Related papers: Accelerating potential evaluation over unstructure…
Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing…
This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…
This paper presents a unified and computationally efficient framework for predicting incompressible, irrotational (potential) flow around multiple immersed bodies in two-dimensional domains, with particular emphasis on quantifying…
We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…
The approximate computation of all gravitational forces between $N$ interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than $\mathcal{O}(N)$ operations. FMM groups…
A new framework is proposed for analyzing staggered-grid finite difference finite volume methods on unstructured meshes. The new framework employs the concept of external approximation of function spaces, and gauge convergence of numerical…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
The growing need for creating surfaces with specific wetting properties, such as superhyrdophobic behavior, asks for novel methods for their efficient design. In this work, a fast computational method for the evaluation of patterned…
Dense 3D convolutions provide high accuracy for perception but are too computationally expensive for real-time robotic systems. Existing tri-plane methods rely on 2D image features with interpolation, point-wise queries, and implicit MLPs,…
We introduce a fast mesh-based method for computing N-body interactions that is both scalable and accurate. The method is founded on a particle-particle--particle-mesh P3M approach, which decomposes a potential into rapidly decaying…
To evaluate electrostatics interactions, Molecular dynamics (MD) simulations rely on Particle Mesh Ewald (PME), an O(Nlog(N)) algorithm that uses Fast Fourier Transforms (FFTs) or, alternatively, on O(N) Fast Multipole Methods (FMM)…
Polymer electrolytes are promising candidates for the next generation lithium-ion battery technology. Large scale screening of polymer electrolytes is hindered by the significant cost of molecular dynamics (MD) simulation in amorphous…
Existing pipelines of semantic correspondence commonly include extracting high-level semantic features for the invariance against intra-class variations and background clutters. This architecture, however, inevitably results in a…
We present an algorithmic framework for matrix-free evaluation of discontinuous Galerkin finite element operators based on sum factorization on quadrilateral and hexahedral meshes. We identify a set of kernels for fast quadrature on cells…
We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic…
Machine learning interatomic potentials have revolutionized complex materials design by enabling rapid exploration of material configurational spaces via crystal structure prediction with ab initio accuracy. However, critical challenges…
Nonlocality brings many challenges to the implementation of finite element methods (FEM) for nonlocal problems, such as large number of queries and invoke operations on the meshes. Besides, the interactions are usually limited to Euclidean…
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…
We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation…
Magnetic Reconnection is an efficient and fast acceleration mechanism by means of direct electric field acceleration parallel to the magnetic field. Thus, acceleration of particles in reconnection regions is a very important topic in plasma…