title: | | A free and open source computational tool | for solving differential equations in the cloud author: Germán Theler email: jeremy@seamplex.com institute: | | Mid-term evaluation, PhD in Nuclear Engineering | Instituto Balseiro, San Carlos de Bariloche, Argentina aspectratio: 169 lang: en-US theme: default innertheme: rectangles fonttheme: professionalfonts outertheme: number colorlinks: true sansfont: Carlito monofont: DejaVuSansMono header-includes: \include{syntax.tex} ...

Background 1/2

\centering $\approx$ 15 years of updates!

2007 Fuzzy logic & chaotic natural convection loops @ IB
2008 Instabilities in the coupled neutronic-thermal-hydraulic problem @ IB
2008 TECNA---CNA2
2009 First attempt at PhD---v1
2010 Paper on stability of point kinetics @ Nuc. Eng. & Design
2010 First presentation of milonga at AATN
2011 First ME with milonga (mrivero) @ UBA
2011 IMEF $\rightarrow$ milonga with FEM @ UBA
2012 Paper generalized boiling channel @ ENIEF
2013 Monograph milonga FEM vs. FVM @ UBA

Background 2/2

2013 Paper unstructured grids for neutron diffusion
2013 Doppler measurement @ CNA1---v2
2014 Design basis @ ENIEF
2014 Doppler measurement @ CNA2
2015 Workshop milonga @ CAC
2016 First PhD with milonga (vitor) @ Belo Horizonte
2017 Fatigue for LTE @ CNE
2018 Opportunity @ KAIST---second attempt at PhD
2020 Remote courses---third attempt at PhD
2021 FeenoX (v3)

How do we write papers/reports/documents?

\newcommand{\todonow}{\textcolor{Plum}{TO-DO}} \newcommand{\todolater}{\textcolor{Orange}{TO-DO}} \newcommand{\good}{\textcolor{OliveGreen}{$\checkmark$}} \newcommand{\bad}{\textcolor{red}{$\times$}} \newcommand{\neutral}{\textcolor{DarkBlue}{$\sim$}}

:::::::::::::: {.columns} ::: {.column width="25%"} \centering \onslide<1->{\includegraphics[height=2cm]{word}} :::

::: {.column width="25%"} \centering \onslide<3->{\includegraphics[height=2cm]{google_docs}} :::

::: {.column width="25%"} \centering \onslide<4->{\includegraphics[height=2cm]{markdown}} :::

::: {.column width="25%"} \centering \onslide<2->{\includegraphics[height=2cm]{tex}} ::: ::::::::::::::

\rowcolors{1}{black!10}{black!0}

Feature	\onslide<1->{Word}	\onslide<3->{Docs}	\onslide<4->{Markdown$^{*}$}	\onslide<2->{\TeX}
Aesthetics	\onslide<1->{\bad}	\onslide<3->{\bad}	\onslide<4->{\good}	\onslide<2->{\good}
Convertibility	\onslide<1->{\neutral}	\onslide<3->{\neutral}	\onslide<4->{\good}	\onslide<2->{\neutral}
Traceability	\onslide<1->{\bad}	\onslide<3->{\neutral}	\onslide<4->{\good}	\onslide<2->{\good}
Mobile-friendliness	\onslide<1->{\bad}	\onslide<3->{\good}	\onslide<4->{\good}	\onslide<2->{\bad}
Collaborative	\onslide<1->{\bad}	\onslide<3->{\good}	\onslide<4->{\good}	\onslide<2->{\neutral}
Licensing/openness	\onslide<1->{\bad}	\onslide<3->{\bad}	\onslide<4->{\good}	\onslide<2->{\good}
Non-nerd friendliness	\onslide<1->{\good}	\onslide<3->{\good}	\onslide<4->{\neutral}	\onslide<2->{\bad}

\onslide<4->{\centering $^*$ \href{https://en.wikipedia.org/wiki/Markdown}{Markdown} + \href{https://pandoc.org/}{Pandoc} + \href{https://git-scm.com/}{Git} + \href{https://github.com/}{Github} / \href{https://about.gitlab.com/}{Gitlab} / \href{https://gitea.com/}{Gitea}}

How do we do scientific/engineering computations?

:::::::::::::: {.columns} ::: {.column width="25%"} \centering \onslide<1->{\includegraphics[height=2cm]{prepomax}} :::

::: {.column width="25%"} \centering \onslide<3->{\includegraphics[height=2cm]{caeplex}} :::

::: {.column width="25%"} \centering \onslide<4->{\includegraphics[height=2cm]{feenox-logo}} :::

::: {.column width="25%"} \centering \onslide<2->{\includegraphics[height=2cm]{libraries}} ::: ::::::::::::::

