Related papers: Fast multipole methods for evaluation of layer pot…
The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general…
We discuss an implementation of adaptive fast multipole methods targeting hybrid multicore CPU- and GPU-systems. From previous experiences with the computational profile of our version of the fast multipole algorithm, suitable parts are…
The Fast Multipole Method (FMM) computes pairwise interactions between particles with an efficiency that scales linearly with the number of particles. The method works by grouping particles based on their spatial distribution and…
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…
The basic idea of fast Monte Carlo (MC) simulations is to perform particle-based MC simulations with the excluded-volume interactions modeled by "soft" repulsive potentials that allow particle overlapping. This gives much faster system…
In this paper, we present a fast multipole method (FMM) for the half-space Green's function in a homogeneous elastic half-space subject to zero normal stress, for which an explicit solution was given by Mindlin (1936). The image structure…
The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners,…
In a recently developed quadrature method (quadrature by expansion or QBX), it was demonstrated that weakly singular or singular layer potentials can be evaluated rapidly and accurately on surface by making use of local expansions about…
Recent studies have demonstrated improved skill in numerical weather prediction via the use of spatially correlated observation error covariance information in data assimilation systems. In this case, the observation weighting matrices…
The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the…
A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed…
We present a new direct logarithmically optimal in theory and fast in practice algorithm to implement the high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. The key points…
The efficient simulation of fluid-structure interactions at zero Reynolds number requires the use of fast summation techniques in order to rapidly compute the long-ranged hydrodynamic interactions between the structures. One approach for…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…
In this letter, a fast Fourier transform (FFT)-enhanced low-complexity super-resolution sensing algorithm for near-field source localization with both angle and range estimation is proposed. Most traditional near-field source localization…
General Matrix Multiplication (GEMM) has a wide range of applications in scientific simulation and artificial intelligence. Although traditional libraries can achieve high performance on large regular-shaped GEMMs, they often behave not…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
Chemically-active colloids modify the concentration of chemical solutes surrounding them in order to self-propel. In doing so, they generate long-ranged hydrodynamic flows and chemical gradients that modify the trajectories of other…
Emerging deep learning workloads urgently need fast general matrix multiplication (GEMM). To meet such demand, one of the critical features of machine-learning-specific accelerators such as NVIDIA Tensor Cores, AMD Matrix Cores, and Google…