CE Seminar by Prof. Dr. Shivasubramanian (Shiva) Gopalakrishnan

Time: 11:30
Location: ENG 208







Speaker: Prof. Dr. Shivasubramanian (Shiva) Gopalakrishnan, Department of Mechanical Engineering, Indian Institute of Technology, Bombay, India.

Title: Higher order and power efficient numerical methods for modeling continuum phenomena on modern computer arch

Date:  18 July 2018

Time: 11:30-12:30

Place: ENG 208

Host: Metin Muradoglu


Most physical processes in nature can be described as sets of partial differential equations. The non-linear nature of these complex systems from various disciplines, such as computational fluid dynamics, computational electromagnetics, geophysics etc, make the numerical solution of these systems inevitable. Traditional numerical methods such as the Finite Difference Method (FDM), Finite Element Method (FEM) and the Finite Volume Method (FVM) suffer from lower orders of spatial accuracies and lack of scalability of large supercomputers. The current talk will focus on High-order continuous Galerkin (CG) and discontinuous Galerkin (DG) methods which have enjoyed much success in obtaining the higher spatial accuracy desired in numerical simulations while resolving complex physical phenomena. The success of CG and DG methods is due to their high-order accuracy and their impressive scalability on massively parallel (multi- core) computers; local high-order methods are perfectly suited for multi-core computing because the on-processor workload is large while the communication stencil is small. Both CG and DG methods are currently able to achieve efficiencies in the terascale and possibly to the petascale ranges. However, a multi-core only approach will not be able to reach the exascale range. To reach the exascale range will require being able to exploit hybrid computing strategies using both central processing units (CPUs) and accelerator systems.

The higher convergence rates of the higher order methods also give an advantage in terms of effort to reach solution accuracy. In this talk, the power efficiency of this class of numerical methods will be discussed and compared with traditional numerical methods.


Shiva Gopalakrishnan currently is an Assistant Professor in the Department of Mechanical Engineering at the Indian Institute of Technology Bombay. He obtained his Ph.D from the University of Massachusetts - Amherst and subsequently was a National Research Council Postdoctoral Fellow in the Department of Applied Mathematics at the Naval Postgraduate School, Monterey, California. His research interests lie in the areas of Fluid Mechanics, Numerical Methods, Computational Fluid Dynamics, Geophysical Fluid Dynamics, Multiphase Flows, Interface Tracking Schemes, Adaptive Mesh Refinement Techniques, Higher Order Methods, Parallel Algorithms for CFD and High Performance Computing