Related papers: An efficient GPU-based h-adaptation framework via …

This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential…

We describe a fast, direct solver for elliptic partial differential equations on a two-dimensional hierarchy of adaptively refined, Cartesian meshes. Our solver, inspired by the Hierarchical Poincar\'e-Steklov (HPS) method introduced by…

GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and…

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…

Particle Image Velocimetry (PIV) is a method of im-aging and analysing fields of flows. The PIV tech-niques compute and display all the motion vectors of the field in a resulting image. Speeds more than thou-sand vectors per second can be…

We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of…

Gravitational $N$-body simulations calculate numerous interactions between particles. The tree algorithm reduces these calculations by constructing a hierarchical oct-tree structure and approximating gravitational forces on particles. Over…

We introduce a GPU-accelerated simulation tool, named Modeling on Shallow Flows with Efficient Simulation for Two-Phase Debris Flows (MoSES_2PDF), of which the input and output data can be linked to the GIS system for engineering…

The treatment of radiative transfer with multiple radiation sources is a critical challenge in simulations of star formation and the interstellar medium. In this paper we present the novel TreeRay method for solving general radiative…

Video generation requires modeling a vast spatiotemporal space, which demands significant computational resources and data usage. To reduce the complexity, the prevailing approaches employ a cascaded architecture to avoid direct training…

The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…

Predicting effective thermal conductivity by solving a Partial Differential Equation (PDE) defined on a high-resolution Representative Volume Element (RVE) is a computationally intensive task. In this paper, we tackle the task by proposing…

A high-order space-time flux reconstruction (FR) method has been developed to solve conservation laws on moving domains. In the space-time framework, the moving domain simulation is similar to that on a stationary domain, except that the…

We show that numerical computations based on tensor renormalization group (TRG) methods can be significantly accelerated with PyTorch on graphics processing units (GPUs) by leveraging NVIDIA's Compute Unified Device Architecture (CUDA). We…

In this paper we focus on the integration of high-performance numerical libraries in ab initio codes and the portability of performance and scalability. The target of our work is FLEUR, a software for electronic structure calculations…

We present an algorithm specifically tailored for solving kinetic equations onto GPUs. The efficiency of the algorithm is demonstrated by solving the one-dimensional shock wave structure problem and a two-dimensional low Mach number driven…

In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier-Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with…

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In…

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…

We propose a general and versatile framework that significantly speeds-up graphical model optimization while maintaining an excellent solution accuracy. The proposed approach relies on a multi-scale pruning scheme that is able to…