Related papers: An Improved Multi-Stage Preconditioner on GPUs for…

Neural preconditioners for real-time physics simulation offer promising data-driven priors, but they often fail to capture long-range couplings efficiently because they inherit local message passing or sparse-operator access patterns. We…

We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the…

In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…

A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to…

We develop a novel fast iterative moment method for the steady-state simulation of near-continuum flows, which are modeled by the high-order moment system derived from the Boltzmann-BGK equation. The fast convergence of the present method…

A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…

Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

A component-splitting method is proposed to improve convergence characteristics for implicit time integration of compressible multicomponent reactive flows. The characteristic decomposition of flux jacobian of multicomponent Navier-Stokes…

Coarse-grained modeling and efficient computer simulations are critical to the study of complex molecular processes with many degrees of freedom and multiple spatiotemporal scales. Variational implicit-solvent model (VISM) for biomolecular…

We provide a preliminary study on utilizing GPU (Graphics Processing Unit) to accelerate computation for three simulation optimization tasks with either first-order or second-order algorithms. Compared to the implementation using only CPU…

This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An…

The large number of possible structures of metal-organic frameworks (MOFs) and their limitless potential applications has motivated molecular modelers and researchers to develop methods and models to efficiently assess MOF performance. Some…

We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…

The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…

In this paper, we propose a mathematical formulation for the management of an oil production network as a multistage optimization problem. The reservoir is modeled as a controlled dynamical system by using material balance equations. We use…

The never-ending computational demand from simulations of turbulence makes computational fluid dynamics (CFD) a prime application use case for current and future exascale systems. High-order finite element methods, such as the spectral…

In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…

We present a MATLAB-based framework for two- and three-dimensional fast Fourier transforms on multiple GPUs for large-scale numerical simulations using the pseudo-spectral Fourier method. The software implements two complementary multi-GPU…

The recent evolution of software and hardware technologies is leading to a renewed computational interest in Particle-In-Cell (PIC) methods such as the Material Point Method (MPM). Indeed, provided some critical aspects are properly…