Related papers: Alternative Tilings for the Fast Multipole Method …
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…
In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on the case of two and three layers in this work. The key…
Algorithmic and architecture-oriented optimizations are essential for achieving performance worthy of anticipated energy-austere exascale systems. In this paper, we present an extreme scale FMM-accelerated boundary integral equation solver…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
Smoothing filter is the method of choice for image preprocessing and pattern recognition. We present a new concurrent method for smoothing 2D object in binary case. Proposed method provides a parallel computation while preserving the…
An important but missing component in the application of the kernel independent fast multipole method (KIFMM) is the capability for flexibly and efficiently imposing singly, doubly, and triply periodic boundary conditions. In most popular…
This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange…
The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…
Fast multipole methods (FMM) were originally developed for accelerating $N$-body problems for particle-based methods. FMM is more than an $N$-body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation…
The Fast Multipole Method (FMM) is an efficient numerical algorithm for computation of long-ranged forces in $N$-body problems within gravitational and electrostatic fields. This method utilizes multipole expansions of the Green's function…
In this paper, we present a fast boundary integral method accelerated by the fast multipole method (FMM) for acoustic wave scattering governed by the scalar Helmholtz equation in multi-layered two-dimensional media. Multiple scatterers are…
Recently, a new framework to compute the photoionization rate in streamer discharges accurately and efficiently using the integral form and the fast multipole method (FMM) was presented. This paper further improves the efficiency of this…
We introduce jaxFMM, an open-source, adaptive, highly parallel point-charge Fast Multipole Method implementation for the Laplace kernel written in JAX. It is based on a non-uniform refinement strategy, which results in extremely concise and…
We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…
The increasing complexity and scale of photonic and electromagnetic devices demand efficient and accurate numerical solvers. In this work, we develop a parallel overlapping domain decomposition method (DDM) based on the finite-difference…
In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles. Because the pair-wise interaction between dislocations is long-range, this…
The Finite Difference Time Domain (FDTD) method is a widely used numerical technique for solving Maxwell's equations, particularly in computational electromagnetics and photonics. It enables accurate modeling of wave propagation in complex…
There is a growing interest in custom spatial accelerators for machine learning applications. These accelerators employ a spatial array of processing elements (PEs) interacting via custom buffer hierarchies and networks-on-chip. The…
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 present work attempts to integrate the independent efforts in the fast N-body community to create the fastest N-body library for many-core and heterogenous architectures. Focus is placed on low accuracy optimizations, in response to the…