PRISM

PRISM (Plasma Research usIng Simulation Methods) is the electromagnetics and plasma application of ADAM. It solves Maxwell's equations for the electric displacement $\mathbf{D}$ and the magnetic induction $\mathbf{B}$ with centred finite differences or finite volumes on block-structured adaptive grids, optionally coupled to charged macro-particles by a particle-in-cell (PIC) method, on CPUs (MPI + OpenMP) and on GPUs (MPI + OpenACC).

What is implemented

Area	Capabilities	Details
Physics	Maxwell's equations in SI or non-dimensional form, with a prescribed current density (coils) or the current and charge of PIC macro-particles; hyperbolic (GLM) divergence cleaning of $\mathbf{D}$, $\mathbf{B}$ or both	Physical models
Space	Centred finite differences or finite volumes of order 2–10 ([fdv]); WENO flux splitting (CPU only)	Numerical methods
Time	Runge–Kutta (SSP 11/22/33/54, low-storage 1/2/3, Yoshida on the CPU), CFL time step on the speed of light	Numerical methods
Grid	Octree/quadtree of Cartesian blocks, AMR at initialization (box and current-variation markers), 2:1 coarse–fine faces, FV reflux	Numerical methods
Coupling	Multi-realm runs glued by a forest manifest, α or β seam cadence	Numerical methods
Sources	Rectangular, circular, solenoid and helicon coils, DC or AC, with a smooth ramp; external rotating or uniform fields (acting on the particles)	Initial conditions and sources
Boundaries	Extrapolation, Neumann, Dirichlet (zero), first-order Silver–Müller, PEC, periodic; perfectly matched layers (four formulations) and a far-wave damping layer	Boundary conditions, Absorbing layers
Particles	Plasma (uniform, cylinder, slab, box) or a single test particle; Maxwellian or drift velocities; charge and current deposition from NGP to sixth order and Gaussian; charge-conserving currents with periodic faces; Runge–Kutta push	Particle-in-cell
t0 fields	The electric field of the initial charge and the magnetic field of the initial current, solved by FLAIL with PRISM's own operator	Numerical methods
Input	One INI file per realm, every value checked, refusals at initialization	Input reference
Output	XDMF + HDF5 field files (ParaView), restart files, slices, probes, residual, energy, divergence, RMS-field and charge-conservation histories	Outputs
Verification	Regression digests on both backends; oracle checks on AMR seams	Verification

Quick start

Build (FoBiS, from the repository root):

fobis build --mode prism-cpu-gnu                         # CPU backend
fobis build --mode prism-fnl-nvf --varset local_nvf      # GPU backend (OpenACC, NVIDIA HPC SDK)

Run the rotating-magnetic-field regression case:

cd src/tests/prism/regression/rmf
mpirun -np 2 ../../../../../exe/adam_prism_cpu input.ini

Without an argument the executable reads input.ini in the working directory. A file with a [forest] section is a forest manifest and runs several realms.

Outputs

File	Content	Enabled by
<basename>-<it>-procNNNNNN.h5 + <basename>-<it>.xdmf	Field files: the state ([IO] save_fields = all) or D and B only (em), plus residuals, curls, divergences and the coils' current densities on request	[IO] it_save and the save_*_fields flags (input)
restart files	State and time, same rank count and grid to restart	[IO] restart_save
<basename>-residuals.dat	L2 norm of every residual	[IO] residuals_save
<basename>-energy_history.dat	the electric and magnetic energies $\frac{1}{2}\sum |\mathbf{D}{|}^2/{\epsilon }_0\mathrm{\Delta }V$ and $\frac{1}{2}\sum |\mathbf{B}{|}^2/{\mu }_0\mathrm{\Delta }V$, the coil power and the Poynting flux	every 10 steps (fixed)
<basename>-divergence_history.dat	max $|\mathrm{\nabla }\cdot \mathbf{D}|$ ($|\mathrm{\nabla }\cdot \mathbf{D}-\rho |$ with PIC), $|\mathrm{\nabla }\cdot \mathbf{B}|$, $|\mathrm{\nabla }\cdot \mathbf{J}|$ outside the absorbing layers, and the residual of the current solver	every step
<basename>-charge_conservation_history.dat	PIC: particle and deposited charge, continuity and Gauss residuals	PIC models
<basename>-grms_history.dat, <basename>-magnetic_field_at_center_domain.dat	RMS of the field over a region; $\mathbf{B}$ at the domain centre	[grms], [magnetic_field_at_center_domain]
<basename>-probe_NN.dat	The state at a fixed point, trilinear	[probes]
<basename>-plane_NN.dat	The state on a plane of probes (per save one row per probe), trilinear	[probes]
rectangular_current_coil_N.dat, helicon_current_coil_N.dat	The current of rectangular and helicon coils	every step, when such a coil exists
single_particle_output.dat	Position, velocity and fields of the test particle	problem_type = single_particle

Pages

• Physical models: equations, state vector, constants, non-dimensional form, GLM cleaning.
• Numerical methods: the centred operators, WENO, time integration, AMR and seams, multi-realm runs, the t0 elliptic solves.
• Initial conditions and sources: field initial conditions, coils, external fields.
• Boundary conditions and absorbing layers: the face kinds, the PML, the far-wave layer.
• Particle-in-cell: particles, deposition, gather, push, particle boundaries, charge conservation.
• Input reference: every section and key, with the refused combinations.
• Backends: CPU and FNL, what each implements, the step structure, device data.
• Verification: the oracle checks.

Known limitations

• Seam div(B). At a 2:1 AMR face the centred operators no longer commute, and the seam injects an $O(h^p)$$\mathrm{\nabla }\cdot \mathbf{B}$ source that converges under refinement but grows in time at fixed $h$ (#29, accepted as truncation; an upwinded GLM coupling is #99). [IO] seam_divB_tol makes it visible (numerics).
• Refinement at initialization only. PRISM has no runtime regrid; the t0 elliptic solves refuse a refined grid.
• Time integration. Only Runge–Kutta runs: leapfrog, Blanes–Moan and commutator-free Magnus are refused, for the fields and for the particles (#55).
• The GPU backend has no WENO and no Yoshida; its PML needs the FD operators and an SSP scheme (backends).
• The CPU charge-conserving deposit and the CPU coherent matched gather run on one block and one rank only.
• Coils (defects, #108): a circular coil injects no current, and the coils after the first take the first coil's amplitude, not their own Amplitude.
• The PML and far-wave-layer profiles are computed per rank, so a layer that spans the blocks of several ranks gives results that depend on the decomposition (#108).
• Verification. Analytic oracles (plane wave, cavity, PML reflection, Biot–Savart, Larmor orbit, plasma frequency) are #106.