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Accurate numerical simulation of fault and fracture mechanics is critical for the performance and safety assessment of many subsurface systems. The discretized representation of discontinuity surfaces and the robust simulation of their…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A…
Neural kernels have drastically increased performance on diverse and nonstandard data modalities but require significantly more compute, which previously limited their application to smaller datasets. In this work, we address this by…
We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially all interior…
Classical multi-scale methods involving two spatial scales face significant challenges when simulating heterogeneous structures with complicated three-scale spatial configurations. This study proposes an innovative higher-order three-scale…
Neural network (NN) accelerators with multi-chip-module (MCM) architectures enable integration of massive computation capability; however, they face challenges of computing resource underutilization and off-chip communication overheads.…
The multi-level hp-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes,…
Scaling models has led to significant advancements in deep learning, but training these models in decentralized settings remains challenging due to communication bottlenecks. While existing compression techniques are effective in…
We study an element agglomeration coarsening strategy that requires data redistribution at coarse levels when the number of coarse elements becomes smaller than the used computational units (cores). The overall procedure generates coarse…
The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint…
Leveraging Trace Theory, we investigate the efficient parallelization of direct solvers for large linear equation systems. Our focus lies on a multi-frontal algorithm, and we present a methodology for achieving near-optimal scheduling on…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…
Large molecular dynamics simulations (millions of atoms, tens of microseconds, thousands of processors) hit the strong scalability wall: simulation on twice as many processors does not take half the time. Inspired by large N-body space…
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…
The Kernel Polynomial Method (KPM) is one of the fast diagonalization methods used for simulations of quantum systems in research fields of condensed matter physics and chemistry. The algorithm has a difficulty to be parallelized on a…
This paper shows how partial differential problems can be solved thanks to cellular computing and an adaptation of the Least Squares Finite Elements Method. As cellular computing can be implemented on distributed parallel architectures,…