Related papers: PittPack: An Open-Source Poisson's Equation Solver…
We develop an exact-curved Lagrange finite element framework for the Poisson problem on two-dimensional curved domains. The element map is factorised as $ F_K=\Psi_K\circ\Phi_{T_K}$, where $\Phi_{T_K}$ maps the reference triangle to an…
For a connected weighted hypergraph, we give a randomized almost-linear-time solver for the Poisson problem for the cut-based hypergraph Laplacian in the natural input size $P=\sum_{e\in E}|e|$, the sum of hyperedge sizes. For every fixed…
A cloud scheduler packs tasks onto machines with contradictory goals of (1) using the machines as efficiently as possible while (2) avoiding overloading that might result in CPU throttling or out-of-memory errors. We take a stochastic…
This paper seeks to combine dictionary learning and hierarchical image representation in a principled way. To make dictionary atoms capturing additional information from extended receptive fields and attain improved descriptive capacity, we…
An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…
In this paper, we develop a low-order three-dimensional finite-element solver for fast multiple-case crust deformation analysis on GPU-based systems. Based on a high-performance solver designed for massively parallel CPU based systems, we…
This paper investigates the multi-GPU performance of a 3D buoyancy driven cavity solver using MPI and OpenACC directives on different platforms. The paper shows that decomposing the total problem in different dimensions affects the strong…
CFD is a ubiquitous technique central to much of computational simulation such as that required by aircraft design. Solving of the Poisson equation occurs frequently in CFD and there are a number of possible approaches one may leverage. The…
Although dominant in natural language processing, transformer-based models remain challenged by the task of long-sequence processing, because the computational cost of self-attention operations in transformers swells quadratically with the…
Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations…
Large scale clusters leveraging distributed computing frameworks such as MapReduce routinely process data that are on the orders of petabytes or more. The sheer size of the data precludes the processing of the data on a single computer. The…
The Fast Multipole Method (FMM) provides a highly efficient computational tool for solving constant coefficient partial differential equations (e.g. the Poisson equation) on infinite domains. The solution to such an equation is given as the…
The emerging edge computing has promoted immense interests in compacting a neural network without sacrificing much accuracy. In this regard, low-rank tensor decomposition constitutes a powerful tool to compress convolutional neural networks…
Modern supercomputers are increasingly requiring the presence of accelerators and co-processors. However, it has not been easy to achieve good performance on such heterogeneous clusters. The key challenge has been to ensure good load…
Recent approaches to distributed model fitting rely heavily on consensus ADMM, where each node solves small sub-problems using only local data. We propose iterative methods that solve {\em global} sub-problems over an entire distributed…
Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
The extremum graph is a succinct representation of the Morse decomposition of a scalar field. It has increasingly become a useful data structure that supports topological feature directed visualization of 2D / 3D scalar fields, and enables…
Modern large-scale scientific applications consist of thousands to millions of individual tasks. These tasks involve not only computation but also communication with one another. Typically, the communication pattern between tasks is sparse…
This work presents the efficient, matrix-free finite-element library hyper.deal for solving partial differential equations in two to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional…