Related papers: Parallelized Solution Method of the Three-dimensio…
This paper investigates parallelization strategies for solving power flow problems in both transmission and unbalanced, three-phase distribution systems by developing a scalable power flow solver, ExaGridPF, which is compatible with…
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…
This paper introduces a novel, lightweight method to solve the visibility problem for 2D grids. The proposed method evaluates the existence of lines-of-sight from a source point to all other grid cells in a single pass with no preprocessing…
We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
The complete tree-level S-matrix of four dimensional ${\cal N}=4$ super Yang-Mills and ${\cal N} = 8$ supergravity has compact forms as integrals over the moduli space of certain rational maps. In this note we derive formulas for amplitudes…
Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel…
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, solving the eigenvalue problem in the finest space is…
In this paper, we develop a new extrapolation cascadic multigrid (ECMG$_{jcg}$) method, which makes it possible to solve 3D elliptic boundary value problems on rectangular domains of over 100 million unknowns on a desktop computer in…
We present a simple and efficient technique in ab initio electronic-structure calculation utilizing real-space double-grid with a high density of grid points in the vicinity of nuclei. This technique promises to greatly reduce the overhead…
In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on…
Problems in astrophysics, space weather research and geophysics usually need to analyze noisy big data on the sphere. This paper develops distributed filtered hyperinterpolation for noisy data on the sphere, which assigns the data fitting…
In this paper two types of multgrid methods, i.e., the Rayleigh quotient iteration and the inverse iteration with fixed shift, are developed for solving the Maxwell eigenvalue problem with discontinuous relative magnetic permeability and…
We lift the recently proposed theories of higher-spin self-dual Yang-Mills (SDYM) and gravity (SDGR) to the twistor space. We find that the most natural room for the twistor formulation of these theories is not in the projective, but in the…
The large-scale integration of renewable generation directly affects the reliability of power grids. We investigate the problem of power balancing in a general renewable-integrated power grid with storage and flexible loads. We consider a…
We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this…
In this paper, we develop an EXCMG method to solve the three-dimensional Poisson equation on rectangular domains by using the compact finite difference (FD) method with unequal meshsizes in different coordinate directions. The resulting…
We present an elementary argument that one can shield linearised gravitational fields using linearised gravitational fields. This is done by using third-order potentials for the metric, which avoids the need to solve singular equations in…
We present a new parallel PM N-body code named PMFAST that is freely available to the public. PMFAST is based on a two-level mesh gravity solver where the gravitational forces are separated into long and short range components. The…