The Freedom of Internet at OSCAL 2022

How old is the Internet? Are we aware of the technologies that are behind this concept? What does it mean to be secure while accessing the Internet? How many antivirus programs have been developed to protect GNU/Linux systems? These were some of the questions I had in mind when I decided to attend OSCAL 2022. To my surprise, this event exceeded my expectations. I discovered really interesting topics and workshops, young tech developers, experienced speakers, hardworking organizers, and a very enthusiastic FLOSS community in Tirana, Albania.

Going to the event

My journey started on Platform 5 in Reading from were I got a train to London Gatwick airport. It was a sunny Friday morning in the UK, and it seemed that many people took the day off because the train was completely full! Laughs all around were part of my journey, smartly dressed people, ladies in glamorous dresses and hats, presumably heading for Ascot races.

A direct flight of about 3 hours was on time and, ironically, when I was trying to connect to Internet at the airport, I had to fill in an online form which not only asked for my personal information such as full name, email, and phone number but it also wanted to know my citizenship status. Why do they need to collect this information?

The distance from the Tirana airport to the centre of Tirana was about 30 – 40 minutes by bus or taxi. From there, I was able to walk to almost everywhere as the centre is quite compact. The city was full of activities for youngsters, over the weekend there were dance performances and concerts every night.

The event

Two days of talks, workshops and the exhibitions were held on the second floor of Tirana European Youth Capital HQ. A lovely patisserie was conveniently located on the first floor, so we could enjoy our food in the same building.  

On the first night I was able to attend the PreParty at Hackerspace. I could see how the community decorated its space. It got my attention how they framed the posters of previous events and I really felt it was a very connected and organized team. I was so glad to finally meet face-to-face the young women who run the Hackerlab in Albania. Some of them are FLOSS developers, security administrators, marketers and promoters in Albania.

Talks 

You can see the detailed list of talks here. I listened to the presentations made by OpenSUSE, LibreOffice, Wikipedia and the Fedora community. Pictured below, the talks by Johannes and Mike. Johannes did 5 live demos to create a secure setup for developers. Mike shared the ongoing efforts done by the Libre Office community.

Censorship of Wikipedia was a controversial talk that kept us very concentrated for more than 25 minutes. Good job Lars! There was also a panel to talk about the FLOSS situation over the past 20 years and future opportunities.

Other talks were focused on the laws and regulations regarding the data we publish and the opinions we express online.

Workshops

I attended two workshops that were full and even people were stood up. One by Endri: Digital Forensics and Incident Response, and the other about TOR by Klesti Fetiu.

Exhibitor stands 

One of the projects that caught my eye was CARBONIO which is an alternative to Office365. I tested the software and it was able to do calls, mark calendars, receive and send emails. One novelty of this software was the feature of using and editing in real time LibreOffice files from emails. 

I definitely recommend this free software. It was full functional and it provides a fresh UI.

Fedora 

It has been almost ten years since I joined Fedora as Ambassador in July 2012. It was so nice to meet in person Mariana Balla from Fedora Albania. It was also a pleasure to meet Nefie Shehu who is a very active FLOSS leader in Albania. It was nice to chat with OpenSUSE.

My presentation

I started my presentation paying my respects to Marina Zhurakhinskaya  who has done so much during her lifetime to promote the participation of women in Linux around the world. To see my presentation, please click here.

Curious facts

  • We had a workshop to unlock a lock.
  • The traffic lights duplicated with long strip-lights
  • The touch-screen controls in an elevator
  • I saw many more women than men in the city.
  • During my flight, for the first time I noticed an aircraft going in an opposite direction – a huge airliner was out of sigh incredibly fast.

Thank you Fedora for sponsoring my traveling to Tirana, Albania! I enjoyed getting around the city!

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Reliving the ISC 2022

My adventure of attending the 5-day conference started with “Looks like we have a little bumpiness ahead. Please return to your seat and buckle up” when I took a plane from Heathrow, London.