\rowcolors{1}{black!10}{black!0}

Feature	\onslide<1->{Desktop GUIs}	\onslide<3->{Web frontends}	\onslide<4->{FeenoX$^{*}$}	\onslide<2->{Libraries}
Flexibility	\onslide<1->{\neutral}	\onslide<3->{\bad}	\onslide<4->{\good}	\onslide<2->{\good}
Scalability	\onslide<1->{\bad}	\onslide<3->{\neutral}	\onslide<4->{\good}	\onslide<2->{\good}
Traceability	\onslide<1->{\bad}	\onslide<3->{\neutral}	\onslide<4->{\good}	\onslide<2->{\good}
Cloud-friendliness	\onslide<1->{\bad}	\onslide<3->{\good}	\onslide<4->{\good}	\onslide<2->{\good}
Collaborative	\onslide<1->{\bad}	\onslide<3->{\good}	\onslide<4->{\neutral}	\onslide<2->{\bad}
Licensing/openness	\onslide<1->{\good/\neutral/\bad}	\onslide<3->{\bad}	\onslide<4->{\good}	\onslide<2->{\good}
Non-nerd friendliness	\onslide<1->{\good}	\onslide<3->{\good}	\onslide<4->{\neutral}	\onslide<2->{\bad}

\onslide<4->{\centering $^*$ \href{https://seamplex.com/feenox}{FeenoX} + \href{http://gmsh.info}{Gmsh} + \href{https://www.paraview.org/}{Paraview} + \href{https://git-scm.com/}{Git} + \href{https://github.com/}{Github} / \href{https://about.gitlab.com/}{Gitlab} / \href{https://gitea.com/}{Gitea}}

Software Requirement Specifications

After a successful project with a foreign company I decided to structure the PhD based on a fictitious & imaginary "Request for Quotation" for a computational tool:

:::::::::::::: {.columns} ::: {.column width="35%"}

Introduction
- 1.1. Objective
- 1.2. Scope
Architecture
- 2.1. Deployment
- 2.2. Execution
- 2.3. Efficiency
- 2.4. Scalability
- 2.5. Flexibility
- 2.6. Extensibility
- 2.7. Interoperability :::

::: {.column width="50%"}

Interfaces
- 3.1. Problem input
- 3.2. Results output
Quality assurance
- 4.1. Reproducibility and traceability
- 4.2. Automated testing
- 4.3. Bug reporting and tracking
- 4.4. Verification
- 4.5. Validation
- 4.6. Documentation ::: ::::::::::::::

FeenoX Software Design Specifications {.example}

A fictitious & imaginary tender applying to the SRS addressing each section.

:::::::::::::: {.columns} :::::: {.column width="50%"}

1. Introduction

Application to industrial problems
- Open source (to allow third-party V&V)
First version should handle some problems
Extensible to other problems & formulations
- Free (as in freedom to hire somebody to modify/extend it)

1.1. Objective

Solve DAEs and/or PDEs
- Heat conduction
- Elasticity
- Electromagnetism
- Fluid mechanics
- ...
State-of-the-art cloud friendly

::::::

. . .

:::::: {.column width="50%"}

FeenoX {.example}

Free as “software libre”
- GPLv3+
- Only FOSS dependencies
- Main target is linux-x86_64
- Development environment is Debian \medskip
Initial version supports
- Dynamical systems (DAE)
- Laplace/Poisson/Helmholtz (FEM)
- Heat (FEM)
- Elasticity (FEM)
- Modal (FEM)
- Neutron transport and diffusion (FEM/FVM)
Templates for more formulations
- Electromagnetism
- Chemical diffusion/reaction
- Fluid mechanics?

:::::: ::::::::::::::

:::::::::::::: {.columns} :::::: {.column width="50%"}

1.2. Scope

The problem should be defined programatically
- One or more input files (JSON, YAML, ad-hoc format), and/or
- An API for high-level language (Python, Julia, etc.)
There is no need to include a GUI
- The tool should allow a GUI to be used
  - Desktop
  - Web
  - Mobile
The mesh can be an input
- As long as its creation meets the SRS
Include documentation about how a...
- Pre-processor should create inputs
- Post-processor should read outputs

::::::

. . .

:::::: {.column width="50%"}

FeenoX {.example}

No GUI, console binary executable
"Transfer-function"-like between I/O
- No need to recompile the binary
  
  {width=90%}\
English-like syntactic-sugared input files
- Nouns are definitions
- Verbs are instructions
Python & Julia API: \todolater
- But already taken into account in the design & implementation
Separate mesher
- Gmsh (GPLv2, meets SRS)
- Anything that writes .msh
Possibility to use GUI
- CAEplex https://www.caeplex.com

:::::: ::::::::::::::

Transfer-function & English-like input: Lorenz’ system

:::::::::::::: {.columns} ::: {.column width="45%"}

Solve $$ \begin{cases} \dot{x} = \sigma \cdot (y - x) \ \dot{y} = x \cdot (r - z) - y \ \dot{z} = x y - b z \end{cases} $$

\noindent for $0 < t < 40$ with initial conditions

$$ \begin{cases} x(0) = -11\\ y(0) = -16\\ z(0) = 22.5\\ \end{cases} $$

\noindent and $\sigma=10$, $r=28$ and $b=8/3$. :::

. . .

