相关论文: A Fast Potential and Self-Gravity Solver for Non-A…

We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our…

The standard particle-in-cell algorithm suffers from grid heating. There exists a gridless alternative which bypasses the deposition step and calculates each Fourier mode of the charge density directly from the particle positions. We show…

Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…

The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…

We present a new direct logarithmically optimal in theory and fast in practice algorithm to implement the high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. The key points…

The well-known ``displace, cut, and reflect'' method used to generate cold disks from given solutions of Einstein equations is extended to solutions of Einstein-Maxwell equations. Four exact solutions of the these last equations are used to…

Fast and high-order accurate algorithms for three dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic imaging, and many other fields of applied science. In this paper, we develop a…

We present a spectrally accurate, efficient FFT-based method for the three-dimensional free-space Poisson equation with smooth, compactly supported sources. The method adopts a super-potential formulation: we first compute the convolution…

The objective of this paper is to discuss anisotropic solutions representing static spherical self-gravitating systems in $f(R)$ theory. We employ the extended gravitational decoupling approach and transform temporal as well as radial…

Polar codes provably achieve the symmetric capacity of a memoryless channel while having an explicit construction. This work aims to increase the throughput of polar decoder hardware by an order of magnitude relative to the state of the art…

We develop several aspects of the theory of gaseous astrophysical discs in which the gravity of the disc makes a significant contribution to its structure and dynamics. We show how the internal gravitational potential can be expanded in…

Following Toomre & Kalnajs (1991), local models of slightly dissipative self-gravitating disks show how inhomogeneous structures can be maintained over several galaxy rotations. Their basic physical ingredients are self-gravity, dissipation…

We present a scheme for numerical simulations of collisionless self-gravitating systems which directly integrates the Vlasov--Poisson equations in six-dimensional phase space. By the results from a suite of large-scale numerical…

We present an efficient and accurate algorithm for solving the Poisson equation in spherical polar coordinates with a logarithmic radial grid and open boundary conditions. The method employs a divide-and-conquer strategy, decomposing the…

A unified treatment for fast and spectrally accurate evaluation of electrostatic potentials subject to periodic boundary conditions in any or none of the three spatial dimensions is presented. Ewald decomposition is used to split the…

A new formalism is presented for finding equilibrium distribution functions for axisymmetric systems. The formalism, obtainded by using the concept of fractional derivatives, generalizes the methods of Fricke (1952), Kalnajs (1972) and…

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first order approximation, the method reduces to a linear…

We present a direct Poisson solver for massively parallel simulations on three-dimensional Cartesian grids with non-uniform spacing. The method uses a tensor-based formulation in which the operator is diagonalized numerically along two…

We formulate and solve by semi-analytic means the axisymmetric equilibria of relativistic self-similar disks of infinitesimal vertical thickness. These disks are supported in the horizontal directions against their self-gravity by a…

We present an accelerated and hardware parallelized integral-equation solver for the problem of acoustic scattering by a two-dimensional surface in three-dimensional space. The approach is based, in part, on the novel Interpolated Factored…