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Jukka Aho
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**Purpose:** Prepare documentation for publishing as blog posts or book **YAML Headers Include:** - title: Document title - subtitle: Optional subtitle for context - description: Brief summary for SEO/indexing - date: Creation date - updated: Last update date (for status docs) - author: Jukka Aho - categories: Taxonomic classification - keywords: Search/indexing keywords - audience: Target reader (users/contributors/researchers) - level: Difficulty level (beginner/intermediate/advanced/expert) - type: Document type (manual/guide/theory/benchmark/status) - series: Which manual it belongs to - chapter: Book structure (for The JuliaFEM Book) - status: Current state (completed/work in progress/active maintenance) - math: Whether document contains mathematical notation - prerequisites: Required background knowledge - tools: Software/packages used (for benchmarks) - context: Background information **Files Updated:** - docs/README.md (main index) - docs/user/README.md (user manual index) - docs/contributor/README.md (contributor manual index) - docs/book/README.md (book index) - docs/contributor/testing_philosophy.md - docs/contributor/status.md - docs/contributor/test_fixes_needed.md - docs/book/lagrange_basis_functions.md - docs/book/benchmarks/shape_function_derivatives_ad_vs_manual.md - scripts/README.md **Benefits:** - Ready for static site generators (Jekyll, Hugo, MkDocs) - Can generate book with proper metadata - SEO-friendly with descriptions and keywords - Clear audience/level targeting - Trackable with dates and status - Organized by series and chapters **Compatible With:** - Jekyll (GitHub Pages) - Hugo (fast static site generator) - MkDocs (Python-based documentation) - Jupyter Book (interactive books) - Docusaurus (React-based docs) - Custom publishing scripts
title, subtitle, description, date, author, categories, keywords, audience, level, type, status
| title | subtitle | description | date | author | categories | keywords | audience | level | type | status | |||||||
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| The JuliaFEM Book | A comprehensive manual mixing theory, software design, and personal experience | Deep dive into FEM theory, design philosophy, and research directions | 2025-11-09 | Jukka Aho |
|
|
researchers and theory enthusiasts | expert | book | work in progress |
The JuliaFEM Book
Audience: Advanced researchers, theory nerds, those who want to understand the "why" and "how" at a deep level. And Jukka.
This is the JuliaFEM Bible - a comprehensive manual mixing theory, philosophy, software design, and personal experience. It's educational, opinionated, and unapologetically deep.
What's Here
- Mathematical Foundations: Lagrange basis functions, weak forms, contact mechanics
- Design Philosophy: Why JuliaFEM exists, what problems it solves (and doesn't)
- Technical Vision: Strategic mistakes from 2015-2019, lessons learned
- Research Directions: Experimental ideas (nodal assembly, matrix-free, etc.)
- Personal Notes: The journey, the failures, the "aha!" moments
- Theory + Code: How mathematics becomes software
What's NOT Here
- "How do I install?" (see
docs/user/) - "How do I add a feature?" (see
docs/contributor/) - Short answers (everything here is DEEP)
Philosophy
"Let me show you how I think about FEM."
This is:
- Educational: Teach FEM through implementation
- Personal: Written in Jukka's voice, reflecting 8+ years of experience
- Opinionated: Strong views on what works and what doesn't
- Comprehensive: From first principles to cutting-edge research
- Honest: Documents failures as much as successes
We assume you:
- Love mathematics AND programming
- Want to understand WHY, not just HOW
- Have time to read deeply
- Are curious about unconventional approaches
- Might be me, 5 years from now, trying to remember why I did this
Structure
Part I: Foundations
- Finite Element Method (brief review)
- Lagrange Basis Functions (deep dive)
- Assembly and Solving
- Contact Mechanics
Part II: Software Design
- Type Stability and Performance
- Zero-Allocation Design
- Immutability and Composition
- Field System Architecture
Part III: History and Vision
- Strategic Mistakes (2015-2019)
- Why JuliaFEM is Different
- Contact Mechanics Focus
- Laboratory Philosophy
Part IV: Research
- Nodal Assembly (experimental)
- Matrix-Free Methods
- Automatic Differentiation
- GPU Acceleration
Part V: The Journey
- Personal Reflections
- Lessons Learned
- Future Directions
- Open Questions
Reading Guide
- For Theory: Start with Part I
- For Design Rationale: Start with Part II
- For History: Start with Part III
- For Research Ideas: Start with Part IV
- For Philosophy: Read Part V first, then everything else
Start here: Mathematical Foundations | Strategic Mistakes | Why JuliaFEM?