Related papers: A quantitative performance analysis for Stokes sol…
Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data…
We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…
We present a design and implementation of the Thomas algorithm optimized for hardware acceleration on an FPGA, the Thomas Core. The hardware-based algorithm combined with the custom data flow and low level parallelism available in an FPGA…
This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…
Large language models have led to state-of-the-art accuracies across a range of tasks. However, training these models efficiently is challenging for two reasons: a) GPU memory capacity is limited, making it impossible to fit large models on…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
The Lattice Boltzmann method (LBM) for solving fluid flow is naturally well suited to an efficient implementation for massively parallel computing, due to the prevalence of local operations in the algorithm. This paper presents and analyses…
In a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the Boltzmann type (G. Dimarco, R. Loubere, Towards an ultra efficient kinetic scheme. Part I: basics on the 689 BGK equation, J. Comp.…
Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth makes it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data…
Stochastic differential equations (SDE) often exhibit large random transitions. This property, which we denote as pathwise stiffness, causes transient bursts of stiffness which limit the allowed step size for common fixed time step explicit…
Recently, the general synthetic iterative scheme (GSIS) has been proposed to find the steady-state solution of the Boltzmann equation in the whole range of gas rarefaction, where its fast-converging and asymptotic-preserving properties lead…
The discontinuous Galerkin (DG) algorithm is a representative high order method in Computational Fluid Dynamics (CFD) area which possesses considerable mathematical advantages such as high resolution, low dissipation, and dispersion.…
In this paper, we address a long-standing challenge: how to achieve both efficiency and scalability in solving semidefinite programming problems. We propose breakthrough acceleration techniques for a wide range of low-rank…
The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixed- point iteration, we explore the use of Anderson…
I describe here the performance of a parallel treecode with individual particle timesteps. The code is based on the Barnes-Hut algorithm and runs cosmological N-body simulations on parallel machines with a distributed memory architecture…
Bloom filters are a fundamental data structure for approximate membership queries, with applications ranging from data analytics to databases and genomics. Several variants have been proposed to accommodate parallel architectures. GPUs,…
In this work, we propose a local Fourier analysis for multigrid methods with coarsening by a factor of three for the staggered finite-difference method applied to the Stokes equations. In [21], local Fourier analysis has been applied to a…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
The paper demonstrates the optimization of the execution environment of a hybrid OpenMP+MPI computational fluid dynamics code (shallow water equation solver) on a cluster enabled with Intel Xeon Phi coprocessors. The discussion includes:…
Accurate performance estimation of future many-node machines is challenging because it requires detailed simulation models of both node and network. However, simulating the full system in detail is unfeasible in terms of compute and memory…