This year, ISC registered 3007 attendees and 137 exhibitors. Definitely, it is one of the most successful worldwide HPC conferences in the past two decades. And, although I am well aware of the agenda and the structure of the event (because I have attended before), it was still like a box chocolate every single moment.

The HPC world-class conference

I would like to share my personal experience and what this HPC conference means to me:

  1. The keynote speakers are in charge of projects that are truly transforming the future of mankind. In my experience, all of them have been approachable to exchange opinions, extremely kind and brilliantly funny. You can only imagine how impressed I was when Prof. Thomas Sterling “the father of HPC” remembered exactly all our conversations we had almost 7 years ago. I was really honoured to talk to him again.
  2. You can definitely get hold of the newest technologies if you are thinking of implementing HPC in your company. In exhibitor space, the stalls had both technical specialists and commercial staff to enlighten and support you.
  3. If you are in the academia, you have the chance to talk with the top researchers of HPC while they are presenting their posters or making their presentations.
  4. The HPC ecosystem is covered by workshops run by teams from the most renowned HPC institutions such as OpenMP, MPI, CUDA/GPU, Amazon and many others. They were really engaged and I literally felt how my brain was being stimulated.
  5. Every single detail in the conference was neat and carefully detailed: the registration, the website, the catering, the internet connection, audio, video, photos. It was an A1 event.
On the photos above you see me hearing about GPU-related projects, watching a virtual factory simulation, meeting one of the coolest HPC scientist in the world, showing off the new parallel programming books I received and having fancy food.

We are the champions

One of the most exciting moments of the event is the announcement of the top1 supercomputer in the world. Frontier is the winner this year. It uses AMD hardware infrastructure. Although it is the most powerful supercomputer today, the problems of the present and future need better infrastructure. To this end, Intel is developing Aurora.

The nodes of Frontier (with AMD), and Aurora (with Intel) respectively.

In my eyes, a really great way to start in the world of HPC is to set up your own supercomputer and the Student Cluster Competition gives you that opportunity. This year, none of the Chinese teams attended the event in person, but they were still victorious online! They are usually the winners at this competition. I was very pleased to see that my favourite teams were on the stage! The team of my university – the University of Edinburgh! The Spanish team stood out because of their team spirit, and of course, the winners from the University of Heidelberg.

It so happens that guys from Heidelberg helped me with my luggage at the train station when I arrived in Hamburg. When we later bumped into each other during a coffee break, they told me that they have been taking part in the competition for 5 years. Call me a clairvoyant but I told them they were going to win this year. And they did.

Congratulations again to the team Heidelbears from the University of Heidelberg

Marvellous members of the HPC community

What a list of notable HPC people from different organizations around the world! The roller-coaster feeling I experienced throughout the event was definitely due to the interaction with the people I met after COVID years in person. Meeting them was a real birthday present to me. Thanks for the selfies to Jack from Nvidia, Ben from the Uni of Edinburgh, Toby from Intel, Mateo from BSC, Laura from Washington DC uni, Prof. Jack from Tennessee, Prof. Satochi from RIKEN, Richard of PETSc, Hartwig, Ieva, Bastian and Oleg from the math session, and Prof. Sterling from Indiana University.

Thanks for the kind attitude to have my HPC selfies at ISC 2022.

New talents

As the HPC community needs to pass on the knowledge to keep growing, I was so glad to meet new and young talent in the HPC field. Thanks to all for the chats, lunch times, cocktails times, debugging ideas, and for the new gifts received at the conference. Innovative ideas are the best gifts ever!

I was so curious about their work in the field of HPC and why they came to ISC 2022. It was very impressive to hear about the new libraries they are developing using parallel algorithms.

Promoting the Women participation in HPC-Science

I can tell that I was able to picture almost all the women attendees in the event. These extraordinary women had to work hard to be exposed in the event. Some of them were speakers, poster presenters, and volunteers in the ISC organization. Glad to see how their institutions promoted their HPC career progression.

The Women in HPC (WHPC) had a space to discuss the challenge women face in HPC field every day because HPC teams are mostly male-dominated.

