Related papers: A parallel implementation of a new fast algorithm …
In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an…
A novel code for the approximate computation of long-range forces between N mutually interacting bodies is presented. The code is based on a hierarchical tree of cubic cells and features mutual cell-cell interactions which are calculated…
We describe a fast approximation algorithm for the $\Delta$-separated sparsity projection problem. The $\Delta$-separated sparsity model was introduced by Hegde, Duarte and Cevher (2009) to capture the firing process of a single Poisson…
A highly recurrent traditional bottleneck in applied mathematics, for which the most popular codes (Mathematica and Matlab) do not offer a solution, is to find all the real solutions of a system of N nonlinear equations in a certain finite…
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…
Ab initio calculations are fundamentally bottlenecked for large systems by the steep computational scaling of solving self-consistent field (SCF) equations. While machine learning offers potential accelerations, existing methods often…
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…
Astrophysical Challenges which demand the solution of the one million (or more) gravitating body problem are briefly discussed for the fields of cosmology, galactic nuclei and globular star clusters. Results from the classical three-body…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
In this paper, we propose an efficient and accurate message-passing interface (MPI)-based parallel simulator for streamer discharges in three dimensions using the fluid model. First, we propose a new second-order semi-implicit scheme for…
We present analysis of the evolution of dark matter halos in dense environments of groups and clusters in dissipationless cosmological simulations. The premature destruction of halos in such environments, known as the overmerging, reduces…
We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach…
Since self-gravity is crucial in the structure formation of the universe, many hydrodynamics simulations with the effect of self-gravity have been conducted. The multigrid method is widely used as a solver for the Poisson equation of the…
We present a parallel implementation of a direct solver for the Poisson's equation on extreme-scale supercomputers with accelerators. We introduce a chunked-pencil decomposition as the domain-decomposition strategy to distribute work among…
Ncorpi$\mathcal{O}$N is a $N$-body software developed for the time-efficient integration of collisional and fragmenting systems of planetesimals or moonlets orbiting a central mass. It features a fragmentation model, based on crater scaling…
This paper presents and analyzes a parallelizable iterative procedure based on domain decomposition for primal-dual weak Galerkin (PDWG) finite element methods applied to the Poisson equation. The existence and uniqueness of the PDWG…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
We present a mean-field approach to simulating merging processes of two spherical collisionless stellar systems. This approach is realized with a self-consistent field (SCF) method in which the full spatial dependence of the density and…
We present a technique designed for parallelizing large rigid body simulations, capable of exploiting multiple CPU cores within a computer and across a network. Our approach can be applied to simulate both unilateral and bilateral…
We have developed a deterministic conservative solver for the inhomogeneous Fokker-Planck-Landau equation coupled with the Poisson equation, which is a {classical mean-field} primary model for collisional plasmas. Two subproblems, i.e. the…