Postdoctoral Researcher – Sparse Linear Systems (Algorithms)

Postdoctoral Researcher – Sparse Linear Systems (Algorithms)

Location: High‑Performance Computing Center Stuttgart (HLRS), Future Computing Group, Stuttgart.

Contract type: 2.5‑year fixed‑term, full‑time (m/f/x), TV‑L 13, reference HLRS_08_2026.

Background and Motivation

Sparse linear systems are ubiquitous in scientific simulation; finite element and finite volume discretizations of PDEs, graph problems, network flows, and many machine‑learning inference tasks reduce to solving A x = b where A is sparse. While decades of progress have been made, solving very large sparse systems remains a dominant computational cost in HPC. At HLRS we investigate how photonic processors can accelerate sparse linear algebra operations that are fundamental to scientific computing.

Research Objectives

• Identify which components of PETSc‑based sparse solvers can benefit from photonic offloading.
• Develop corresponding algorithmic strategies, including compression, reformulation, and accuracy control.
• Investigate mixed‑precision strategies for photonic acceleration (e.g., low‑precision smoothers in multigrid, inner iterations in flexible Krylov methods).
• Validate algorithmic approaches on benchmark problems from CFD and structural mechanics.
• Contribute to hardware‑software co‑design through performance profiling and identification of optimization opportunities.

Key Tasks

• Develop photonic‑focused reformulations of preconditioners and solvers.
• Design library components for sparse linear systems.
• Perform numerical validation on benchmark problems from CFD and structural mechanics.
• Collaborate closely with the implementation team for joint library development.
• Benchmark and evaluate photonic hardware suitability for HPC tasks.
• Support photonic hardware development to enable fast execution of numeric implementations on photonic processors.
• Publish methods and results in peer‑reviewed journals and conferences.

Essential Qualifications

• PhD in mathematics, computer science, or engineering with a strong focus on iterative methods for linear systems.
• Strong analytical and problem‑solving skills.
• Ability to work independently and as part of an interdisciplinary team.
• Excellent communication skills in English (written and spoken).
• Willingness to publish and communicate results to academia.

Beneficial Experience

• Expertise in Krylov solvers, preconditioning, and multigrid methods.
• Hands‑on experience with PETSc, Ginkgo, or comparable large‑scale solver libraries.
• Experience with mixed‑precision numerical methods.
• Familiarity with high‑performance computing environments.
• Background in numerical linear algebra or computational science.

Benefits

• Flexible working hours.
• Transportation subsidy.
• Professional development opportunities.
• Health and wellness offerings.

Equal Employment Opportunity Statement

The University of Stuttgart aims to increase the proportion of women in academic and academic support roles and is therefore particularly interested in applications from women. Full‑time positions may generally be split into part‑time positions. Individuals with severe disabilities will be given priority in hiring if equally qualified.