arXiv subjects

Shubham Kumar Goswami

Publications and source records attributed to Shubham Kumar Goswami.

3 recordsLinked to original sources

arXiv2026

Scalability of the asynchronous discontinuous Galerkin method for compressible flow simulations

The scalability of time-dependent partial differential equation (PDE) solvers based on the discontinuous Galerkin (DG) method is increasingly limited by data communication and synchronization requirements across processing elements (PEs) at extreme scales. To address these challenges, asynchronous computing approaches that relax communication and synchronization at a mathematical level have been proposed. In particular, the asynchronous discontinuous Galerkin (ADG) method with asynchrony-tolerant (AT) fluxes has recently been shown to recover high-order accuracy under relaxed communication, supported by detailed analyses of its accuracy and stability. However, the scalability of this approach in modern large-scale parallel DG solvers has not yet been systematically investigated. In this paper, we address this gap by implementing the ADG method coupled with AT fluxes in the open-source finite element library deal.II. We employ a communication-avoiding algorithm (CAA) that reduces the frequency of inter-process communication while accommodating controlled delays in ghost value exchanges. We first demonstrate that applying standard numerical fluxes in this asynchronous setting degrades the solution to first-order accuracy, irrespective of the polynomial degree. By incorporating AT fluxes that utilize data from multiple previous time levels, we successfully recover the formal high-order accuracy of the DG discretization. The accuracy of the proposed method is rigorously verified using benchmark problems for the compressible Euler equations. Furthermore, we evaluate the performance of the method through extensive strong-scaling studies for both two- and three-dimensional test cases. Our results indicate that CAA substantially suppresses synchronization overheads, yielding speedups of up to 1.9x in two dimensions and 1.6x in three dimensions compared to a baseline synchronous DG solver.

physics.comp-ph↗

arXiv2025

Accuracy and scalability of asynchronous compressible flow solver for transitional flows

To overcome the communication bottlenecks observed in state-of-the-art parallel time-dependent flow solvers at extreme scales, an asynchronous computing approach that relaxes communication and synchronization at a mathematical level was previously developed. This approach preserves high-order accuracy of computations near processing element boundaries using asynchrony-tolerant (AT) schemes while significantly improving the scalability. The numerical properties of the AT schemes were studied based on simple linear and nonlinear partial differential equations (PDEs) in previous works. Allowing asynchrony in numerical schemes can minimize communication overheads in a parallel setting in two ways: one that avoids communication over a few predetermined time steps, and the other that initiates communications without enforcing synchronization. In this study, the asynchronous algorithms are incorporated into the high-order compressible flow solver COMP-SQUARE, which solves practically relevant flow problems in complex geometries in a multi-block framework. The numerical efficacy and scalability of the two asynchronous algorithms are demonstrated for three test cases: isentropic advection of a vortex, the Taylor-Green vortex, and a much more sensitive case of the flow transitioning on a NACA0012 airfoil. Speed-ups of up to $4\times$ with respect to the baseline synchronous algorithm are observed in the scaling experiments performed on up to 18,432 cores. The results of this study demonstrate the applicability of AT schemes on established CFD solvers to improve scalability at extreme scales as the scientific computing environment moves to the exascale era.

physics.comp-ph↗

arXiv2024

An asynchronous discontinuous Galerkin method for massively parallel PDE solvers

The discontinuous Galerkin (DG) method is widely being used to solve hyperbolic partial differential equations (PDEs) due to its ability to provide high-order accurate solutions in complex geometries, capture discontinuities, and exhibit high arithmetic intensity. However, the scalability of DG-based solvers is impeded by communication bottlenecks arising from the data movement and synchronization requirements at extreme scales. To address these challenges, recent studies have focused on the development of asynchronous computing approaches for PDE solvers. Herein, we introduce the asynchronous DG (ADG) method, which combines the benefits of the DG method with asynchronous computing to overcome communication bottlenecks. The ADG method relaxes the need for data communication and synchronization at a mathematical level, allowing processing elements to operate independently regardless of the communication status, thus potentially improving the scalability of solvers. The proposed ADG method ensures flux conservation and effectively addresses challenges arising from asynchrony. To assess its stability, Fourier-mode analysis is employed to examine the dissipation and dispersion behavior of fully-discrete equations that use the DG and ADG schemes along with the Runge-Kutta (RK) time integration scheme. Furthermore, an error analysis within a statistical framework is presented, which demonstrates that the ADG method with standard numerical fluxes achieves at most first-order accuracy. To recover accuracy, we introduce asynchrony-tolerant (AT) fluxes that utilize data from multiple time levels. Extensive numerical experiments were conducted to validate the performance of the ADG-AT scheme for both linear and nonlinear problems.

physics.comp-ph↗