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Jukka Aho ded16ee1dc docs: Multi-GPU nodal assembly algorithm design

Complete algorithm for GPU-resident FEM solver with nodal assembly:
- Data partitioning by node ownership (domain decomposition)
- GPU-resident data structures (nodes, elements, connectivity, state)
- Three GPU kernels: residual, matvec, state update
- MPI communication patterns for interface nodes
- Full Newton-GMRES loop on GPU (data stays resident)

Architecture:
- Each GPU owns subset of nodes (exclusive ownership)
- Ghost elements copied for gathering during assembly
- node_to_elements connectivity enables nodal assembly
- No atomic operations (each GPU writes to owned DOFs only)

Key features:
- Data moves to GPU once at start, back once at end
- GMRES iterations entirely on GPU (Arnoldi steps)
- Material state updates on GPU (integration points)
- MPI exchanges only for interface DOFs between iterations
- O(N) memory per GPU (matrix-free)

Handles nonlinearity:
- Element state contains σ, ε_plastic, α, C (tangent)
- Residual kernel uses current stress/tangent
- State update kernel after convergence
- Natural for contact mechanics (nodal forces)

Status: Design document for future GPU implementation

2025-11-09 16:16:43 +02:00

benchmarks

feat: Separation of concerns architecture with zero-allocation foundation

2025-11-09 05:46:34 +02:00

adr-002-topology-without-node-count.md

docs(book): Add ADR-002 for topology without hardcoded node counts

2025-11-09 09:33:41 +02:00

element_architecture.md

docs(architecture): Complete rewrite explaining topology vs basis separation

2025-11-09 09:29:58 +02:00

element_field_architecture.md

docs: Design document for element field architecture

2025-11-09 16:15:52 +02:00

gpu_benchmark_milestone.md

feat(gpu): Multi-GPU MPI benchmark with nodal assembly

2025-11-09 15:59:00 +02:00

lagrange_basis_functions.md

docs(book): Update Lagrange basis generation references

2025-11-09 08:27:18 +02:00

matvec_krylov_pattern.md

docs: Matrix-free Krylov pattern with ElementSet

2025-11-09 16:16:13 +02:00

multigpu_nodal_assembly.md

docs: Multi-GPU nodal assembly algorithm design

2025-11-09 16:16:43 +02:00

nodal_assembly_multigpu.md

docs(book): Add nodal assembly and multi-GPU strategy document

2025-11-09 10:52:38 +02:00

README.md

Integrate topology/integration modules with comprehensive testing

2025-11-09 06:13:40 +02:00

roadmap_to_hpc.md

docs: Add 'Roadmap to HPC' - justifying hard performance choices

2025-11-09 05:01:34 +02:00

zero_allocation_fields_v2.md

docs(book): Add concise type-stability rationale for field storage

2025-11-09 11:10:37 +02:00

zero_allocation_fields.md

docs(book): Add comprehensive zero-allocation field storage design

2025-11-09 11:09:19 +02:00

README.md

title, subtitle, description, date, author, categories, keywords, audience, level, type, status

title

subtitle

description

date

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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?