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PETSc / MPI static route

Algorithm / execution · assumptions, essential equations, full derivation, algorithm, code and verification references.

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Algorithm / executionOWNER-ACCEPTED BOUNDED EVIDENCE · two ranks

Current evidence covers selected one-element linear-static cases with replicated input and root-side assembly.

01 Model and scope

The recorded route launches selected linear-static cases with replicated input and root-side assembly across two ranks. It demonstrates that bounded execution path only; it does not show partitioned finite-element assembly or nonlinear distributed scaling.

Route assumptions and calculation checks

  1. It does not establish distributed assembly, nonlinear MPI, contact, dynamics, mixed distributed MPC, or arbitrary-mesh scaling.
  2. Historical structured-TET4 large-model workloads are environment-specific records, not portable performance promises.
  3. No general GPU support claim is made.

02 Essential equations and symbols

This sheet records a scope or execution boundary. Its detailed steps explain the relevant conditions.

Definitions and conventions

MPI ranks
Processes participating in the recorded run.
replicated input
Each participating rank receives the model input.
root-side assembly
Assembly location in this bounded route.
NOT_VALIDATED
No general distributed capability claim.
PETSc / MPI static route · method mapThe recorded execution layout is replicated input with root-side assembly, bounded to its named static workload.
3 detailed steps

03 Step by step derivation

Follow the assumptions, equations and discrete operations in order. The full explanation stays visible.

1 · Describe the evidenced execution layout

The recorded route launches selected one-element linear-static cases with replicated input and root-side assembly across the declared ranks. This describes where data and assembly live in that experiment; it is not a claim of distributed finite-element assembly.

Ax=b,input replicated; assembly on root for the recorded route\mathbf A\mathbf x=\mathbf b,\qquad \text{input replicated; assembly on root for the recorded route}

2 · Separate execution from scaling evidence

An MPI job starting successfully proves that a bounded parallel execution path ran. It does not establish partitioning, communication efficiency, arbitrary-mesh scalability, nonlinear distributed mechanics, contact, or dynamic workflows. Large structured-TET4 records are separate named workloads.

Sp=T1Tp,Ep=Spponly when comparable runs existS_p=\frac{T_1}{T_p},\qquad E_p=\frac{S_p}{p}\quad\text{only when comparable runs exist}

3 · Bind every metric to environment and workload

Record mesh identity, active DOFs, rank count, backend, solver/preconditioner, hardware, timing boundary, memory, residual, and replay count. Historical records are observations for those exact configurations; no hardware-independent speedup or general GPU capability follows.

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

OWNER-ACCEPTED BOUNDED EVIDENCE · two ranks

Each reference supports its own model, observable and analysis route. Read the original contract and limitations before transferring a conclusion.

06 Sources and related sheets

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