::: {.column width="55%"}

$ feenox lorenz.fee
0.000000e+00    -1.100000e+01   -1.600000e+01   2.250000e+01
2.384186e-07    -1.100001e+01   -1.600001e+01   2.250003e+01
4.768372e-07    -1.100002e+01   -1.600002e+01   2.250006e+01
[...]
3.997567e+01    4.442995e+00    3.764391e+00    2.347301e+01
3.998290e+01    4.399950e+00    3.886609e+00    2.314602e+01
3.999012e+01    4.368713e+00    4.016860e+00    2.282821e+01
$

::: ::::::::::::::

Lorenz’ system

Web interface: CAEplex, finite elements in the cloud

\centering {width=70%}

https://www.seamplex.com/feenox/videos/caeplex-ipad.mp4

https://www.caeplex.com

:::::::::::::: {.columns} ::: {.column width="50%"}

2. Architecture

\newcommand{\unix}{{\textcolor{cyan}{UNIX}}} \newcommand{\ruleof}[1]{{\textcolor{cyan}{Rule of {#1}}}} \newcommand{\ruleofpar}[1]{\vspace{-0.25cm}\hfill{\footnotesize\textcolor{cyan}{(Rule of {#1})}}}

Should run on mainstream cloud servers
- GNU/Linux
- Multi-core Intel-compatible CPUs
- Several levels of memory cache
- A few Gb of RAM
- Several Gb of SSD
- Either
  - Bare metal
  - Virtualized
  - Containerized
Standard compilers, libraries and dependencies
- Available in common GNU/Linux repositories
- Preferable 100% open source
- Adhere to well-established standards

:::

. . .

::: {.column width="50%"}

FeenoX {.example}

Third-system effect (after v1 & v2)
\unix philosophy: "do one thing well"
- \ruleof{separation}: no GUI
- \ruleof{composition}: Gnuplot, Gmsh, ...
- ...more rules to come!
Third-party math libraries
- GNU GSL, PETSc, SLEPc, SUNDIALS
- \ruleof{modularity}

Dependencies available in APT

apt-get install git gcc make automake autoconf
apt-get install libgsl-dev
apt-get install lib-sundials-dev petsc-dev slepc-dev

Sources on github.com/seamplex/feenox

git clone https://github.com/seamplex/feenox

Autotools & friends for compilation
```
./autogen.sh && ./configure && make
```

::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="50%"}

2. Architecture

Small coarse problems should be run in single hosts to check inputs
- Local desktop/laptops (not needed but suggested)
- Windows and MacOS (not needed but suggested)
- Small cloud instances
Large actual problems should be split into several hosts
- HPC clusters
- Scalable cloud instances
Mobile devices (not needed but suggested)
- As control/monitoring devices :::

. . .

::: {.column width="50%"}

FeenoX {.example}

Tested on
- Raspberry Pi
- Laptop (GNU/Linux & Windows 10)
- Macbook
- Desktop PC
- Bare-metal servers
- Vagrant/Virtualbox
- Docker/Kubernetes
- AWS/DigitalOcean/Contabo
Parallelization: \todolater
- Gmsh partitioning with METIS
- PETSc/SLEPc with MPI
Web: https://www.caeplex.com (v2)

\centering {width=30%}
{width=30%}

\raggedright
Mobile: \todolater ::: ::::::::::::::

How to solve a maze without AI 1/3

\renewcommand{\vec}{\mathbf}

:::::::::::::: {.columns} ::: {.column width="50%"} \centering {height=8cm} ::: ::: {.column width="50%"}

{width=48%} {width=48%}

Go to http://www.mazegenerator.net/
Create a maze
Download it in PNG

Perform some conversions

PNG $\rightarrow$ PNM $\rightarrow$ SVG $\rightarrow$ DXF $\rightarrow$ GEO

$ wget http://www.mazegenerator.net/static/orthogonal_maze_with_20_by_20_cells.png
$ convert orthogonal_maze_with_20_by_20_cells.png \ 
  -negate maze.png
$ potrace maze.pnm --alphamax 0  --opttolerance 0 \ 
  -b svg -o maze.svg
$ ./svg2dxf maze.svg maze.dxf
$ ./dxf2geo maze.dxf 0.1

::: ::::::::::::::

How to solve a maze without AI 2/3

:::::::::::::: {.columns} ::: {.column width="50%"} 5. Open it with Gmsh

![](gmsh-maze.png)\ 

- Add a surface
- Set physical curves for "start" and "end"

Mesh it
```
gmsh -2 maze.geo
```

:::

::: {.column width="50%"} \centering\includegraphics[height=8cm]{maze2.png} ::: ::::::::::::::

How to solve a maze without AI 3/3

:::::::::::::: {.columns} ::: {.column width="50%"} 7. Solve $\nabla^2 \phi = 0$ with BCs \vspace{-0.5cm} $$ \begin{cases} \phi=0 & \text{at “start”} \ \phi=1 & \text{at “end”} \ \nabla \phi \cdot \hat{\vec{n}} = 0 & \text{everywhere else} \ \end{cases} $$

\vspace{-0.5cm}

```{.feenox include="maze/maze.fee"}
```

```terminal
$ feenox maze.fee
$
```

\ruleofpar{silence}

Go to start and follow the gradient\ $\nabla \phi$!

:::

::: {.column width="50%"} \only<1 | handout:0>{\centering\includegraphics[height=8cm]{maze2.png}}\only<2>{\centering\includegraphics[height=8cm]{maze3.png}} ::: ::::::::::::::

The life of an influencer...

