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RIKEN Center for Computational Science (R-CCS) will hold a hybrid school in March 2023 titled "RIKEN International HPC Spring School 2023 ~ Toward Society 5.0~ Parallel computation of ill-conditioned sparse matrix in finite element analysis".
This program will be provided in English.

The program consists of 3 days in hybrid with on-site and online. The on-site attending is only for those who can commute to R-CCS without accommodation.

The lecture is focusing on parallel linear solver for finite element analysis. Finite element method is a strong tool for various type of industrial problems by utilizing consolidated knowledge of mathematics and engineering. To obtain finite element solution, at the final stage, linear system with large sparse matrix needs to be solved and the condition number of such matrix becomes very large due to spatial jump of physical parameters and to complex coupling of multi-physics.

Participants will gain knowledge to solve linear and nonlinear systems with large sparse matrices on parallel computers. Foundation of linear solver, such as Krylov subspace methods with preconditioner based on domain decomposition, will be explained.

Hands-on session in each day will treat parallel programing using MPI, OpenMP, numerical libraries, METIS and PETSc.

At the end of the lecture, a domain specific language for finite element simulation, FreeFEM is briefly introduced with an example of nonlinear elasticity problem with large deformation, which will be solved by the Newton-Krylov-Schwarz method.

Day 1 : sparse matrix and Krylov subspace method, GMRES and CG
Day 2 : distribution of sparse matrix with overlapping domain and additive Schwarz preconditioner
Day 3 : introduction of domain specific language FreeFEM to generate nonlinear equation with sparse matrix for hyper elasticity problem with Green-St Venant strain tensor

Date Mon, March 13 - Wed, March 15, 2023
City Kobe, Japan/Online



RIKEN Center for Computational Science


Introduction of Lecturers

Administrative Office

Collaborations Group
RIKEN Computational Science Promotion Office


Eligible individuals are as follows.

  • Students who are enrolled in a Ph.D. program, post-doctoral scientists and early career scientists affiliated with universities or research institutions.
  • Scientists and engineers affiliated with private companies.

Please understand that individuals who do not meet requirements shown below may be declined to participate in the program.

Ideal participants

  • Participants who have programming experience using C or Fortran.
  • Participants who are accustomed to copying, deleting, searching and editing files on Linux operating system and have basic parallel programing experience with MPI or OpenMP.

Please be aware that online participants need an internet environment as follows.
-Network bandwidth with a stable connection when using video and audio for the teleconference system, Zoom.
-Possible to connect remotely to Wisteria system at the University of Tokyo via ssh protocol.


Mon, March 13(JST)
Time Program Materials
09:00 - 09:30 Introduction
09:30-12:00 Krylov subspace method with sparse matrix Text 1
13:30-15:00 Implementation of GMRES and CG Text 2
15:15-17:15 Hands-on exercise for serial computation

Tue, March 14(JST)
Time Program Materials
09:00 - 12:00 Distribution of sparse matrix based on domain decomposition
13:30-15:00 Introduction of additive Schwarz preconditionerText 3
15:15-17:15 Hands-on exercise for parallel computation with METIS

Wed, March 15(JST)
Time Program Materials
09:00 - 12:00 Introduction of finite element method Text 4
13:30-14:45 Domain specific language: FreeFEM Text 5
15:00-17:00 Hands-on exercise for parallel computation with PETSc
17:00-17:15 Closing

Application for participation

  • Maximum number of participants: About 40. Participants will be selected by screening based on application information. Necessary adjustment may be made to avoid having a large number of participants from one university or institution. We may also decline applicants who do not meet the requirements listed in Qualifications.
  • Application deadline: Noon, January 20 9, 2023 (JST) *CLOSED *The application deadline has been extended.
  • To apply for the spring school, click "RIKEN International HPC Spring School 2023" (online application form).The webpage will open in a new tab.
  • After the application period ends, the spring school secretariat will notify all the applicants whether they are accepted for the program, and inform them regarding documents to submit.
  • In principle, participants must attend all sessions of the spring school.
  • RIKEN will bear commuting expenses to full-time students who can commute to R-CCS without accommodation. The expenses will be paid based on the RIKEN’s regulations via bank transfer after the school ends.

Note: Handling of personal information
Personal information submitted will be used only for RIKEN to inform participants of the school schedule and changes or to collect materials related to the school operations. Personal information will not be used for other purposes.

*If you are a resident of the European Economic Area (the EU zone), you are required to submit the GDPR consent form (PDF 21KB)PDF will open in a new tab with your signature.
You will find detailed information about General Data Protection Regulation (GDPR) in the website below:
European Commision Data Protection RulesPDF will open in a new tab


RIKEN Computational Science Plannning Officen7-1-26, Minatojima-minamimachi, Chuo-ku, Kobe, 650-0047, JAPAN

  • mail addressrenkei_hrd[at]*
  • *Please change [at] to @ when sending email

(Apr 7, 2023)