Related papers: Iterative Poisson Solvers for Self-gravity with th…
Research on smooth vector graphics is separated into two independent research threads: one on interpolation-based gradient meshes and the other on diffusion-based curve formulations. With this paper, we propose a mathematical formulation…
Machine learning solvers for partial differential equations (PDEs) have attracted growing interest. However, most existing approaches, such as neural network solvers, rely on stochastic training, which is inefficient and typically requires…
We study parallel particle-in-cell (PIC) methods for low-temperature plasmas (LTPs), which discretize kinetic formulations that capture the time evolution of the probability density function of particles as a function of position and…
Coarse grid projection (CGP) is a multiresolution technique for accelerating numerical calculations associated with a set of nonlinear evolutionary equations along with the stiff Poisson equations. In this article we use CGP for the first…
In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…
BATSRUS, our state-of-the-art extended magnetohydrodynamic code, is the most used and one of the most resource-consuming models in the Space Weather Modeling Framework. It has always been our objective to improve its efficiency and speed…
We have developed a gravity solver based on combining the well developed Particle-Mesh (PM) method and TREE methods. It is designed for and has been implemented on parallel computer architectures. The new code can deal with tens of millions…
The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…
We develop a matrix-free Full Approximation Storage (FAS) multigrid solver based on staggered finite differences and implemented on GPU in MATLAB. To enhance performance, intermediate variables are reused, and an X-shape Multi-Color…
Self-gravity plays an important role in the evolution of rotationally supported systems such as protoplanetary disks, accretion disks around black holes, or galactic disks, as it can both feed turbulence or lead to gravitational…
We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…
High-order DG methods have become a popular technique in computational fluid dynamics because their accuracy increases spectrally in smooth solutions with the order of the approximation. However, their main drawback is that increasing the…
Divergence constraints are present in the governing equations of numerous physical phenomena, and they usually lead to a Poisson equation whose solution represents a bottleneck in many simulation codes. Algebraic Multigrid (AMG) is arguably…
A Fourier-based Library of Unbounded Poisson Solvers (FLUPS) for 2D and 3D homogeneous distributed grids is presented. It is designed to handle every possible combination of periodic, symmetric, semi-unbounded and fully unbounded boundary…
This paper introduces a framework for solving alternating current optimal power flow (ACOPF) problems using graphics processing units (GPUs). While GPUs have demonstrated remarkable performance in various computing domains, their…
We present a GPU-accelerated numerical integrator specifically optimized for stability calculations of small bodies in planetary systems. Specifically, the integrator is designed for cases when large numbers of test particles (tens or…
This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and…
Solving the shallow water equations efficiently is critical to the study of natural hazards induced by tsunami and storm surge, since it provides more response time in an early warning system and allows more runs to be done for…
We describe a strategy for code modernisation of Gadget, a widely used community code for computational astrophysics. The focus of this work is on node-level performance optimisation, targeting current multi/many-core IntelR architectures.…
We present a grid-free fluid solver featuring a novel Gaussian representation. Drawing inspiration from the expressive capabilities of 3D Gaussian Splatting in multi-view image reconstruction, we model the continuous flow velocity as a…