Great scientific and HPC work done showed in their posters

I think that the message was that being in the right place helps to find inner peace, happiness, and then you can grow. Thanks again to this group since 2016.

My ISC mentor

Having a top A1 event recognized around the HPC world demanded several years of assiduous work. Ms. Nages Sieslack, the ISC Marketing Communications has been demonstrated dedication and love for her job. She is truly an inspirational mentor. She actively rose me to the top-class HPC universe, since I was a teacher in Peru at UNI, she kindly respected my dreams about developing HPC tech in Peru, and my willingness to spread the HPC word around the world.

An immense appreciation to Nages.

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ISC 2022 – Third Day

Conference Day

I attended the Mixed Precision in Low-Rank Approximation and Randomization talks. I was very interested in their work that involves the use of preconditioners, Krylov Subspaces, and scalability of direct methods such as LU.

HPC Research Posters

The research posters related to HPC were posted all around the ground and second floor. I found some implementations on HPC cloud and migrations from AWS to Azure. Other interesting research we found was related to the infinite and the Conjugate Gradient.

Women in HPC

Today, we celebrated the reception of Women in HPC, present were all people in favour of the promotion and the development of the careers of women in HPC.

Closing up Keynote

Laura Barba and JeffMcVeigh gave the keynote in the afternoon. Laura highlighted the 10 years of PI Manifiesto and the impact in OpenSience. The Intel CEO presented new sustainable technologies towards the Zetaflops era (The Aurora core, Channel, I/O, storage).

Workshops and Cluster Competition

HPC organisations are still presenting their products and services in their booths.

The students from different universities are still competing with their clusters.

Lovely connections

I had the chance to meet people from Estonia, Arabia Saudita and USA (Laura)!

HPE dinner

Hewlett Packard Enterprise offered tonight an extraordinary dinner by the river.

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ISC 2022 – Second Day

We keep transforming the future of industry and academia. Thanks to the effort and guidance of many people involved around the world in making it possible. This year, the keynote talks were the charge of NVIDIA leaders, followed by more exciting events. This is how the HPC community celebrated their milestones.

Opening Keynotes

The Vice President of Omniverse and Simulation Technology at NVIDIA, Rev Lebaredian, presented the Digital Work they have been working on using different open-source applications in modern manufacturing industries, a fantastic example was presented shortly afterwards by Michele Melchiorre from BMW presenting digital twins of manufacturing facilities. He also emphasised the importance of AI to get more accurate calculations to simulate real world complexity.

The house was full and I was glad to see that tech was incredibly used when the Q&A through the ISC app. In real time, the best questions were up-voted in order to be asked to the keynote speakers.

The alarm

Immediately after the first break, the fire alarmed rang and we all had to evacuate the building. I think more tweets were posted due to this incident, comments such as “cluster on fire?” were shared on the media.

The Nobel Prize of HPC

I have the sensation the greatest winners of the event were ORNL and Jack Dongarra from the University of Tennessee! It was a big ovation from the audience. I had the chance to interact with him a couple of times and I think he is an incredible person! Congratulations again!

The top 500 list

Frontier at ORNL beated the exaflops this year! The ORNL director revealed the difficulties they had since 2020 during COVID lockdown to make it. It was challenging to support Frontier and SUMMIT in production at the same time. The top tree supercomputers are reaching the exascale barrier. Neat work also presented by the LUMI team!

The Exhibition

Outstanding stands were ready today at 3pm! HPC industry and organisations offered novelty and useful gifts this time such as luggage tags and personalised mat for coffee cups. Some of them are offering everyday the opportunity to win a Lego Star Wars Helmet :O

Food and icecream

Attendees are still enjoying the delicious food served in “batch containers?” 🙂

Chocolate ice-creams were able at any time today!

Networking

Thanks for all the good vibes HPC people! Today was a very long and very excited day!

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ISC 2022 – First Day

After two years off due to pandemic, on Sunday 29th the HPC conference, namely the ISC returned.

