Current deposition is selected by:

current_calculation = "j_from_rhov"

or

current_calculation = "esirkepov"

See Current Deposition for behavior and tradeoffs.