PhD Position Computational Mathematics: High-Performance Solvers for Indefinite Systems

Job description
The Numerical Analysis group within the Delft Institute of Applied Mathematics at TU Delft is offering a full-time PhD position in the area of advanced iterative solvers and preconditioning strategies for large-scale indefinite systems.

Indefinite systems are at the heart of some of the most pressing challenges in modern science and technology. They occur in magnetohydrodynamic (MHD) stability problems for plasma fusion, and in discretized nonlinear Schrödinger equations arising in quantum many-body physics, both giving rise to large indefinite systems that challenge existing solvers.The mathematical and computational hurdles of solving such systems are immense: slow or unstable convergence, lack of robustness, and scalability bottlenecks on modern parallel architectures.

As a PhD researcher, you will be at the frontier of tackling these challenges. The project will focus on mapping and understanding the convergence behavior of methods for indefinite systems, and on translating these insights into effective novel preconditioning and parallelization strategies. The ultimate aim is to deliver solvers that are both theoretically grounded and practically viable for real-world applications.

The PhD will be supervised by Vandana Dwarka in the Numerical Analysis group at TU Delft. The group is internationally recognized for its contributions to iterative methods, numerical linear algebra, and parallel computing. The project will be carried out in close interaction with experts from the Max Planck Institute for Plasma Physics (Garching), the University of Toulouse, and IBM, ensuring strong connections to application domains.

Besides carrying out mathematical research and preparing scientific publications, you will be expected to actively participate in seminars and discussions within the department, as well as present your work at (inter)national conferences and workshops. You will also carry out minor teaching tasks (at most 15% of your time). Teaching and communication will be in English. If desired, you can take Dutch language courses offered by the TU Delft Language Center.

The project has a duration of 4 years. The starting date 1st of March.
Doctoral candidates will be offered a 4-year period of employment in principle, but in the form of 2 employment contracts. An initial 1,5 year contract with an official go/no go progress assessment within 15 months. Followed by an additional contract for the remaining 2,5 years assuming everything goes well and performance requirements are met.

Job requirements

• Strong Background: You hold a Master’s degree (MSc) in Applied Mathematics, Computational Science, Physics, or a closely related field. You have a solid foundation in numerical analysis, partial differential equations, and linear algebra.
• Theoretical and Practical Balance: You enjoy developing and analyzing mathematical theory, but also have the skills and motivation to implement algorithms and test them in practice on large-scale problems.
• Programming Skills: You are proficient in at least one scientific programming language (such as Python, Julia, C++, or MATLAB) and are motivated to work with parallel computing environments.
• Collaborative Communicator: You are able to communicate your ideas clearly and work effectively with a diverse set of researchers and stakeholders, both within mathematics and in application domains.
• Curious and Open-Minded: You are eager to explore connections between mathematics, physics, and computing, and motivated to learn new techniques.
• Internship Experience: An internship or collaboration outside academia is considered a pre.
• Inclusive Outlook: We welcome applications from researchers who will add to the diversity of our team, in the broad and intersectional sense of the word.

TU Delft (Delft University of Technology)
Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context.

At TU Delft we embrace diversity as one of our core values and we actively engage to be a university where you feel at home and can flourish. We value different perspectives and qualities. We believe this makes our work more innovative, the TU Delft community more vibrant and the world more just. Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale. That is why we invite you to apply. Your application will receive fair consideration.

Challenge. Change. Impact!

Faculty of Electrical Engineering, Mathematics and Computer Science
The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) brings together three scientific disciplines. Combined, they reinforce each other and are the driving force behind the technology we all use in our daily lives. Technology such as the electricity grid, which our faculty is helping to make completely sustainable and future-proof. At the same time, we are developing the chips and sensors of the future, whilst also setting the foundations for the software technologies to run on this new generation of equipment – which of course includes AI. Meanwhile we are pushing the limits of applied mathematics, for example mapping out disease processes using single cell data, and using mathematics to simulate gigantic ash plumes after a volcanic eruption. In other words: there is plenty of room at the faculty for ground-breaking research. We educate innovative engineers and have excellent labs and facilities that underline our strong international position. In total, more than 1000 employees and 4,000 students work and study in this innovative environment.