As an early bird I arrived at our venue first thing this morning. This is how the entrance of our home for the next few days, the CCH, and the registration desk, look like, :

Tutorial Day

There were many tutorials to choose from during the first day. Following German punctuality, all talks followed the agenda and were on time. Personally, it was a very hard to decide whether to attend the GPU day or the half day of OpenMP and the other half for MPI parallel programming. Pictured here is the OpenMP team that had planned to release OpenMP 6.0 in November 2023. In the right side of the picture, you can see a lady running an HPC tutorial. It was so great to see a woman presenting her expertise.

HPC people

Meeting HPC people I already know was fantastic! I am very glad to have had warm greetings from them.

And of course, such conferences are a wonderful opportunity to meet many new, friendly people.

The HPC Community

HPC companies stalls

People from all over the world are working hard to make everything perfect for the exhibition booths.

Student Cluster Competition

Students from related HPC programs at many universities have arrived today and prepare their clusters to boost them up for the student cluster competition.

Bytes Size Food

Food came well prepared in perfectly sized individual portions (or bytes?) 🙂

The breakfast, the lunch and the breakfast were all first class.

An ISC Team

I was delighted to meet the ladies who are so important behind the scenes of one of the prominent HPC conferences in the world such as ISC which has been held since 1986.

The AMD night celebration

The partnership of Hewlett Packard and AMD organised the exquisite dinner.

Overall, I am enjoying the event. Many thanks to the ISC committee 2022 for the welcoming tweet!

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HPC Talks during Lockdown

Homeworking was one of the challenges we faced during the lock-down (2020 – 2022). During that period, I was also adapting to my first professional job in the UK as well as to a new society rules in England. As a single woman from overseas, my resilience was tested by cultural barriers and obstacles. Then, I was so excited to see my profile at the @Womeninfusion page.
At that moment I realized that all my struggles had only strengthened my resolve to stay true to my objective: to become an HPC Software Specialist.

Here are some of the HPC events I participated during the lockdown period in the UK:

HPC Webinar 2020

The first HPC event I organised was namely HPC webinar 2020 during the lunch time. I was quite new employee, so I was thrilled to see Prof. Ian Chapman announcing it!

Spanish Fusion HPC Workshop

In 2020, I presented a work I did to benchmark preconditioners on basic multiphysics. You can see my talk recorded here.

In 2021, a deep studying of the preconditioners scaling was presented, I only focused this time in the displacement 3D problem. You can see my talk recorded here.

DevConf.cz 2022

I presented my work of preconditioners using different mesh sizes in the online conference sponsored by RedHat.

Using MOOSE and HPC

Internally, in the UK 2022, my team lead by Helen Brooks organized a MOOSE Workshop were I gave a talk in regards to the HPC performance on MOOSE.

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Activities in my workplace

Going back onsite after around two years of lock-down brought me some nice surprises. Here are some of the activities I attended this year at UKAEA.

STEP Showcase

On May 12th, I was able to present what our team in STEP has done in the past two years. The team is leaded by Andrew Davis. Under his supervision, I work on the digitalization of the divertor monoblock. I had a sparkling day! I met Adamos Lukenskas who is working on the optimization of the design of the divertor monoblock in real life! 🙂

During the showcase, I’ve encountered more nice STEP people. I was glad to find a rainbow of diversity. Here are some pictures of people from Italy, Bermuda Island, Chile, Brasil, and of course… me from Peru! 🙂

Let’s talk about gender

“Men are from Mars, Women are from Venus”. UKAEA is aware about, then an event to promote the women networking as part of our health and wellbeing in our daily. This event was hold on Wednesday 27 April.

It was great connecting with outstanding women in the fusion field and those who work in support of other women rights.

Star Makers

On April 13th, an informative movie was presented during our break. This documentary film highlighted the record energy produced over five seconds at UKAEA. This world record-breaking fusion energy demonstration was the work of several years as well as the effort of passionate and dedicated employees. I was pleased to meet in person one of the starmakers: Damian King!

In my eyes, this movie evidences the work of a great woman and professional: Ferrnanda Rimini

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DRI Retreat 2022

From 28 March 2022 to 1st April 2022, N8 CIR organized the Digital Research Infrastructure(DRI) Retreat in the University of Manchester. You might find more about the N8 partnership here.

