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Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…
As part of the Exascale Computing Project (ECP), a recent focus of development efforts for the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been to enable GPU-accelerated time integration in scientific…
A new molecular simulation toolkit composed of some lately developed force fields and specified models is presented to study the self-assembly, phase transition, and other properties of polymeric systems at mesoscopic scale by utilizing the…
Unstructured-mesh ocean models are increasingly used for coastal applications due to their ability to represent complex geometries and apply local grid refinement where needed. However, their broader use has been hindered by their high…
The immersed boundary (IB) method has become a leading approach in cardiac fluid-structure interaction (FSI) modeling due to its ability to handle large deformations and complex geometries without requiring mesh regeneration. However, the…
This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many…
The conservative Post-Newtonian (PN) Hamiltonian formulation of spinning compact binaries has six integrals of motion including the total energy, the total angular momentum and the constant unit lengths of spins. The manifold correction…
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…
In this paper we present a new GPU-oriented mesh optimization method based on high-order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global…
High-fidelity simulations of unsteady fluid flow are now possible with advancements in high-performance computing hardware and software frameworks. Since computational fluid dynamics (CFD) computations are dominated by linear algebraic…
Adaptive mesh refinement (AMR) reduces computational costs in CFD by concentrating resolution where needed, but efficiently embedding complex, non-aligned geometries on GPUs remains challenging. We present a GPU-native algorithm for…
The recent trend of using Graphics Processing Units (GPU's) for high performance computations is driven by the high ratio of price performance for these units, complemented by their cost effectiveness. At first glance, computational fluid…
First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…
Hardware accelerators, such as those based on GPUs and FPGAs, offer an excellent opportunity to efficiently parallelize functionalities. Recently, modern embedded platforms started being equipped with such accelerators, resulting in a…
We present the Fluid Transport Accelerated Solver, FluTAS, a scalable GPU code for multiphase flows with thermal effects. The code solves the incompressible Navier-Stokes equation for two-fluid systems, with a direct FFT-based Poisson…
Achieving high performance for GPU codes requires developers to have significant knowledge in parallel programming and GPU architectures, and in-depth understanding of the application. This combination makes it challenging to find…
Obtaining a thermodynamically accurate phase diagram through numerical calculations is a computationally expensive problem that is crucially important to understanding the complex phenomena of solid state physics, such as superconductivity.…
The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows. Although many highly efficient algorithms have been proposed for simulating each type of the flows, the…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
The simulation of partial differential equations is a central subject of numerical analysis and an indispensable tool in science, engineering and related fields. Existing approaches, such as finite elements, provide (highly) efficient tools…