Click here to go to the website of the Faculty of Electrical Engineering, Mathematics and Computer Science.

PhD Position Computational Mathematics: High-Performance Solvers for Indefinite Systems

Job description
The Numerical Analysis group within the Delft Institute of Applied Mathematics at TU Delft is offering a full-time PhD position in the area of advanced iterative solvers and preconditioning strategies for large-scale indefinite systems.

Indefinite systems are at the heart of some of the most pressing challenges in modern science and technology. They occur in magnetohydrodynamic (MHD) stability problems for plasma fusion, and in discretized nonlinear Schrödinger equations arising in quantum many-body physics, both giving rise to large indefinite systems that challenge existing solvers.The mathematical and computational hurdles of solving such systems are immense: slow or unstable convergence, lack of robustness, and scalability bottlenecks on modern parallel architectures.

As a PhD researcher, you will be at the frontier of tackling these challenges. The project will focus on mapping and understanding the convergence behavior of methods for indefinite systems, and on translating these insights into effective novel preconditioning and parallelization strategies. The ultimate aim is to deliver solvers that are both theoretically grounded and practically viable for real-world applications.

The PhD will be supervised by Vandana Dwarka in the Numerical Analysis group at TU Delft. The group is internationally recognized for its contributions to iterative methods, numerical linear algebra, and parallel computing. The project will be carried out in close interaction with experts from the Max Planck Institute for Plasma Physics (Garching), the University of Toulouse, and IBM, ensuring strong connections to application domains.

Besides carrying out mathematical research and preparing scientific publications, you will be expected to actively participate in seminars and discussions within the department, as well as present your work at (inter)national conferences and workshops. You will also carry out minor teaching tasks (at most 15% of your time). Teaching and communication will be in English. If desired, you can take Dutch language courses offered by the TU Delft Language Center.

The project has a duration of 4 years. The starting date 1st of March.
Doctoral candidates will be offered a 4-year period of employment in principle, but in the form of 2 employment contracts. An initial 1,5 year contract with an official go/no go progress assessment within 15 months. Followed by an additional contract for the remaining 2,5 years assuming everything goes well and performance requirements are met.

Job requirements

• Strong Background: You hold a Master’s degree (MSc) in Applied Mathematics, Computational Science, Physics, or a closely related field. You have a solid foundation in numerical analysis, partial differential equations, and linear algebra.
• Theoretical and Practical Balance: You enjoy developing and analyzing mathematical theory, but also have the skills and motivation to implement algorithms and test them in practice on large-scale problems.
• Programming Skills: You are proficient in at least one scientific programming language (such as Python, Julia, C++, or MATLAB) and are motivated to work with parallel computing environments.
• Collaborative Communicator: You are able to communicate your ideas clearly and work effectively with a diverse set of researchers and stakeholders, both within mathematics and in application domains.
• Curious and Open-Minded: You are eager to explore connections between mathematics, physics, and computing, and motivated to learn new techniques.
• Internship Experience: An internship or collaboration outside academia is considered a pre.
• Inclusive Outlook: We welcome applications from researchers who will add to the diversity of our team, in the broad and intersectional sense of the word.

TU Delft (Delft University of Technology)
Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context.

At TU Delft we embrace diversity as one of our core values and we actively engage to be a university where you feel at home and can flourish. We value different perspectives and qualities. We believe this makes our work more innovative, the TU Delft community more vibrant and the world more just. Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale. That is why we invite you to apply. Your application will receive fair consideration.

Challenge. Change. Impact!

Faculty of Electrical Engineering, Mathematics and Computer Science
The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) brings together three scientific disciplines. Combined, they reinforce each other and are the driving force behind the technology we all use in our daily lives. Technology such as the electricity grid, which our faculty is helping to make completely sustainable and future-proof. At the same time, we are developing the chips and sensors of the future, whilst also setting the foundations for the software technologies to run on this new generation of equipment – which of course includes AI. Meanwhile we are pushing the limits of applied mathematics, for example mapping out disease processes using single cell data, and using mathematics to simulate gigantic ash plumes after a volcanic eruption. In other words: there is plenty of room at the faculty for ground-breaking research. We educate innovative engineers and have excellent labs and facilities that underline our strong international position. In total, more than 1000 employees and 4,000 students work and study in this innovative environment.

