Dr. Shubham Kumar Goswami

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Postdoctoral Researcher at Faculty of Mathematics
Ruhr University Bochum

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About Me

I am currently a postdoctoral researcher at Ruhr University, Bochum, Germany, working with Dr. Martin Kronbichler. I completed my PhD under the supervision of Dr. Konduri Aditya in the FLAME Lab at CDS, IISc Bangalore, in July 2024, where I worked on asynchronous numerical schemes for partial differential equations. My PhD research was focused on the development of novel asynchronous numerical schemes based on finite difference and discontinuous Galerkin methods, analyzing their numerical properties and demonstrating scalability on massively parallel supercomputers. The objective of my PhD thesis was to develop a highly scalable DG-based PDE solver for massively parallel flow simulations.

Apart from research, my other interests are traveling and trekking, and I love exploring new places.

Interests

Education

Awards

Projects

Asynchronous discontinuous Galerkin method

The objective of this work was to introduce an asynchronous computing approach to the discontinuous Galerkin method by relaxing communication/synchronization at a mathematical level while solving time-dependent partial differential equations in a distributed memory setting, analyze the numerical properties of the new formulation, and demonstrate its scalability. The final goal was to develop a highly scalable DG-based PDE solver for massively parallel supercomputers within the open-source finite element library deal.II.

Homology groups for simplicial complexes defined by product graphs and joins

The purpose of this project was to derive relations between betti numbers of simplicial complexes of graphs and their products. It was a part of the final year M.Sc. Project in the Department of Mathematics at IIT Kharagapur, where I was supervised by professor Bibhas Adhikari. We mainly worked on Corona products and Kronecker products of graphs and derived direct relations to obtain betti numbers of the products, provided we have all the information about the graphs taking part in products. It makes the task of studying the topological properties of big networks very easy, assuming there are generation processes available to generate the big network using small ones.

Conferences and Publications

An asynchronous discontinuous Galerkin method for massively parallel PDE solvers
S.K. Goswami, K. Aditya
CMAME 2024, doi.org/10.1016/j.cma.2024.117218
Implementation of low-storage Runge-Kutta time integration schemes in scalable asynchronous partial differential equation solvers
S.K. Goswami, V.J. Matthew, K. Aditya
Journal of Computational Physics 2023, doi.org/10.1016/j.jcp.2023.111922
An asynchronous discontinuous-Galerkin method for solving PDEs at extreme scales
S. K. Goswami, K. Aditya
AIAA Aviation Forum 2022, doi.org/10.2514/6.2022-4165
Implementation of the asynchronous discontinuous-Galerkin method for reacting flow simulations
S. K. Goswami, D. Vidyesh, K. Aditya
APS Division of Fluid Dynamics 2023, Abstract
Stability analysis of the asynchronous discontinuous-Galerkin method
S. K. Goswami, K. Aditya
SIAM Conference on Computational Science and Engineering 2023, Abstract
A scalable asynchronous discontinuous-Galerkin method for massively parallel PDE solvers
S. K. Goswami, K. Aditya
APS Division of Fluid Dynamics 2022, Abstract
A low-storage Runge-Kutta time integration method for scalable asynchrony-tolerant numerical schemes
S. K. Goswami, V. J. Matthew, K. Aditya
APS Division of Fluid Dynamics 2021, Abstract

Contact

Mail Id: shubham.goswami@rub.de
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