Kundan Kumar receives a Research Fellowship from the Alexander von Humboldt Foundation

Kundan Kumar is currently a professor in the Porous Media Group at the University of Bergen. He has been awarded a Humboldt Research Fellowship for Experienced Researchers by the Alexander von Humboldt Foundation. Kundan Kumar, SFB 1313 Mercator Fellow (research project C02) will be a visiting researcher in Stuttgart, Germany for a period of 14 months and be a guest at the Institute of Applied Analysis and Numerical Simulation (Analysis, modeling and numerical methods for partial differential equations) at the University of Stuttgart during the following periods: 

• 01.05.2026 – 31.07.2026
• 01.05.2027 – 31.12.2027
• 01.05.2028 – 31.07.2028

Kundan Kumar is employed as a professor in the Porous Media Group at the Department of Mathematics, University of Bergen, Norway. His research specializes in the mathematical analysis and numerical simulation of coupled multiphysics processes in porous media, with applications to energy and environmental systems. He received his Bachelor of Technology in Mechanical Engineering from the Indian Institute of Technology, Delhi in 2005. He pursued his further studies (2006-08) under the Erasmus Mundus programme in Industrial and Applied Mathematics, obtaining Master's degrees from Eindhoven University of Technology, The Netherlands, and the Technical University of Kaiserslautern, Germany. He obtained his Ph.D. (cum laude) from the Eindhoven University of Technology under the supervision of Prof. Sorin Pop in 2012. Subsequently, he did his postdoc with Prof. Mary F. Wheeler at the Oden Institute, University of Texas at Austin.  Following a fixed-term position at the University of Bergen and a Senior Lecturer position at Karlstad University, Sweden, he returned to the University of Bergen in 2020 as a permanent faculty. His contributions have been recognized with several prestigious awards, including the SIAM Geosciences Early Career Prize and the Lauritz Meltzer Prize. He has been a Mercator Fellow at the SFB 1313 (Interface-Driven Multi-Field Processes in Porous Media – Flow, Transport and Deformation) at the University of Stuttgart since 2024. 

Within the framework of the Humboldt Research Fellowship, Prof. Kundan Kumar will develop novel mathematical tools for coupled multiphysics processes in fractured porous media, with a focus on the interaction of fluid flow, mechanical deformation, and frictional contact along fractures and faults. The central mathematical challenge is the mixed-dimensional nature of these systems: flow and mechanics evolve in three-dimensional porous rock, while fractures are represented as two-dimensional surfaces carrying their own flow and contact mechanics. Coupling these subsystems requires trace operators and interface conditions that are non-trivial at both the continuous and discrete levels. The governing equations combine poroelasticity, fluid transport, and contact mechanics, with nonlinear friction laws — including Coulomb and rate-and-state models — introducing non-smooth variational structure that distinguishes fractured from intact porous media and governs phenomena such as fault reactivation and induced seismicity.

The project is structured along three main research directions: 1. Dimensional reduction of the poroelasticity equations in the fractured porous medium and the well-posedness of mixed dimensional models extending the theory of variational inequalities and contact mechanics to account for fluid–structure interaction and frictional effects in fractured media. 2. Design and analysis of robust discretization schemes and efficient solver strategies tailored to these complex systems. A key innovation is the development of multirate and splitting methods, which exploit the different time scales of the physical processes to achieve computational efficiency while preserving accuracy and stability. 3. Exploration of randomized numerical linear algebra techniques to construct efficient preconditioners and reduced representations of solution operators, enabling scalable simulations for strongly coupled systems.

The research targets reliable and efficient simulation tools for sustainable energy and environmental applications: geothermal energy systems, carbon capture and storage, underground energy storage, and the assessment and mitigation of induced seismicity.

In providing Humboldt Research Fellowships for experienced researchers, the Alexander von Humboldt Foundation enables highly-qualified scientists and scholars from abroad, who completed their doctorates less than twelve years ago to spend extended periods of research (6-18 months; may be divided up into a maximum of three blocks) in Germany. Candidates are expected to have their own, clearly defined research profile. Scientists and scholars from all disciplines and countries may apply.

The research outline is carried out in cooperation with academic hosts at research institutions in Germany. Applicants choose their own topic of research and their host in Germany. Details of the research outline including information on the intended duration of the fellowship must be agreed with the intended host before applying. The duration of the research fellowship (6-18 months) may be divided up into a maximum of three visits lasting a minimum of three months each. No more than 36 months may elapse between the beginning of the first stay and the end of the last stay. Short-term visits for study and training purposes or for attending conferences are not eligible for sponsorship.