The goal of N8 CIR is to create a Centre of Excellence in Computationally Intensive Research, sharing methods, skills and facilities to underpin the strategic research objectives of the N8 universities.

Topics and Panelists

One of my favorites discussions was about the academia. I met Dr. Sarah Harris who is a passionate biologist who also is a user of High Performance Computing (HPC) resources, and RSE services.

Unconference Activities

One of the activities I enjoyed the most was the unconference. We listed in an online document our ideas of how to improve different issues such as sustainable learning, interaction in a team, as others.

Networking

I was able to meet a great mathematician who helped me with some Linear Algebra concepts. Felt good in using again chalkboard at the university. Really appreciate the kind help received during the event.

Exquisite Food and Impeccable Service

The organization arranged our stay at Hyatt, and we all enjoyed fine catering and dinners.

Getting around the city

Manchester is definitely a jam-packed city with ancient and modern architectures. I was so happy to walk again in this marvelous place!

Manchester City Stadium | Manchester Central City | Piccadilly Gardens

Great organization! Again… Congratulations! I was very happy to meet great people and professionals within the UK!

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How fusion could change the world

Today, we offered an online talk in the University of Edinburgh for free.

Last week, Bella, Lorenzo and myself were able to outline the main points of the talk. We did an online rehearsal to anticipate some questions and answers.

Last week, Bella, Lorenzo and myself were able to outline the main points of the talk. We did an online rehearsal to anticipate some questions and answers.

Bella is a well-informed educator in the fusion field and she explained the process of getting and releasing the energy source using a lithium blanket in a tokamak. I particular liked how she explained the physics behind the scenes of the purple colour of a plasma in simple words to the students.

Lorenzo gave an overview about fusion and the role of Artificial Intelligence to make fusion possible for everyone is the upcoming years. Hopefully in 2040s.

Julita (me) was trying to emphasized the digitalization of a tokamak, and the effort done for around 100 years for several scientists around the world.

I was very glad to see that we reached an audience of about of 52 people.

Some curious questions were raised after our presentations, such as how many tokamaks are in the world, when it will be possible to have sustainable fusion, how IA contributes to this challenge, among other numerical accuracy questions.

Other questions were solved in the box Q/A online by others such as Gulio:

Thanks to Xinran and all the organizers for the opportunity to share our knowledge with more students and future scientists!

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UKAEA at the TYC London event

A group of enthusiastic employees of UKAEA attended to an event organized by the TYC in the Queen Mary University located in London, UK on May 10th.

UKAEA talents

Michelle Tindall traveled to London from South Yorkshire where UKAEA has a new site with scientists allied to achieve the commercial fusion in upcoming years. She shared her fusion’s experience with the PhD students.

Priti and Bella are two inspirational women involved in the fusion field. They emphasized the importance of the studies of materials, and their behavior at nano-scale level at extreme temperatures. Most of the students at the event have expertise in this matter.

Jacob and Sam are the two scientists working for the STEP project. They have more than five years experience and know-how of prototyping and integration of components in a tokamak (JET and ITER).

Julita (myself) recently joined STEP and the tokamak digitalisation challenge. I am striving for simulating different components of a tokamak. I shared my knowledge with the students.

The talks

I was very pleased to hear that most of the studies involved the application of IA with GPUs and Tensor Flow, as well as HPC cluster Tier 1 such as ARCHER, and some other chemical researches that use Tier 3 clusters that London Universities own. Some projects are still using local cores in their studies, that is the case of the lovely chair: Chengcheng Xiao. Congratulations also to Fabian, who won the poster competition by doing a study of the graphene deformation.

Latino American Scientist in the UK

I was thrilled to speak face-to-face in Spanish (my mother tongue) with successful scientists in the UK: Jorge Ontaneda and Rachel Crespo Otero.

Event Catering

We enjoyed an extensive range of the finest and delicious coffee breaks, lunch, and our happy ending with wine and snacks. Thank you very much to the organizers for the invitation and kindness received throughout the event.

