Related papers: Parallelized Solution Method of the Three-dimensio…
We present a generalized algorithm based on a spherical harmonics expansion method for efficient computation of the three-dimensional gravitational potential on a multi-patch grid in spherical geometry. Instead of solving for the…
A new kind of overset grid, named Yin-Yang grid, for spherical geometry is proposed. The Yin-Yang grid is composed of two identical component grids that are combined in a complemental way to cover a spherical surface with partial overlap on…
A type of overlapping grid in spherical coordinates called the Yin-Yang grid is successfully implemented into a 3D version of the explicit Eulerian grid-based code PROMETHEUS including self-gravity. The modified code successfully passed…
We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…
A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
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 solution of the Poisson equation is a ubiquitous problem in computational astrophysics. Most notably, the treatment of self-gravitating flows involves the Poisson equation for the gravitational field. In hydrodynamics codes using…
The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be modified to include a novel parity-preserving interaction term, with inverse mass parameter, in addition to a possible topological mass term. The novelty is that the…
A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the…
Aims. Our aim is to derive a fast and accurate method for computing the gravitational potential of astrophysical objects with high contrasts in density, for which nested or adaptive meshes are required. Methods. We present an extension of…
We present an optimised multipole algorithm for computing the three-point correlation function (3PCF), tailored for application to large-scale cosmological datasets. The algorithm builds on a $in\, situ$ interpretation of correlation…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…
Multilevel, multiarea, and hierarchically interconnected electrical power grids confront substantial challenges with the increasing integration of many volatile energy resources. The traditional isolated operation of interconnected power…
The bulk power grid is divided into regional grids interconnected with multiple tie-lines for efficient operation. Since interconnected power grids are operated by different control centers, it is a challenging task to realize coordinated…
The gravitational potential is a key function involved in many astrophysical problems. Its evaluation inside continuous media from Newton's law is known to be challenging because of the diverging kernel 1/|r-r'|. This difficulty is…
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…
With tens of petaflops supercomputers already in operation and exaflops machines expected to appear within the next 10 years, efficient parallel computational methods are required to take advantage of such extreme-scale machines. In this…
Disk self-gravity could play an important role in the dynamic evolution of interaction between disks and embedded protoplanets. We have developed a fast and accurate solver to calculate the disk potential and disk self-gravity forces for…