From macroscopic to microscopic

¹

From microscopic to macroscopic

²

Metamaterials

⁶

Truss lattices

¹⁰

Discrete Beams

¹³

Areas

• Experiments
• Methods
• High-performance computing

Team

¹⁶

Tasks

• Architecture and design
• Performance
• Support, onboarding

Overview

• Finite element method framework
• Custom elements and material models
• Minimize energy of system

Starting point

• C++ libraries
• Templated classes
• Single-threaded
• Closed source

Challenges

• Stability
• Performance
• Modifiability

Stability

¹⁷

• Continuous integration (Jenkins, GitLab)
• Integration tests
• Unit tests (GoogleTest)
• Documentation (Doxygen, Sphinx)

Finite element method

¹⁸

Math

• Energy: \(E \to \textrm{min}\)
• Forces: \(F = E' = 0\)
• Stiffness matrix: \(E''\)

Solution: Find zeroes of \(F\).

Computational graph

Domain decomposition

PETSc

¹⁹

Performance

• Linear solver performant on single core
• Boost depends on amount of local work
• Replaced other approaches

Modifiability

“open for extension, but closed for modification”²⁰

• Plugin-based assembler (via templates)
• Functional programming

Result

• Open source libraries (core)
• MPI-based parallelization
• High test coverage

The Quasicontinuum method - Problem

• Key Quantity: Energy \(E\), depending on the state of individual atoms in a solid state body
• Problem: order of magnitude of \(10^{13}\) - \(10^{15}\) atoms in a sample of interest
• but only \(10^9\) feasible in current simulations
• Solution: QC method

The Quasicontinuum method

Full problem (e.g. QM)

\[ E^{\mathrm{tot}} = \sum_{i=1}^N E_i(\boldsymbol{u}_i), \]

\(E_i(\boldsymbol{u}_i)\): Energy of atom \(i\), dependent on its displacement \(\boldsymbol{u}_i\).

QC method

Combine regions, represented by one “repatom”

Remeshing

Challenge: Find “good” choice of the mesh.

Goals

• Model copper using Gaussian quasistatics
• High performance, distributed mesh optimization

Project Roadmap

• Basic functionality, including mesh optimization with edge removal only, on one core only
• Add unit tests
• Refactor monolithic codebase into multiple compilation units
• Integrate face removal into mesh optimization algorithm
• Multicore support
• Open Source release

Team

Mechanics & Materials

Prateek Gupta

Lead Researcher

Postdoc

Miguel Spinola

PhD Student

Shashank Saxena

PhD Student

SIS

Manuel Weberndorfer

Developer

Gerhard Bräunlich

Developer

GPUs

²¹

• Previously no GPUs on Euler
• Infrastructure now available

Work stealing

• Static share of work problematic
• Trade-off with communication cost

Sources

• Mechanics & Material Laboratory

Slides

• Reveal.js, MIT
• MathJax, Apache 2.0
• Pandoc, GPLv2+, BSD 3-clause