Numerical Methods Engineer

Qdot is a spin-out from the University of Oxford. Our mission is to combat the causes and effects of climate change by creating zero-emissions, sustainable UAVs for critical logistics applications including offshore and remote. Key to this mission is the development of its hybrid battery and fuel cell powertrain technology. We are based at Oxford Airport and currently have 13 employees.

What we offer you

• Salary: Competitive
• Working arrangements: Hybrid working, flexible working hours
• Benefits:

• EMI share options in fast growing start-up
• 25 days + bank holidays (+1 per year of service up to a maximum of +5)
• 5 days carried forward, used within 6 months
• Enhanced sick leave
• Enhanced paternity/maternity leave
• Salary sacrifice pension scheme +5% company contribution
• Up to £400/year reimbursement of professional registration fees
• 2x salary life insurance
• Private virtual GP for immediate family
• Employee Assistance Programme
• Cycle to work scheme
• Shopping discounts
• Visa sponsorship and costs covered

Culture:

At Qdot, you will be part of a friendly and welcoming team of passionate innovators, every single one making a real difference in the path towards the dream of clean, sustainable flight. We encourage healthy work-life balance by supporting flexible working hours and hybrid working, while also strengthening team bonds with company-wide social events. Every team member is kept informed about top-level strategy, and encouraged to have their say about where we go as a company.

Job summary

As a Numerical Methods Engineer, you will take a central role in developing numerical models and simulation tools to solve complex physical problems—particularly related to sintering and material deformation—governed by partial differential equations (PDEs). Your work will involve building discrete numerical solvers from first principles, validating simulation outputs, and converting these into reliable, reusable software modules—specifically applied to metal additive manufacturing processes, such as metal binder jetting, sintering and co-sintering.

This role requires strong mathematical modelling expertise, proficiency in MATLAB and Python, and a deep understanding of numerical methods for ODEs/PDEs. You’ll be responsible for advancing our current 2D sintering models into 3D, supporting simulations involving multiple interacting bodies, and contributing to the creation of user-ready computational tools. Candidates with backend programming experience in C++ or high-performance computing will have additional opportunities to optimize solver performance and scalability.

You’ll work closely with domain experts and experimentalists, playing a key part in the design and validation of next-generation materials simulation platforms.

Your responsibilities

• Develop and implement numerical solvers for PDE-based physical models for metal sintering.
• Extend existing 2D sintering models to 3D and multi-body configurations.
• Write clean, modular, and documented code primarily in MATLAB and Python.
• Translate research models into usable software tools for internal or external use.
• Validate and verify models against physical data or published benchmarks.
• Collaborate with R&D engineers, experimentalists, and external research groups.

Selection criteria

Essential

• University degree in applied mathematics, computer science, physics, materials or related field.
• Minimum 3 years of combined academic and industry experience.
• Strong background in numerical methods for ODEs/PDEs (e.g., finite element, finite difference, or finite volume methods).
• Proficiency in MATLAB and Python for numerical computing and algorithm development.
• Experience building or modifying custom simulation solvers from scratch.
• Familiarity with 3D geometries, meshing, and computational grids.
• Experience writing and implementing codes for parallel and high-performance computing.
• Understanding of physical processes such as sintering, heat transfer, diffusion, or mechanics of materials.
• Strong problem-solving ability and attention to mathematical rigor.
• Familiar with software development practices such as version control (e.g., Git) and modular coding.

Desirable

• Post-graduate university degree in applied mathematics, computer science, physics, materials or related field.
• Minimum 5 years of combined academic and industry experience.
• Experience with C++.
• Experience with multiphysics solvers or simulation frameworks (e.g., COMSOL, FEniCS, OpenFOAM).
• Experience with GUI development or integrating simulations into user-facing tools.
• Knowledge of numerical stability and convergence analysis techniques.
• Knowledge of metal additive manufacturing processes, particularly design for manufacturing.