---
title: "The JuliaFEM Book"
subtitle: "A comprehensive manual mixing theory, software design, and personal experience"
description: "Deep dive into FEM theory, design philosophy, and research directions"
date: 2025-11-09
author: "Jukka Aho"
categories: ["theory", "research", "philosophy"]
keywords: ["fem theory", "contact mechanics", "design philosophy", "research"]
audience: "researchers and theory enthusiasts"
level: "expert"
type: "book"
status: "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](foundations.md) | [Strategic Mistakes](strategic_mistakes.md) | [Why JuliaFEM?](philosophy.md)