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JuliaFEM.jl/docs
Jukka Aho f2b306f68e docs(book): Add nodal assembly and multi-GPU strategy document
New 588-line comprehensive strategic document explaining winning architecture:

Executive Summary (lines 1-19):
- Key results demonstrated on real hardware
- 9-92× CPU speedup, GPU kernel compilation, MPI working, Krylov convergence
- Multi-GPU workflow validated end-to-end

Problem: Traditional FEM doesn't scale (lines 21-59):
- v0.5.1 limitations: global matrix O(N²) memory, direct solver O(N³) time
- Scalability ceiling ~100K DOF
- Cannot scale: memory N², time N³

Solution: Nodal + Matrix-Free + Multi-GPU (lines 61-193):
- Architecture diagram with MPI ranks and local GPUs
- Three pillars: nodal assembly (row-by-row), matrix-free (matvec only), multi-GPU with MPI
- Each pillar explained with code examples and advantages

Why type stability required (lines 195-241):
- GPU kernel compilation: concrete types required, abstract fails
- MPI fast path: typed buffers vs slow serialization
- Krylov solvers: matrix-free operators need concrete types
- Demonstrated with code examples

Performance characteristics (lines 243-289):
- Complexity analysis: O(N²)→O(N) memory, O(N³)→O(N·k) time
- Scalability comparison table: 10K→10M DOF
- Demonstrated results: 10×10 system, 9 iterations, 7.73×10⁻¹⁴ error

Contact mechanics killer app (lines 291-340):
- Why nodal assembly natural for contact (contact is nodal not element-based)
- Contact workflow: detect→assemble→solve→update
- Element-based assembly is mismatch for contact

Implementation strategy v1.0 (lines 342-407):
- Phase 1: Foundation (complete) - type-stable design, GPU/MPI demos, Krylov validation
- Phase 2: Core implementation - nodal assembly API, matrix-free operator, GPU accel, MPI distribution
- Phase 3: Contact integration - detection, contribution to rows, iterative solve

Comparison with other strategies (lines 409-455):
- Global matrix assembly: dead end for scalability
- Element-based matrix-free: works but suboptimal for contact
- Nodal + matrix-free + multi-GPU (ours): best for large-scale contact

Validation and evidence (lines 457-533):
- Three demonstrations: gpu_mpi_demo, krylov_mpi_gpu_demo, field_storage_comparison
- Real-world applicability: LAMMPS, GROMACS use similar patterns
- Why traditional FEM codes don't do this: legacy constraints

Conclusion (lines 535-588):
- Five validated achievements proving path forward
- Not speculation: working code on real hardware
- Path is clear: type stability foundation, nodal assembly pattern, Krylov+MPI solver
- Related documentation links

Purpose: Strategic justification for v1.0 architecture with real evidence
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title, description, date, author, categories, keywords, type
title description date author categories keywords type
JuliaFEM Documentation Three-tier documentation structure for users, contributors, and researchers 2025-11-09 Jukka Aho
documentation
guide
juliafem
finite element
documentation
manual
index

JuliaFEM Documentation

Welcome! JuliaFEM documentation is organized into three manuals for three different audiences:


📘 User Manual - "Just Get It Done"

For: End users, engineers, students who want to run simulations.

Style: Simple, practical, step-by-step.

Contents:

  • Quick start and installation
  • Tutorials and examples
  • API reference
  • Troubleshooting

Philosophy: Show me how to solve my problem, skip the lectures.

👉 Start Here if you want to run simulations.


🔧 Contributor Manual - "Show Me the Code"

For: Developers, contributors, advanced users who want to extend JuliaFEM.

Style: Technical, detailed, design rationale.

Contents:

  • Testing philosophy
  • Code style and architecture
  • Performance guidelines
  • How to add elements
  • CI/CD and git workflow

Philosophy: Explain HOW the code works and WHY we made these choices.

👉 Start Here if you want to contribute code.


📖 The JuliaFEM Book - "Let Me Show You How I Think"

For: Advanced researchers, theory nerds, those who want to understand deeply. And Jukka.

Style: Comprehensive, educational, opinionated, personal.

Contents:

  • Mathematical foundations (Lagrange basis, contact mechanics, etc.)
  • Design philosophy and technical vision
  • Strategic mistakes and lessons learned (2015-2019)
  • Research directions (nodal assembly, matrix-free, etc.)
  • Personal reflections on the journey

Philosophy: Mix theory, software design, and personal experience. Teach FEM through implementation.

👉 Start Here if you love deep dives and want to understand the "why" behind everything.


Quick Navigation

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Documentation Philosophy

Why Three Manuals?

Different readers have different needs:

  1. Users don't care about implementation details - they just want working code.
  2. Contributors need technical depth but not necessarily all the theory.
  3. Researchers (and Jukka) want to understand everything from first principles.

Mixing these audiences in one manual makes it too complex for users and too shallow for researchers.

Design Principles

  • User Manual: Optimize for time-to-first-result
  • Contributor Manual: Optimize for correctness and maintainability
  • Book: Optimize for understanding and education

Cross-References

Manuals link to each other when appropriate:

  • User manual links to theory when deeper understanding helps
  • Contributor manual links to book for design rationale
  • Book links to code examples and practical guides

Contributing to Documentation

Documentation improvements are always welcome!

  • User docs: Fix errors, add examples, improve clarity
  • Contributor docs: Update for new features, clarify architecture
  • Book: Add theory, share insights, document research

See Contributor Manual for guidelines.


License: MIT (same as code)
Questions? Open an issue or discussion on GitHub