:::::::::::::: {.columns} ::: {.column width="50%"}

\centering {width=80%}

:::

::: {.column width="50%"}

http://www.mazegenerator.net/Examples.aspx

\centering {width=45%} \centering {width=45%}

\centering {width=45%} \centering {width=45%} ::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="50%"}

2.1. Deployment

Automatically compile from source
- Particular optimization flags
Availability of pre-compiled binaries
- Common architectures and options
Both of them have to be available online

2.2. Execution

Remote execution, either
- By a direct user action
- From a higher-level workflow
Outer loops have to be supported
- scripted
- parametric
- optimization
Ways to read data from the outer loop
Ways to write scalar figures of merit

:::

. . .

::: {.column width="50%"}

FeenoX {.example}

Compile optimized dependencies

$ cd $PETSC_DIR
$ export PETSC_ARCH=linux-fast
$ ./configure --with-debug=0 COPTFLAGS="-Ofast"
$ make -j8

Configure FeenoX with particular flags

$ git clone https://github.com/seamplex/feenox
$ cd feenox
$ ./autogen.sh
$ export PETSC_ARCH=linux-fast
$ ./configure MPICH_CC=clang CFLAGS=-Ofast
$ make -j8
# make install

Or use pre-compiled binaries

wget http://gmsh.info/bin/Linux/gmsh-Linux64.tgz
wget https://seamplex.com/feenox/dist/linux/feenox-linux-amd64.tar.gz

Everything is Docker-friendly
Execution examples follow $\rightarrow$

::: ::::::::::::::

Direct execution: three ways of getting the first 20 Fibonacci numbers

:::::::::::::: {.columns} ::: {.column width="60%"}

. . .

:::

. . .

::: {.column width="40%"}

$ feenox fibo_formula.fee | tee one
1	1
2	1
3	2
4	3
5	5
6	8
7	13
8	21
9	34
10	55
11	89
12	144
13	233
14	377
15	610
16	987
17	1597
18	2584
19	4181
20	6765
$ feenox fibo_vector.fee > two
$ feenox fibo_iterative.fee > three
$ diff one two
$ diff two three
$

::: ::::::::::::::

Parametric execution: shear locking in cantilevered beam

:::::::::::::: {.columns} ::: {.column width="60%"}

\ruleofpar{generation}

:::

::: {.column width="40%"}

\ruleof{simplicity}
- Only one material, no need to link volumes with materials
```
E = 2.1e11   # Young modulus in Pa
```

::: ::::::::::::::

Parametric execution: shear locking in cantilevered beam

Optimization loop: finding the right length of a tuning fork

:::::::::::::: {.columns} ::: {.column width="20%"}

\centering

$\ell_1$ to have 440\ Hz? :::

. . .

::: {.column width="40%"}

import math
import gmsh
import subprocess  # to call FeenoX and read back

def create_mesh(r, w, l1, l2, n):
  gmsh.initialize()
  ...
  gmsh.finalize()
  return len(nodes)
  
def main():
  target = 440    # target frequency
  eps = 1e-2      # tolerance
  r = 4.2e-3      # geometric parameters
  w = 3e-3
  l1 = 30e-3
  l2 = 60e-3

  for n in range(1,7):   # mesh refinement level
    l1 = 60e-3              # restart l1 & error
    error = 60
    while abs(error) > eps:   # loop
      l1 = l1 - 1e-4*error
      # mesh with Gmsh Python API
      nodes = create_mesh(r, w, l1, l2, n)
      # call FeenoX and read scalar back
      # TODO: FeenoX Python API (like Gmsh)
      result = subprocess.run(['feenox', 'fork.fee'], stdout=subprocess.PIPE)
      freq = float(result.stdout.decode('utf-8'))
      error = target - freq
    
    print(nodes, l1, freq)

\ruleofpar{parsimony}

:::

::: {.column width="40%"}

\ruleofpar{simplicity}

. . .

$ python fork.py > fork.dat
$

::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="47.5%"}

2.3. Efficiency

Similar to to other tools in terms of
- CPU/GPU
- RAM
- Storage

2.4. Scalability

Small problems to check correctness
Large problems in parallel
- Reasonable weak & strong scalability

2.5. Flexibility

Engineering problems with
- Multiple materials
- Space-dependent properties
- Space & time-dependent BCs
Handle point-wise data
- Properties
- Time-dependent scalars

:::

. . .

::: {.column width="52.5%"}

FeenoX {.example}

First make it work, then optimize
- \ruleof{optimization}
Premature optimization is the root of all evil
- Optimization: \todolater
- Parallelization: \todolater
- Comparison: \todolater
Linear solvers
- Direct solver MUMPS
  - Robust but not scalable
- GAMG-preconditioned KSP
  - Near-nullspace improves convergence
Non-linear & transient solvers
- Scalable as PETSc
Written in ANSI C99 (no C++ nor Fortran)
- Autotools & friends, POSIX
- Tested with gcc, clang and icc
- Rust & Go, can't tell (yet)
- \ruleof{transparency}
Flexibility follows $\rightarrow$ ::: ::::::::::::::

Flexibility I: one-dimensional thermal slab

:::::::::::::: {.columns} ::: {.column width="45%"}

Solve heat conduction on the slab $x \in [0:1]$ with boundary conditions

$$ \begin{cases} T(0) = 0 & \text{(left)} \\ T(1) = 1 & \text{(right)} \\ \end{cases} $$

\noindent and uniform conductivity. Compute $T\left(\frac{1}{2}\right)$.

