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Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to…
Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…
Load Balancing is a fundamental technology for scaling cloud infrastructure. It enables systems to distribute incoming traffic across backend servers using predefined algorithms such as round robin, weighted round robin, least connections,…
The work aims to improve the existing fast load shedding algorithm for industrial power system to increase performance, reliability, and scalability for future expansions. The paper illustrates the development of a scalable algorithm to…
Parallel real-time embedded applications can be modelled as directed acyclic graphs (DAGs) whose nodes model subtasks and whose edges model precedence constraints among subtasks. Efficiently scheduling such parallel tasks can be challenging…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
In this treatise, my research on methods to improve efficiency, reliability, and security of reconfigurable hardware systems, i.e., FPGAs, through partial dynamic reconfiguration is outlined. The efficiency of reconfigurable systems can be…
The growing demand for computational resources in machine learning has made efficient resource allocation a critical challenge, especially in heterogeneous hardware clusters where devices vary in capability, age, and energy efficiency.…
We propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable…
In this paper, we extend the adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse to the multistage stochastic programming setting. The proposed algorithms integrate the adaptive partition-based…
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…
A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
Many real-world applications operate on dynamic graphs that undergo rapid changes in their topological structure over time. However, it is challenging to design dynamic algorithms that are capable of supporting such graph changes…
This paper is focused on the convergence analysis of an adaptive stochastic collocation algorithm for the stationary diffusion equation with parametric coefficient. The algorithm employs sparse grid collocation in the parameter domain…
We demonstrate neural-network runtime prediction for complex, many-parameter, massively parallel, heterogeneous-physics simulations running on cloud-based MPI clusters. Because individual simulations are so expensive, it is crucial to train…
Evolving smart grids require flexible and adaptive control methods. A harmonized hybrid cyber-physical framework, which considers both physical and cyber layers and ensures adaptability, is one of the critical challenges to enable…
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…