Phd Student

**Job Reference**:

- 24_25_CASE_PNM_R1

**Position**:

- PHD Student - Algebraic Solvers in Computational Strcuture Dynamics (R1)

**Closing Date**:

- Friday, 24 January, 2025

**Reference**: 24_25_CASE_PNM_R1

**Job title**: PHD Student - Algebraic Solvers in Computational Strcuture Dynamics (R1)

**About BSC**
- The Barcelona Supercomputing Center - Centro Nacional de Supercomputación (BSC-CNS) is the leading supercomputing center in Spain. It houses MareNostrum, one of the most powerful supercomputers in Europe, was a founding and hosting member of the former European HPC infrastructure PRACE (Partnership for Advanced Computing in Europe), and is now hosting entity for EuroHPC JU, the Joint Undertaking that leads large-scale investments and HPC provision in Europe. The mission of BSC is to research, develop and manage information technologies in order to facilitate scientific progress. BSC combines HPC service provision and R&D into both computer and computational science (life, earth and engineering sciences) under one roof, and currently has over 1000 staff from 60 countries.

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**Context And Mission**
- The Finite Element Method (FEM) has significantly expanded as a computational framework due to its versatility and robustness in solving a wide range of structural analysis problems. At its core, FEM operates by discretizing a physical domain into finite elements and solving the governing equations as a system of linear equations to approximate the solution. However, when FEM is applied to highly anisotropic materials—where properties such as stiffness, conductivity, or strength vary significantly in different directions—numerical challenges arise.

One of the key issues in these scenarios is that the resulting system of equations often leads to an ill-conditioned matrix, where small perturbations in input values can cause large variations in the output. This ill-conditioning makes the system highly sensitive to numerical errors, reducing the robustness of the solvers as well as the convergence rates.

The Barcelona Supercomputing Center (BSC) is home of the Physical and Numerical Modeling research group, which research activities include numerical and physical modeling, computational mechanics and high performance computing. Central to the group’s endeavors is Alya, a computational mechanics simulation tool designed to tackle coupled multi-physics, multi-scale, and multi-domain problems.

From scratch, Alya was specially designed for massively parallel supercomputers, and the parallelization embraces four levels of the computer hierarchy. 1) A substructuring technique with MPI as the message passing library is used for distributed memory supercomputers. 2) At the node level, both loop and task parallelisms are considered using OpenMP as an alternative to MPI. Dynamic load balance techniques have been introduced as well to better exploit computational resources at the node level. 3) At the CPU level, some kernels are also designed to enable automatic vectorization. 4) Finally, accelerators like GPU are also partially exploited through OpenACC pragmas or with CUDA to further enhance the performance of the code on heterogeneous computers.

The main objective is to develop “Robust and efficient high performance computational techniques in structural mechanics”, which includes 4 main subobjectives: 1) preconditioning techniques for structure mechanics: Local preconditioning to account for anisotropies and mesh stretching and multilevel techniques; 2) Accelerating Newton’s convergence; 3) HPC, intra and inter-node performance; 4) To demonstrate the proposed methodology through the solutions of relevant industrial cases

**Key Duties**
- State of the art in algebraic solvers
- Analysis of available numerical tool (Alya)
- Specialization in algebraic solver kernels and solid mechanics module
- Numerical investigation and implementation following the CI/CD of Alya
- Identification and resolution of benchmark problems
- Documentation

**Requirements**:

- Education
- Master in science or numerical methods
- Essential Knowledge and Professional Experience
- Programming
- Numerical methods
- Linear Algebra
- Parallelization techniques (MPI, OpenMP)
- Additional Knowledge and Professional Experience
- Finite element
- Fortran 2008
- Linux
- Functional analysis
- Competences
- Team work
- High level of English

**Conditions**
- The position will be located at BSC within the CASE Department
- We offer a full-time contract (37.5h/week), a good working environment, a highly stimulating environment with state-of-the-art infrastructure, flexible working hours, extensive training plan, restaurant tickets, private health insurance, support to the relocation procedures
- Dur