Related papers: A Very Fast And Angular Momentum Conserving Tree C…
The tree code for the approximate evaluation of gravitational forces is extended and substantially accelerated by including mutual cell-cell interactions. These are computed by a Taylor series in Cartesian coordinates and in a completely…
Tree codes that approximate groups of distant particles with multipole expansions are the standard way to accelerate the computation of self-gravity on particles. While momentum-conserving fast multipole methods exist, parallelisation is…
We present tests of comparison between our versions of the Fast Multipole Algorithm (FMA) and ``classic'' tree-code to evaluate gravitational forces in particle systems. We have optimized the Greengard's original version of FMA allowing for…
We present a new very fast tree-code which runs on massively parallel Graphical Processing Units (GPU) with NVIDIA CUDA architecture. The tree-construction and calculation of multipole moments is carried out on the host CPU, while the force…
We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to…
Numerical methods have become a powerful tool for research in astrophysics, but their utility depends critically on the availability of suitable simulation codes. This calls for continuous efforts in code development, which is necessitated…
We discuss the conservation of angular momentum in nuclear time-dependent Hartree-Fock calculations for a numerical representation of wave functions and potentials on a three-dimensional cartesian grid. Free rotation of a deformed nucleus…
This paper presents a fast, economical particle-multiple-mesh N-body code optimized for large-N modelling of collisionless dynamical processes, such as black-hole wandering or bar-halo interactions, occurring within isolated galaxies. The…
Due to the variety and importance of applications of treecodes and FMM, the combination of algorithmic acceleration with hardware acceleration can have tremendous impact. Alas, programming these algorithms efficiently is no piece of cake.…
Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…
In this work, a nonlinear momentum method is introduced to enhance the convergence performance of momentum-based gradient optimization algorithms. Classical momentum methods, such as the Heavy Ball method, can be viewed as a dynamical…
I describe an `oct-tree' N-body code which randomly shifts, reorients, and resizes the root cell at each time step. Averaging over a plurality of root cell positions and orientations statistically restores translational and rotational…
Modeling of collisionless galactic systems is based on the N-body model, which requires large computational resources due to the long-range nature of gravitational forces. The most common method for calculating gravity is the TreeCode…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
We describe the TreePM method for carrying out large N-Body simulations to study formation and evolution of the large scale structure in the Universe. This method is a combination of Barnes and Hut tree code and Particle-Mesh code. It…
We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even…
We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement is bounded for any bipartite split along an edge of the tree. This is achieved by expanding the {\em time-evolving block decimation}…
In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation. For the momentum-preserving scheme, the key idea is based…
We present a forward semi-Lagrangian numerical method for systems of transport equations able to advect smooth and discontinuous fields with high-order accuracy. The numerical scheme is composed of an integration of the transport equations…
I describe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a "gridlet") of effective masses. The effective masses on a gridlet…