. . .

English self-evident ASCII input
- Syntactic sugar
- Simple problems, simple inputs
- Robust (heat or thermal)
Mesh separated from problem
- Git-friendly .geo & .fee
Output is 100% user-defined
- No PRINT no output
- \ruleof{silence}
There is no node at $x=1/2=0.5$!

:::

::: {.column width="55%"}

\ruleofpar{composition}

\ruleofpar{simplicity}

$ gmsh -1 slab.geo
[...]
Info    : 4 nodes 5 elements
Info    : Writing 'slab.msh'...
[...]
$ feenox thermal-1d-dirichlet-uniform-k.fee 
0.5
$

\ruleofpar{economy} :::

::::::::::::::

Flexibility II: one-dimensional thermal slabs

:::::::::::::: {.columns} ::: {.column width="45%"}

. . .

Everything is an expression
Similar problems need similar inputs
\ruleof{least surprise}: $k(x)=1+x$

:::

::: {.column width="55%"}

for i in uniform space temperature; do
  feenox thermal-1d-dirichlet.fee ${i} > ${i}.dat
done

\centering {width=75%}

FeenoX can tell that $k(T)$ is non-linear
- It switchs from KSP to SNES

:::

::::::::::::::

Flexibility III: two squares in thermal contact

:::::::::::::: {.columns} ::: {.column width="50%"}

\centering {width=65%}

\ruleofpar{clarity} :::

. . .

::: {.column width="50%"}

\centering {width=70%}

Volumes $\Leftrightarrow$ materials now needed
FeenoX detects the problem is non-linear
\todolater: roughish output ::: ::::::::::::::

Flexibility IV: thermal transient with time-dependent BCs

:::::::::::::: {.columns} ::: {.column width="50%"}

\centering {width=75%}

:::

. . .

::: {.column width="50%"}

$ feenox nafems-t3.fee 
0.000   0.062   0.00    0.00
0.002   0.002   0.01    0.00
[...]
30.871  0.565   65.71   36.04
31.435  0.565   62.31   36.33
32.000  1.050   58.78   36.56
# result =      36.5636 ºC
$

::: ::::::::::::::

Flexibility V: 3D thermal transient with $k(\vec{x})$

\centering {width=70%}

https://www.seamplex.com/feenox/videos/temp-valve-smooth.mp4

Flexibility VI: point kinetics with point-wise reactivity

:::::::::::::: {.columns} ::: {.column width="45%"}

$$ \begin{cases} \dot{\phi}(t) = \displaystyle \frac{\rho(t) - \Beta}{\Lambda} \cdot \phi(t) + \sum_{i=1}^{N} \lambda_i \cdot c_i \\ \dot{c}_i(t) = \displaystyle \frac{\beta_i}{\Lambda} \cdot \phi(t) - \lambda_i \cdot c_i \end{cases} $$

\vspace{-0.5cm}

$t$ [s]	$\rho(t)$ [pcm]
0	0
5	0
10	10
30	10
35	0
100	0

\vspace{-0.5cm}

\noindent for $0 < t < 100$ starting from steady-steate conditions at full power. :::

. . .

::: {.column width="55%"}

$ feenox reactivity-from-table.fee > flux.dat
$

::: ::::::::::::::

\centering

Flexibility VI: inverse kinetics

:::::::::::::: {.columns} ::: {.column width="50%"}

. . .

:::

. . .

::: {.column width="50%"}

$ feenox inverse-dae.fee flux.dat > inverse-dae.dat
$ feenox inverse-integral.fee flux.dat > inverse-integral.dat

\centering {width=80%}

::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="50%"}

2.6. Extensibility

Possibility to add more features
- More PDEs
- New material models (i.e. stress-strain)
- Other element types
Clear licensing scheme for extensions

2.7. Interoperability

Ability to exchange data with other tools following this SRS
- Pre and post processors
- Optimization tools
- Coupled multi-physics calculations

:::

. . .

::: {.column width="50%"}

FeenoX {.example}

Think for the future! \ruleof{extensibility}
- GPLv3**+**: the '+' is for the future
Nice-to-haves: \todolater
- Lagrangian elements, DG, $h$-$p$ AMR, ...
Other problems & formulations: \todolater
- Each PDE has an independent directory
- "Virtual methods" as function pointers
- Use Laplace as a template (elliptic)
Coupled calculations: \todolater
- Wide experience from CNA2 (v2)
- Plain (RAM-disk) files
- Shared memory & semaphores
- MPI
Interoperability
- Gnuplot, matplotlib, etc.
- Gmsh (+ Meshio), Paraview
- CAEplex
- PrePoMax, FreeCAD, ...: \todolater

::: ::::::::::::::

Laplace equation with both Gmsh & Paraview as post-processors

:::::::::::::: {.columns} ::: {.column width="60%"}

Solve $\nabla^2 \phi = 0$ over $[-1:+1]\times[-1:+1]$ with

$$ \begin{cases} \phi(x,y) = +y & \text{for $x=-1$ (left)} \\ \phi(x,y) = -y & \text{for $x=+1$ (right)} \\ \nabla \phi \cdot \hat{\vec{n}} = \sin\left(\frac{\pi}{2} x\right) & \text{for $y=-1$ (bottom)} \\ \nabla \phi \cdot \hat{\vec{n}} =0 & \text{for $y=+1$ (top)} \\ \end{cases} $$

\ruleofpar{diversity}

:::

. . .

