Ongoing Projects/Research Topics

MANDALA (MPI+X Accelerated Numerics on hybriD Architecture with acceLerAtors): An Exascale Computing Project

NSM India, supported by Department of Science and Technology (DST) and Department of Electronics and Information Technology (DeitY), India  

This project aims to develop an MPI+X parallel and scalable finite element library for computations on clusters with multicore processors and accelerators. Further, parallel data structure, numerical scheme, and implementation will be designed to support asynchronous and multi-precision computations. The main focus will be to break the scalability barrier to accomplish exascale computations. The developed MPI+X parallel finite element library will be made available in a public domain.

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  • Development and analysis of hardware-aware finite element and temporal discretizations.
  • Asynchronous numerical algorithms and implementation
  • Multiprecision multigrid solver for sparse systems
  • Task-based parallel implementation
  • MPI+X implementations
  • Hardware-aware algorithms in Scientific Computing (HAASC) - Indo-German Partnership Program

    ... jointly with IWR, Universität Heidelberg   and   Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany   and   TIFR-CAM Bangalore, India.   NVIDIA-India (Industrial Partner).

    The purpose of this four-year program (2020 - 2024) is to foster hardware-aware numerical schemes and scalable algorithms to harness future multi-node, multi-GPU supercomputers. The key focus is not only developing hardware-aware algorithms but to train young researchers in scientific computing through joint supervision, workshops, summer/winter schools.

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  • Exchange of master students from three relevant master programs in Heidelberg and Bangalore. These programs are all two-year programs and their syllabuses fit ideally together so that students would find relevant courses easily.
  • In addition we will offer joint supervision of master thesis with three months spent in each supervisor's group. This initiative will provide opportunities for masters students to get exposed to international research and motivate to join for PhD.
  • Exchange of doctoral candidates of the two involved graduate schools in Heidelberg and Bangalore.
  • to build up a leading network of researchers in India and Germany in high-performance scientific computing,
  • to establish collaboration on joint research projects among the project partners, and in the long term perspective
  • to establish a cotutelle Ph.D. program between Heidelberg University and IISc along the lines of the existing IWR-DBT program, which is concentrating on Big Data Research in the biosciences.
  • SPADE - Stochastic ParMooN for Analysis, Design and Estimation

    STARS   supported by Department of Higher Education, MHRD, India

    Combining Finite Element Modeling with rigorous uncertainty quantification and optimal sensing strategies for monitoring condition, predicting failure modes, and optimizing design of energy and process infrastructure, focusing on nuclear power plants and manufacturing plants.

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  • Derive and implement efficient finite element numerical schemes for deterministic governing equations of all components of safety critical infrastructure.
  • Derive dynamically orthogonal stochastic model order reduced governing equations for the stochastic governing equations
  • Develop and implement efficient stochastic solvers for the above equations
  • Develop a sensor optimization software package that predicts the optimal location of sensors to monitor all the components for efficient fault detection
  • Implement machine learning techniques that optimally combine observations and model predictions to estimate and forecast accurate operating conditions
  • Develop a simulation and data-driven recommender system for risk-optimal design and operation of safety critical infrastructure
  • Efficient and Robust Numerical Scheme for Computations of Liquidized Alloy

    supported by Science and Engineering Research Board, DST

    Aim of this project is to develop a robust and efficient finite element scheme for computations of dislocation and accumulation of liquidized alloy coating on a solid substrate. The targeted application of the proposed project is to investigate the dislocation and accumulation phenomenon of alloy coating from a hot region to a cold region during Hot Forming Die Quenching (HFDQ) in an ultra-high-strength steel production.

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    The mathematical model consists of time-dependent Navier-Stokes and energy equations in a time-dependent (moving) domain. Further, the Marangoni effect and a temperature-dependent dynamic contact angle will also be incorporated in the model. The domain will be handled by the arbitrary Lagrangian-Eulerian approach. Moreover, the PDEs will be discretized by finite elements in space and by a fractional step-theta scheme in time. Since the density of the alloy is very high, the PDEs become convection dominated, and therefore a local projection stabilization will be used.

    The developed numerical scheme will be used to get an insight into the effects of Marangoni convection on the dislocation and accumulation of the liquidized alloy coating. Further, parametric studies will be performed to study the dislocation phenomenon. we believe that the findings of this numerical study will help to develop technologies to use high heating rates to increase ultra-high-strength steel production in HFDQ process.

    In addition to the targeted application, the considered type of problems initiate new scientific questions in fundamental areas of computational mathematics. Moreover, the findings will have a huge impact in automobile industries.

