Selected 1.029M, 3.0M, 5.013M, and approximately 10.125M active-DOF cases used declared PETSc/MPI routes.
01 Model and scope
These workload records measure selected structured meshes at different active-DOF counts and on declared hardware/backend configurations. They are observations for those runs; they do not provide a hardware-independent performance law or general mixed-mesh scaling result.
Route assumptions and calculation checks
- The 5.013M case records two complete Silver replays.
- The ~10.125M entry is a bounded observation; it does not prove a general scaling law.
- These workloads are separate from the compact learning fixtures.
Useful foundations and prerequisites
02 Essential equations and symbols
Definitions and conventions
- nDOF
- Active degrees of freedom.
- Twall
- Elapsed wall-clock time for the recorded run.
- memory
- Observed or estimated peak storage, as declared by the record.
- configuration
- Hardware, backend, mesh and solver settings tied to each measurement.
03 Step by step derivation
Follow the assumptions, equations and discrete operations in order. The full explanation stays visible.
1 · Treat each size as a frozen workload
The recorded active-DOF counts—1.029M, 3.0M, 5.013M, and approximately 10.125M—refer to particular structured TET4 meshes, solver settings, rank counts, and environments. They are not interchangeable samples from one hardware-independent performance law.
2 · Separate convergence, memory, and cost
For each run, capture wall time, peak memory, residual, iteration count, ranks, solver/preconditioner, source revision, and replay status. The 5.013M-DOF record includes two complete Silver replays; the approximately 10.125M entry is a bounded observation rather than a repeated scaling campaign.
3 · Do not transfer scale claims to learning examples
The million-DOF workloads use separate declared PETSc/MPI routes and infrastructure. They do not establish general mixed-mesh performance, partitioned assembly, nonlinear scaling, GPU support, or reproducibility on unrelated hardware. The compact JSON examples serve a different purpose.
04 Algorithm and implementation
This sheet provides explanatory references rather than an inline source excerpt. Use the labeled sources to inspect the precise boundary.
05 Verification and limitations
HISTORICAL ENVIRONMENT-SPECIFIC RECORDS
Each reference supports its own model, observable and analysis route. Read the original contract and limitations before transferring a conclusion.