::: {.column width="40%"}

\centering \hspace{0.5cm}{width=70%}\

\centering {width=80%}\

::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="50%"}

3. Interfaces

Fully human-less execution
- Input files (1 or more)
- Output files (0 or more)
Ability to remotely report status
- Progress
- Errors

3.1. Input

Problem fully defined in input files
- Ad-hoc syntax
- API for high-level languages
- Other files (data, meshes, scripts)
Preferably ASCII (for DCVS)
- Avoid mixing problem and mesh data
GUI not mandatory but possible
- Ok to have basic usage through GUI
- Advanced features through API

:::

. . .

::: {.column width="50%"}

FeenoX {.example}

Already deployed industrial human-less production workflow (based on v2)
There are ASCII progress bars
- Build matrix
- Solve equations
- Gradient recovery
Heartbeat: \todolater

\medskip

English self-evident ASCII input
- Syntactically-sugared
  - Nouns are definitions
  - Verbs are instructions
- Simple problems, simple inputs
- Similar problems, similar inputs
- Everything is an expression!
- \ruleof{least surprise}: $f(x)=\frac{1}{2} \cdot x^2$
```
f(x) = 1/2 * x^2  
```
- Expansion of command line arguments ::: ::::::::::::::

CAEplex progress status on the cloud

\centering {width=70%}

https://www.seamplex.com/feenox/videos/caeplex-progress.mp4

NAFEMS LE10: English-like problem definition & user-defined output

:::::::::::::: {.columns} ::: {.column width="50%"}

\centering {width=75%}

:::

. . .

::: {.column width="50%"}

\ruleofpar{clarity}

$ gmsh -3 nafems-le10.geo
[...]
Info    : Done meshing order 2 (Wall 0.433083s, CPU 0.414008s)
Info    : 205441 nodes 59892 elements
Info    : Writing 'nafems-le10.msh'...
$ feenox nafems-le10.fee 
sigma_y @ D =  -5.38361 MPa
$

\ruleofpar{economy} ::: ::::::::::::::

NAFEMS LE11: everything is an expression (especially temperature)

:::::::::::::: {.columns} ::: {.column width="50%"}

\centering {width=75%}

:::

. . .

::: {.column width="50%"}

\ruleofpar{least surprise}

$ gmsh -3 -clscale 0.5 nafems-le11.geo
[...]
Info    : 8326 nodes 1849 elements
Info    : Writing 'nafems-le11.msh'...
$ feenox nafems-le11.fee 
sigma_z(A) =  -105.043 MPa
$

3D distributions in VTK

::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="50%"}

3.2. Output

Clean output expected
Do not clutter the output with
- ASCII art
- Notices
- Explanations
- Page separators
Output should interpreted by both
- A human
- A computer
Open standards and well-documented formats should be preferred

:::

. . .

::: {.column width="50%"}

FeenoX {.example}

\ruleof{economy}: output is completely defined by the user
\ruleof{silence}: no PRINT no output
ASCII columns
- PRINT & PRINT_FUNCTION
- Gnuplot & compatible
- Markdown/LaTeX tables
Post-processing formats
- .msh
- .vtk
- .vtu: \todolater
- .hdf5: \todolater
- .frd: \todolater ?
Dumping of vectors & matrices
- ASCII
- PETSc binary
- Octave (sparse)

::: ::::::::::::::

100% user-defined output: cycle loads

:::::::::::::: {.columns} ::: {.column width="50%"}

For the model below, draw the sequence of loading and unloading for different levels of strains. All bars have the same geometry and elastic properties but different yield stresses.

for i in 1 2 3 4; do
  feenox 3bars.fee ${i}
  pyxplot 3bars.ppl
  mv 3bars-sigma-vs-eps.pdf 3bars-sigma-vs-eps-${i}.pdf 
done

:::

::: {.column width="50%"}

::: ::::::::::::::

100% user-defined output: cycle loads

:::::::::::::: {.columns} ::: {.column width="50%"} \centering {width=80%} :::

::: {.column width="50%"} \centering {width=80%} ::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="50%"} \centering {width=80%} :::

::: {.column width="50%"} \centering {width=80%} ::: ::::::::::::::

Markdown table: natural oscillation frequencies of a wire

:::::::::::::: {.columns} ::: {.column width="40%"}

Experimental Physics 101 (2004)

\centering {width=70%} :::

::: {.column width="60%"}

# compare the frequencies
PRINT "  \$n\$ |   FEM  | Euler | Relative difference [%]"
PRINT ":----:+:------:+:-----:+:-----------------------:"
PRINT_VECTOR i         f(2*i-1) f_euler   100*(f_euler(i)-f(2*i-1))/f_euler(i)
PRINT
PRINT ": $2 wire over $1 mesh, frequencies in Hz"