    Computational Ship Hydrodynamics: Modeling of Free Surface and Two-Phase Flows Around Ships

    supported by Naval Research Board, DRDO
    supported by Department of Higher Education, MHRD, India

    A finite element method (FEM) for simulations of free surface and two-phase flows around ships will be developed. The ALE-FEM scheme can be used for computations of free surface/two-phase flows around ships, in particular, tank tests and hydrodynamics coefficients estimation.

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    The free surface/two-phase flow will be described by the time-dependent Navier-Stokes equations in a moving domain, whereas the rigid body (ship) motion will be described by the equations of variation of linear and angular momentum. Apart from the other challenges associated with the solution of the coupled Navier-Stokes and momentum equations, tracking and/or capturing the moving free surface/interface makes the computation more complicate. In this project, finite element schemes based on the arbitrary Lagrangian-Eulerian (ALE) will be developed for the coupled equations.

    The developed scheme can be used to solve the ship resistance problem, that is, to predict the resistance of the ship moving at low speed through still water. In practice, a very high accuracy of resistance prediction is often required to determine the hull form of design, and the proposed ALE-FEM will be well suited for these models, and will be capable of simulating free surface/two-phase flows around ships very accurately.

    SUPG Finite Element Method for Parabolic Partial Differential Equations in Time-Dependent Domains

    supported by Council of Scientific and Industrial Research (CSIR), India

    The aim of the project is to develop a Streamline Upwind Petrov--Galerkin finite element method for parabolic partial differential equations in a time-dependent domain, and to study the stability and convergence analysis of the SUPG-FEM. Further, an efficient and robust parallel algorithm will be developed for the proposed numerical scheme.

    Finite Element Methods for Simulation of Complex Fluids

    supported by TATA Consultancy Service (TCS)

    This research work focuses on development and implementation of stable, efficient and robust finite element scheme for free surface and/or interface flows with non-linear relation between shear stress and shear rate, commonly known as non-Newtonian or complex fluids.

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    The mathematical model consists of time-dependent Navier-Stokes and viscoelastic constitutive equations in a time-dependent (moving) domain. Moreover, the partial differential equations are discretized by finite elements in space and by backward Euler scheme in time. Since the PDEs are convection dominated, a local projection stabilization (LPS) is used to obtained a stable finite element scheme.

    The developed numerical scheme can be used to get an insight into the effects of viscoelasticity on the flow dynamics of a droplet spreading upon impact on flat substrate and a bubble rising in a viscoelastic fluid due to buoyancy. Further, parametric studies will be performed to study the flow dynamics.

    Findings of this numerical study can be used to develop technologies related to polymer additives in controlled droplet deposition and enhanced oil recovery mechanisms.

    Variational Multiscale Methods (VMS) for Turbulent Incompressible Navier-Stokes Equation on Time-Dependent Domains

    supported by Department of Higher Education, MHRD, India

    The aim of this project is to develop computationally efficient finite element scheme to study the liquid metal flow and heat transfer behind a cylinder in a duct under the presence of a strong axial magnetic field. The targeted application of the proposed project is to investigate the behaviour of liquid metal blanket used in nuclear fusion reactor (such as International Thermonuclear Experiment reactor) to transfer heat from main core to the turbines.

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    The mathematical model consists of Magnetohydrodynamics (MHD) equations that involves time-dependent Navier-stokes equations and Maxwell’s equations of electromagnetism. To calculate heat transfer convection-diffusion equation is coupled with MHD equations. The PDEs are discretized by finite elements in space and by a fraction step-theta scheme in time. Further, for simulating the flow with high Reynolds number, a projection based variational multiscale scheme (VMS) is used. The VMS allows the separation of entire range of scales in the flow field into three groups enabling different numerical treatment for different groups.

    The developed scheme can be used to study the effect on heat transfer in MHD flows. Further, effects on heat transfer due to the introduction of obstacle of various shapes and sizes, inside the duct, can be investigated to efficiently design a nuclear reactor.

    Magnetohydrodynamics Flows at High Reynolds Numbers

    supported by Department of Higher Education, MHRD, India

    Our interest is to develop a new projection based scheme for scale separation in turbulent flow simulations which is much simpler to implement for various flow problems. More specifically, we planned to extend the variational multiscale methods for moving domains (time-dependent domains) and fluid-structure interactions problems.

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    Due to the presence of multitude of scales in turbulent flows, the standard Galerkin approach has severe limitations. Variational multiscale method (VMS) is relatively a new technique that can be used to solve the Navier-Stokes equations accurately for turbulent flows. Much like LES (large eddy simulation), VMS separates flow scales into resolved and unresolved scales, and the effects of the unresolved scales are incorporated into the resolved scales by a turbulence model.