Personally, I had nostalgic feelings towards parts of university in Edinburgh by hearing about CP2K on ARCHER. I can say that this conference somehow took me to the past at uni moments, and oddly also to the future, I had the opportunity to talk more with colleagues about the fusion business. Thanks UKAEA for this! ❤

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My presence at Culham Plasma Physics Summer School

I was able to attend the 58th edition of the Culham Plasma Physics Summer School held at the UKAEA site. This event which consists of students and professionals related to Physics, Maths, Computer Science, and researches from around the world who are working in favour to develop nuclear fusion.  

The lectures 

As it was planned in the schedule, the first day started with an overview of what UKAEA is doing in order to achieve its mission. The first talk was presented by the CEO, Ian Chapman. It was followed by Chris Warrick from UKAEA comms to talk about the history of Plasma. One of the renowned researchers (Mr. Chippy Thyagaraja) presented on both Mathematics and Plasma physics. 

From the right to left, Dr. Chapman, Dr. Chris, and Dr. Chippy.

My favourite talks

I chose these talks because in my eyes, being a scientist and communicator is extremely challenging. Prof. Nicholas Braithwaite from The Open University gave us an idea of the progress overtime in the subject of Low Temperature Plasma. Dr. Kate Lancaster who was also an attendee of the Culham Summer School 20 years ago (wow!) talked about inertial confinement plasma. One of the youngest lecturer was Phd. Hardman from Oxford, who really did a hard job in kindly presenting the talk twice since he did it online and also, in behalf of his colleagues.  

The attendees

The organization provided some tea and biscuits during break times in the middle of morning and afternoons. Paul Hiret, was the winner of the poster presentation with his study in plasma. The launch time was a great opportunity to meet more researchers and thanks to all for kindly accepted my unexpected photos 🙂  

Closing event

A dinner was organized in the Edmund Hall at Oxford University after two intense weeks. We enjoyed an exquisite menu with wine. I had the chance to meet a well experienced professional in Plasma in Business: Adam Woods, who is working for STEP!  

My appreciation 

I am glad that now I have a better understanding of the structure of a tokamak, the studies of plasma done in the UK, the USA, Russia and throughout the EU. 

In the future Culham Plasma School events, I would suggest arranging the order of topics (e.g. We had “What is a Tokamak” on Wednesday, instead of Monday). Starting from the simplest concepts for the first day, makes easy to understand the complexity of plasma concepts and other work related. 

I also was pleased to meet different scientists with different personalities and cultures ❤  

Friendly support 

I want to give a special thanks to some participants for making me feel welcome in this new world of science. They kindly offered some explanations on what is going on in the lectures and in general, in the UK.  

Pictured from the left to the right: Emily Lewis, Luke Humphrey and Michelle Tindall.

The content of this post was approved by UKAEA’s comms: Chris Warrick, Nick Holloway, Nikolaus Muldal. Special Thanks to Tara Robinson for the English corrections.

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GNOME Latam 2021

Today, we have “celebrated” a year of the lock-down in the UK. It is also been a year that I was not able to travel to anywhere to celebrate with the GNOME community all the advances that this organization has been done for years in pro-FLOSS.

I have been invited to be a presenter in this new endeavor! The GNOME Latam 2021! Thanks to Daniel Gallegillos who gave me more details about this event, where mostly the languages used in the talks are going to be Spanish, and Portuguese.

You are more than welcome to join us, and to listen to these interesting talks this Saturday, March 27, 2021. To see the entire content of the talks, click here!

See you there! UTC – 13:00 hrs.

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Building an application on MOOSE

Yesterday, I attended to the workshop of MOOSE held by members of the Idaho National Laboratory. There were two days, where they showcased around 11 exercises of MOOSE. One of them was the hands-ons by Andrew Slaughter, and I want to share that experience.

First of all, we can clone the repository to see the structure of the folders of a MOOSE app.

git clone https://github.com/aeslaughter/MurderHornet.git

Inside the application which in this case is called MurderHornet, we are going to build it in parallel to finally run the tests previously set. We have to see a message PASS for this test.

cd MurderHornet/
make -j 4
./run_tests

Now, it is time to run the input file with the executable developed by Andrew inside the kernel folder. Usually, the input is located inside the problem folder.