$ feenox wire.fee copper hex > copper-hex.md
$

$n$ | FEM | Euler | Relative difference [%] :----:+:------:+:-----:+:-----------------------: 1 | 45.8374|45.8448|0.0161707 2 | 287.126|287.302|0.0611787 3 | 803.369|804.454|0.134888 4 | 1572.59|1576.41|0.242324 5 | 2595.99|2605.92|0.381107

: copper wire over hex mesh, frequencies in Hz

::: ::::::::::::::

Professional tables: environmentally-assisted fatigue

:::::::::::::: {.columns} ::: {.column width="55%"}

:::

::: {.column width="45%"}

\vspace{1cm}

Computation of NUREG-EPRI sample problem for Environmentally-assisted fatigue in NPP piping

\bigskip

Top is a table from a publication by a multi-billion dollar agency
Bottom is a PDF from FeenoX output piped through
- AWK
- \LaTeX

::: ::::::::::::::

Data for videos I: four double pendulums (v2)

\centering {width=50%}

https://www.seamplex.com/feenox/videos/pendulums.webm

Data for videos II: boiling channel with sinusoidal power profile (v2)

\centering {width=65%}

https://www.seamplex.com/feenox/videos/sine.webm

Data for videos III: modal analysis for seismic analysis of piping (v2)

\centering {width=75%}

https://www.seamplex.com/feenox/videos/mode5.mp4 https://www.seamplex.com/feenox/videos/mode6.mp4 https://www.seamplex.com/feenox/videos/mode7.mp4

Complex figures: 2D IAEA PWR Benchmark (v2)

:::::::::::::: {.columns} ::: {.column width="50%"} \centering :::

::: {.column width="50%"} \centering ::: ::::::::::::::

Complex figures: 2D IAEA PWR Benchmark (v2)

:::::::::::::: {.columns} ::: {.column width="50%"} \centering :::

::: {.column width="50%"} \centering ::: ::::::::::::::

Core-level neutronics over unstructured grids: the $S_2$ Stanford Bunny (v2)

:::::::::::::: {.columns} ::: {.column width="50%"}

\centering {height=4cm}

::: ::: {.column width="50%"}

\vspace{1cm}

One-group neutron transport
The Stanford Bunny as the geometry
$S_2$ method in 3D (8 angular directions)
Finite elements for spatial discretization

::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="25%"} \centering {height=2cm} ::: ::: {.column width="25%"} \centering {height=2cm} ::: ::: {.column width="25%"} \centering {height=2cm} ::: ::: {.column width="25%"} \centering {height=2cm} ::: :::::::::::::: :::::::::::::: {.columns} ::: {.column width="25%"} \centering {height=2cm} ::: ::: {.column width="25%"} \centering {height=2cm} ::: ::: {.column width="25%"} \centering {height=2cm} ::: ::: {.column width="25%"} \centering {height=2cm} ::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="50%"}

4. Quality Assurance

Generic good software QA practices
- Distributed version control system
- Automated testing suites
- User-reported bug tracking support
- Signed releases
- etc.

4.1. Reproducibility and traceability

Both the source and the documentation should be tracked with a DVCS
Repository should be accessible online
- Might need credentials even for RO
Version reporting
- Executables must allow --version
- Libraries must provide an API call
The files needed to solve a problem should be simple & traceable by a DVCS

:::

. . .

::: {.column width="50%"}

FeenoX {.example}

Hosted on Github (git)
- Previously on Bitbucket (hg)
- Previously on Launchpad (bzr)
- Previously on-premise (svn)
https://github.com/seamplex/feenox
https://seamplex.com/feenox
Mailing list (Google group)
Build a community! \todolater
- Code of conduct

$ feenox
FeenoX v0.1.12-gb9a534f-dirty 
a free no-fee no-X uniX-like finite-element(ish) computational engineering tool

usage: feenox [options] inputfile [replacement arguments]
[...]
$

-v/--version: copyright notice
-V/--versions: linked libraries
\ruleof{generation}: inputs from M4

::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="50%"}

4.2. Automated testing

A mean to test the code is mandatory
After each change
- Check for regressions
- Problems with already-computed solutions
- Different from verification
The compiler should not issue warnings
Dynamic memory allocation checks are recommended
Good practices are suggested
- Unit testing
- Continuous integration
- Test coverage analysis

4.3. Bug reporting and tracking

Users should be able to report bugs
- A task should be created for each report
- Address and document :::

. . .

::: {.column width="50%"}

FeenoX {.example}

Standard test suite

$ make check
Making check in src
[...]
PASS: tests/trig.sh
PASS: tests/vector.sh
=============================================
Testsuite summary for feenox v0.1.12-gb9a534f
=============================================
# TOTAL: 26
# PASS:  25
# SKIP:  0
# XFAIL: 1
# FAIL:  0
# XPASS: 0
# ERROR: 0
=============================================
$

Periodic valgrind runs
Integration tests: \todolater
CI & test coverage: \todolater

\medskip

Github issue tracker
Branching & merging procedures: \todolater

::: ::::::::::::::

:::::::::::::: {.columns} ::: {.column width="50%"}

4.4 Verification

Code must be always verified
Check it solves right the equations
- MES (mandatory)
- MMS (recommended)
One test case has to be added to the automated testing
Third-party verification should be allowed
Per-problem documentation

4.5. Validation

Code should be validated as required
Check it solves the right equations
- Against experiments
- Against other codes
Third-party validation should be allowed
Per-application/industry documentation
- Procedures following standards

:::

. . .