Click here to go to the website of the Faculty of Electrical Engineering, Mathematics and Computer Science.

PhD in N-Dimensional Point Cloud Data Management for Adaptive Meshfree Urban Wind Simulation

Job description

Accurate urban wind simulations are vital for understanding microclimate, urban heat, and pollutant dispersion. Yet conventional Computational Fluid Dynamics (CFD) workflows rely on watertight geometric models and volumetric meshes that are slow, complex, and costly to produce. Within the POINT-TWINS project, you will help transform this field by enabling meshfree simulations directly on massive, real-world airborne LiDAR point clouds.

Nationwide LiDAR datasets contain billions of points and are increasingly enriched with additional time and scale dimensions for dynamic, space- and time-adaptive simulations. Managing this n-dimensional data efficiently is a central challenge. In your PhD research, you will explore advanced data structures, Spatial and non-spatial Database Management Systems, and high-performance computing strategies to enable fast, scalable handling of these datasets. You will also investigate deep learning methods for local data augmentation and adaptive point density control, addressing the anisotropy and uneven sampling typical of urban LiDAR.

You will work on a four-year doctoral project jointly supervised by Dr. Azarakhsh Rafiee, Prof. Peter van Oosterom, and Dr. Frits de Prenter. Your home base will be the Department of Architectural Engineering + Technology (Faculty of Architecture and the Built Environment), where you will collaborate closely with a parallel PhD project within the Faculty of Aerospace Engineering focused on meshfree numerical methods. Together, you will work across disciplines to develop the foundations of next-generation urban wind simulation.

The project also offers collaboration opportunities with leading research and industry partners including Fraunhofer ITWM, Dassault Systèmes, ActiFlow, the Dutch Water Boards Association, and the Municipality of The Hague. You will join an international research environment with access to state-of-the-art computational facilities, and you will have ample opportunities for academic growth, conference participation, and scientific publication.

Requirements

• You hold a Master’s degree in Aerospace Engineering, Mechanical Engineering, Applied Physics, Applied Mathematics, Computer Science/Engineering, Geomatics, or a related field.
• You have knowledge of distributed, parallel, and high-performance computing suitable for handling large scientific datasets.
• You preferably have familiarity with Computational Fluid Dynamics (CFD) principles.
• You have experience with Spatial or non-spatial Database Management Systems.
• You have strong programming skills in C++ and Python.
• You enjoy conducting independent research and are self-motivated, curious, and eager to learn.
• You are enthusiastic about linking real-world urban challenges to fundamental research questions.
• You have good communication skills and can work effectively in an international, multidisciplinary team.

TU Delft (Delft University of Technology)
Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context.

At TU Delft we embrace diversity as one of our core values and we actively engage to be a university where you feel at home and can flourish. We value different perspectives and qualities. We believe this makes our work more innovative, the TU Delft community more vibrant and the world more just. Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale. That is why we invite you to apply. Your application will receive fair consideration.

Challenge. Change. Impact!

Faculty Architecture & the Built Environment
The Faculty of Architecture and the Built Environment has a leading role in education and research worldwide. The driving force behind the faculty’s success is its robust research profile combined with the energy and creativity of its student body and academic community. It is buzzing with energy from early in the morning until late at night, with four thousand people studying, working, designing, conducting research and acquiring and disseminating knowledge. Our faculty has a strong focus on 'design-oriented research’, which has given it a top position in world rankings.

Staff and students are working to improve the built environment with the help of a broad set of disciplines, including architectural design, urban planning, building technology, social sciences, process management, and geo-information science. The faculty works closely with other faculties, universities, private parties, and the public sector, and has an extensive network in the Netherlands as well as internationally.

Click here to go to the website of the Faculty of Architecture and the Built Environment.