Related papers: A parallel shared-memory implementation of a high-…
We present the first fast solver for the high-frequency Helmholtz equation that scales optimally in parallel, for a single right-hand side. The L-sweeps approach achieves this scalability by departing from the usual propagation pattern, in…
This paper describes a new fast and implicitly parallel approach to neighbour-finding in multi-resolution Smoothed Particle Hydrodynamics (SPH) simulations. This new approach is based on hierarchical cell decompositions and sorted…
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on power series to locate the closest singular parameter value. On…
We present a shared memory implementation of a parallel algorithm, called delta-stepping, for solving the single source shortest path problem for directed and undirected graphs. In order to reduce synchronization costs we make some…
We investigate the parallel performance of Parallel Spectral Deferred corrections, a numerical approach that provides small-scale parallelism for the numerical solution of initial value problems. The scheme is applied to the shallow-water…
Vico et al. (2016) suggest a fast algorithm for computing volume potentials, beneficial to fields with problems requiring the solution of the free-space Poisson's equation, such as beam and plasma physics. Currently, the standard is the…
This chapter provides an introduction to Hybrid High-Order (HHO) methods. These are new generation numerical methods for PDEs with several advantageous features: the support of arbitrary approximation orders on general polyhedral meshes,…
Hypergraph partitioning is an important preprocessing step for optimizing data placement and minimizing communication volumes in high-performance computing applications. To cope with ever growing problem sizes, it has become increasingly…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
This work introduces hybrid stochastic differential equations with memory (mH-SDEs), a new class of stochastic systems where transition rates depend on the joint history of both Euclidean and discrete components. This extends existing…
A parallel implementation of a compatible discretization scheme for steady-state Stokes problems is presented in this work. The scheme uses generalized moving least squares to generate differential operators and apply boundary conditions.…
Polyspectral estimation is a problem of great importance in the analysis of nonlinear time series that has applications in biomedical signal processing, communications, geophysics, image, radar, sonar and speech processing, etc. Higher…
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…
To efficiently scale large model (LM) training, researchers transition from data parallelism (DP) to hybrid parallelism (HP) on GPU clusters, which frequently experience hardware and software failures. Existing works introduce in-memory…
Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by…
This paper introduces a high performance implementation of \texttt{Zolo-SVD} algorithm on distributed memory systems, which is based on the polar decomposition (PD) algorithm via the Zolotarev's function (\texttt{Zolo-PD}), originally…
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…
This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…
Persistent homology (PH) is a powerful mathematical method to automatically extract relevant insights from images, such as those obtained by high-resolution imaging devices like electron microscopes or new-generation telescopes. However,…
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…