::: {.column width="50%"}

FeenoX {.example}

There is a V&V report for the industrial human-less workflow project
- Medical devices
- Based on ASME V&V 40
There is a lot to do!
MES
- Set of well-known benchmarks
- NAFEMS, IAEA, etc.
MMS
- Everything is an expression
- Parametric runs
- MESH_INTEGRATE allows to compute $L_2$ norms directly in the .fee

\bigskip

TL;DR: \todolater

::: ::::::::::::::

Experimental Validation

\centering {width=65%}

https://fusor.net/board/viewtopic.php?f=13&t=14087 $\leftarrow$ because it is FOSS!

:::::::::::::: {.columns} ::: {.column width="50%"}

4.6. Documentation

Documentation should be complete
- User manual
  - Tutorial
  - Reference
- Developer guide
Quick reference cards, video tutorials, etc. not mandatory but recommended
Non-trivial mathematics and methods
- Explained
- Documented
Should be available as hard copies and mobile-friendly online
Clear licensing scheme for the documentation
- People extending the functionality ought to be able to document their work

::: ::: {.column width="50%"}

FeenoX {.example}

FeenoX is not compact!
- Even I have to check the reference
Commented sources: \todonow
- Keywords
- Functions
- Functionals
- Variables
- Material properties
- Boundary conditions
- Solutions
Shape functions: \todonow
Gradient recovery: \todonow
Mathematical models: \todonow

\medskip

Code is GPLv3+
Documentation is GFDLv1.3+

::: ::::::::::::::

Conclusions---FeenoX...

closes a 15-year loop (2006--2021) with a third-system effect
is to FEA what Markdown is to documentation
is (so far) the only tool that fulfills 100% a fictitious SRS:
- Free and open source (GPLv3+)
- No recompilation needed
- Cloud and web friendly
- Human-less workflow
follows the \unix philosophy: "do one thing well"
is already usable (and used!)
- FeenoX v1.0 coincident with the PhD (\todonow)
  - Laplace, heat, elasticity, modal, neutron transport & diffusion
  - Every current feature is there because there was at least one need from an actual project
- Future versions online (\todolater)
  - Electromagnetism? CFD? Schrödinger's equation?
  - Python & Julia API
  - Coupled & multiphysics computations
  - Free and open-source online community

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Background 1/2

Background 2/2

How do we write papers/reports/documents?

How do we do scientific/engineering computations?

Software Requirement Specifications

FeenoX Software Design Specifications {.example}

1. Introduction

1.1. Objective

FeenoX {.example}

1.2. Scope

FeenoX {.example}

Transfer-function & English-like input: Lorenz’ system

Lorenz’ system

Web interface: CAEplex, finite elements in the cloud

2. Architecture

FeenoX {.example}

2. Architecture

FeenoX {.example}

How to solve a maze without AI 1/3

How to solve a maze without AI 2/3

How to solve a maze without AI 3/3

The life of an influencer...

2.1. Deployment

2.2. Execution

FeenoX {.example}

Direct execution: three ways of getting the first 20 Fibonacci numbers

Parametric execution: shear locking in cantilevered beam

Parametric execution: shear locking in cantilevered beam

Optimization loop: finding the right length of a tuning fork

2.3. Efficiency

2.4. Scalability

2.5. Flexibility

FeenoX {.example}

Flexibility I: one-dimensional thermal slab

Flexibility II: one-dimensional thermal slabs

Flexibility III: two squares in thermal contact

Flexibility IV: thermal transient with time-dependent BCs

Flexibility V: 3D thermal transient with $k(\vec{x})$

Flexibility VI: point kinetics with point-wise reactivity

Flexibility VI: inverse kinetics

2.6. Extensibility

2.7. Interoperability

FeenoX {.example}

Laplace equation with both Gmsh & Paraview as post-processors

3. Interfaces

3.1. Input

FeenoX {.example}

CAEplex progress status on the cloud

NAFEMS LE10: English-like problem definition & user-defined output

NAFEMS LE11: everything is an expression (especially temperature)

3.2. Output

FeenoX {.example}

100% user-defined output: cycle loads

100% user-defined output: cycle loads

Markdown table: natural oscillation frequencies of a wire

Professional tables: environmentally-assisted fatigue

Data for videos I: four double pendulums (v2)

Data for videos II: boiling channel with sinusoidal power profile (v2)

Data for videos III: modal analysis for seismic analysis of piping (v2)

Complex figures: 2D IAEA PWR Benchmark (v2)

Complex figures: 2D IAEA PWR Benchmark (v2)

Core-level neutronics over unstructured grids: the $S_2$ Stanford Bunny (v2)

4. Quality Assurance

4.1. Reproducibility and traceability

FeenoX {.example}

4.2. Automated testing

4.3. Bug reporting and tracking

FeenoX {.example}

4.4 Verification

4.5. Validation

FeenoX {.example}

Experimental Validation

4.6. Documentation

FeenoX {.example}