相关论文: One-way multigrid method in electronic structure c…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…
The multigrid methodology is reviewed. By integrating numerical processes at all scales of a problem, it seeks to perform various computational tasks at a cost that rises as slowly as possible as a function of $n$, the number of degrees of…
The ongoing process of smart grid digitalisation is increasing the volume of automated information exchange across distributed energy systems. This has driven the development of new information and data models when existing models fail to…
Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach…
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…
We propose a sparse interpolation construction and a practical coarsening algorithm for the algebraic multigrid (AMG) method, tailored towards H(curl). Building on the generalized AMG framework, we introduce an interior/exterior splitting…
While there have been many developments in computational probes of both strongly-correlated molecular systems and machine-learning accelerated molecular dynamics, there remains a significant gap in capabilities in simulating accurate…
In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms Fast Fourier Transform, Batcher's sorting schemes and prefix sum -exhibit recursive structure. We propose a data structure,…
We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of…
Energy distribution networks are crucial for human societies and since they often cover large geographical areas, their physical analysis is challenging. Modeling and simulation can be used to analyze such complex energy networks. In this…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
Microgrids are recognized as a relevant tool to absorb decentralized renewable energies in the energy mix. However, the sequential handling of multiple stochastic productions and demands, and of storage, make their management a delicate…
We propose a non grid-based interpolation scheme based on the information from the data collected from the vicinity of the query point. As a non-grid-based interpolation, the data points can be distributed randomly in a small region, and…
This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the…
We describe the object-oriented implementation of a higher-order finite-difference density-functional code in Fortran 90. Object-oriented models of grid and related objects are constructed and employed for the implementation of an efficient…
In this paper, we conduct an in-depth investigation of the structural intricacies inherent to the Invariant Energy Quadratization (IEQ) method as applied to gradient flows, and we dissect the mechanisms that enable this method to uphold…
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries…
We discuss how multi-grid computing schemes can be used to design hierarchical coordination architectures for energy systems. These hierarchical architectures can be used to manage multiple temporal and spatial scales and mitigate…
A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially…
The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners,…