Related papers: Smoothers with localized residual computations for…

We construct solvers for an isogeometric multi-patch discretization, where the patches are coupled via a discontinuous Galerkin approach, which allows the consideration of discretizations that do not match on the interfaces. We solve the…

We propose a new algorithm for curve skeleton computation which differs from previous algorithms by being based on the notion of local separators. The main benefits of this approach are that it is able to capture relatively fine details and…

The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…

Reducing memory traffic is critical to accelerate Lattice QCD computations on modern processors, given that such computations are memory-bandwidth bound. A commonly used strategy is mixed-precision solvers, however, these require careful…

A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…

Minimizing the Mumford-Shah functional is frequently used for smoothing signals or time series with discontinuities. A significant limitation of the standard Mumford-Shah model is that linear trends -- and in general polynomial trends -- in…

The sheer sizes of modern datasets are forcing data-structure designers to consider seriously both parallel construction and compactness. To achieve those goals we need to design a parallel algorithm with good scalability and with low…

Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…

Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…

Programmers using native languages such as C, C++, or Rust can implement custom memory allocation strategies to improve execution time. In their paper titled "Reconsidering Custom Memory Allocation" almost 25 years ago, Berger et al. showed…

Adaptive meshing includes local refinement as well as coarsening of meshes. Typically, coarsening algorithms are based on an explicit refinement history. In this work, we deal with local coarsening algorithms that build on the refinement…

We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw's benchmark collection we improve the best known partitioning.…

We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to…

We propose a decentralised "local2global"' approach to graph representation learning, that one can a-priori use to scale any embedding technique. Our local2global approach proceeds by first dividing the input graph into overlapping…

Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to…

We propose an algorithm based on Hilbert space-filling curves to reorder mesh elements in memory for use with the Spectral Element Method, aiming to attain fewer cache misses, better locality of data reference and faster execution. We…

In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…

Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…

Deep learning models trained on large data sets have been widely successful in both vision and language domains. As state-of-the-art deep learning architectures have continued to grow in parameter count so have the compute budgets and times…

The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these…