~/projects/MurderHornet/problems
../murder_hornet-opt -i laplace_young.i

Lastly, we can view the simulation using peacock by executing the following command:

~/projects/moose/python/peacock/peacock -r laplace_young_out.e

Thanks so much to Jason Miller and to  Alex Angelou for the help with MOOSE 🙂

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Understanding the Hello World of PDEs

According to the tutorial of FEniCS (software that solves PDEs using the Finite Elements method), solving the Poisson equation in 2D is programming the “Hello World” of PDEs.

The mathematical aspects

We have to consider that the Poisson equation involves these two conditions:

-∇² u (x) = f(x), x in Ω       (01)

u(x) = uD (x), x on δΩ       (02)

In (01), f(x) is a known function, Ω is the domain of the solution, ∇² is the Laplace operator (Δ), and we have to solve u(x). In 2D, we can represent -∇² u (x) as: -(δ²u/δx²) – (δ²u/δy²) = f(x,y).

In (02), Ω is the boundary of Ω, and u=uD represents the boundary condition.

FEniCS uses the Finite Elements method to solve PDEs, then it is compulsory to express the PDE (01) in a variational form. In order to get the variational form, we can multiply the PDE by a function called v(test function) with a premise that v=0 on δΩ, then we can integrate it over the domain Ω, having this:

  (03)

 

Analysing the right side of (03), we can do integration by parts to finally get a result such:

(04)

 

Both v(TestlFunction) and u(TrialFunction) are going to be defined in the same V domain that contains a mesh with the number of vertex selected to discrete the domain. Since the functions located in the domain V are continuous, a technique used by FEniCS is to discrete to make it computational. Then, FEniCS only considers a set of functions called V_h which are also included in V. Later, it is also convenient to assign the left side of (04) to the variable L, and the right side of the equation to the variable a, as follows:

(05)

The author in the tutorial indicates that he has constructed a problem with a known analytical solution so that it can be easily checked the correctness in computational terms. The following values have been selected in this matter:

f(x,y)=6,

uD(x,y)=1+x²+2y²,

Ω=[0,1]×[0,1].

The computational aspects

Let’s do a review line by line throughout this “hello world” FEniCS implementation.

from fenics import *

Firstly, we are importing all the libraries of FEnicCS to be used in the program. To install FEniCS, I used Python3, Dolfin and podman on Fedora 32. Other tools can be found here.

mesh = UnitSquareMesh(8, 8)

We are setting a mesh of a shape of square of dimension 1(Unit square mesh). It will be divided by 8 parts in 2D, 8 on x axis, and 8 on y.

V = FunctionSpace(mesh, 'P', 1)

The previous mesh defined, is used in a finite element function space called V. The Lagrange method of order 1 is applied to solve the equation with the Poisson restrictions explained before. A note aside, is the use of order greater than 1, can generate more errors.

u_D = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]', degree=2)

The u_D function is a known input which defines the boundary conditions. In this case, the formula implies a polynomial order 2. x[0] denotes the value of x, and x[1] denotes y.

def boundary(x, on_boundary):
    return on_boundary

The on_boundary function has previously been coded on FEniCS to validate if a point belongs to the current boundary of the domain, or not.

bc = DirichletBC(V, u_D, boundary)

The boundary condition (bc) is stated in the space V, to be applied on boundary of the function u_D. By using the type of boundary condition “Dirichlet”, it will specify the values that a solution needs to take along the boundary in the domain V.

u = TrialFunction(V)

It was mentioned that the u function is the PDE we are looking for. In order to find the solution, it was also explained that we need the variational formula. In this case, “u” is the new problem to solve and it will be called as TrialFunction in a TrialSpace V.

v = TestFunction(V)

It was taking into consideration a v function that will have the value of zero in the border.  This v function is going to be called TestFunction in the V TestSpace. It will be computed against the trial function u to satisfy the variational problem.

f = Constant(-6.0)

The f function, is a function that is known to solve the EDP. In this case, is a constant = -6.

a = dot(grad(u), grad(v))*dx

The left side of the variational formula is going to be assigned to a. It will compute the trial function u versus all the v test functions in V.

L = f*v*dx

The right side of the variational formula considers the function f on all the test functions v.

u = Function(V)

Since u is the Function that solves the EDP, we need to prepare this variable to receive the final solution in the domain V.

solve(a == L, u, bc)

The operation to solve u requires that, a is equal to L, as well as the calculation of bc. The solution will be assigned to u.

plot(u)

The solution u can be plot and could be visualized using tools such as Paraview or Visit.

plot(mesh)

We can also display the mesh to the see the highness of the PDE in regards its domain.

vtkfile = File('poisson.pvd')

We are going to save our solution in the vtkfile variable, under the name of poisson.pvd.

vtkfile << u

Again, u is the final answer (PDE) that will be stored in the vtkfile.

error_L2 = errornorm(u_D, u, 'L2')

After finding u, we need to know how far we are in comparison to the correct solution. It is known that the U_D is the solution, then we have to calculate the error with the error_L2 formula which utilizes spaces of Gilbert to find the norm in u.

vertex_values_u_D = u_D.compute_vertex_values(mesh)

The error is also computed in the vertexes of the mesh, in this case, the ones in the border.

vertex_values_u = u.compute_vertex_values(mesh)

This line compute the error in the vertexes of the mesh inside the border of the PDE.

import numpy as np

We are going to import the library numpy with the alias np to use max and abs functions:

error_max = np.max(np.abs(vertex_values_u_D - vertex_values_u))

This calculates the maximum error found in the solution including border and content.

print('error_L2  =', error_L2)

This line only prints the error found in the calculation of error_L2.

print('error_max =', error_max)

This line prints the maximum error found in the PDE.

The simulation 

Paraview shows both, the domain and the PDE as follows:You can find more PDEs tested from the tutorial in my github. Thanks to Manuel Merino!

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My first MOOSE simulation

MOOSE is a tool that allows the use of many physics and maths libraries to run simulations of finite elements of any shape, including unstructured meshes.

My purpose is to run simulations in parallel. My laptop that already is using Fedora 32, has four cores to process calculations.

According to the official MOOSE Website, we can install MOOSE using Conda.

1. In case you already have installed Conda, and its configuration; please go to the step 3.

You might install conda on Linux, by executing the following command:

curl -L -O https://repo.anaconda.com/miniconda/Miniconda3-latest-Linux-x86_64.sh
bash Miniconda3-latest-Linux-x86_64.sh -b -p ~/miniconda3

2. Then, please set the global environment in our system to use conda:

export PATH=$HOME/miniconda3/bin:$PATH

3. Let’s add the channel conda-forge that will allow us to create the moose environment:

conda config --add channels conda-forge
conda config --add channels https://mooseframework.org/conda/moose
conda create --name moose moose-libmesh moose-tools

4. You need to activate the new moose env to use it. Do an update if it is possible:

conda activate moose
conda update --all

5. Clone the moose code and the examples provided in the new moose environment:

mkdir ~/projects
cd ~/projects
git clone https://github.com/idaholab/moose.git
cd moose
git checkout master

6. You can run the project in parallel, in this case we are using only four cores:

cd ~/projects/moose/test
make -j 4
./run_tests -j 4

If everything is a success, a message that the passed tests done in parallel, is displayed:Now, were are ready to run our first MOOSE program. I followed this workshop

cd ~/projects/moose/tutorials/darcy_thermo_mech/step01_diffusion
make -j 4 # use number of processors for your system
cd problems
../darcy_thermo_mech-opt -i step1.i

Remember to copy the content of sept1.i, and execute the output with Peacock, as follows:

~/projects/moose/python/peacock/peacock -r step1_out.e

Now, we have our simulation in action 🙂Thanks to my friend Manuel Merino for his support during my new age as a scientist.

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