Spectral examples sequence¶

This page gives a reading and running order through three programs that add one concept at a time: a spectral model, simulator orchestration, and a conserved nonlinear model.

Sequence¶

Step	Executable	New idea
1	`04_diffusion_model`	Apply a backward-Euler multiplier to a distributed Fourier field
2	`05_simulator`	Add `pfc::sim::run`, `Time`, host ICs, and lifecycle orchestration
3	`12_cahn_hilliard`	Declare conserved nonlinear physics and advance it with native ETD1

Read the Quarto lessons for implicit heat, driver hooks, and Cahn–Hilliard. They develop the equations, show source excerpts and give independent checks. The snapshot-series lesson covers visualization output separately.

Build and run¶

From the repository root:

./scripts/build.sh

mpirun -n 1 ./builds/release/examples/04_diffusion_model
mpirun -n 1 ./builds/release/examples/05_simulator
mpirun -n 1 ./builds/release/examples/12_cahn_hilliard

Begin with one rank. After all three programs exit with status zero, repeat with a rank count supported by your launcher allocation and the example dimensions. The programs do not share one mandatory success message; see Example run output.

Read the sources¶

File	Look for
`examples/heat/implicit-euler/model.cpp`	Field allocation, Fourier-space operator construction, and forward/backward transforms
`examples/heat/driver-hooks/model.cpp`	`pfc::sim::run`, host IC callable, time control
`examples/phase-fields/cahn-hilliard/model.cpp`	Linear/nonlinear symbols, pointwise cubic, state declaration and diagnostics

Treat these compiled examples as the code-level source of truth. This page explains their order rather than copying their implementations.

Continue by goal¶

Goal	Next document
Understand `Domain`, decomposition, and FFT first	Library basics
Build a JSON-driven application	Minimal custom application
Understand JSON-to-simulator wiring	Application pipeline
Inspect output in ParaView	VTK and ParaView workflow
Find every runnable example	Examples catalog
Look up API-focused snippets	API examples walkthrough
Run linear \(k^4\) surface diffusion as a JSON app	`apps/surface_diffusion` (`#79`)
Run odd-order \(ik^3\)/\(ik^5\) Kawahara waves	`apps/kawahara` (`#80`)
Run sixth-order EHD film under a flexible plate	`apps/ehd_film` (`#81`)
Run Helmholtz–Navier strain-gradient elasticity	`apps/gradient_elasticity` (`#82`)