Related papers: Multigrid Methods in Electronic Structure Calculat…
In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…
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…
Current state-of-the-art deep neural networks for image classification are made up of 10 - 100 million learnable weights and are therefore inherently prone to overfitting. The complexity of the weight count can be seen as a function of the…
High throughput screening of materials for technologically relevant areas, like identification of better catalysts, electronic materials, ceramics for high temperature applications and drug discovery, is an emerging topic of research. To…
In the distributed nucleus approximation we represent the singular nucleus as smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus allows us to solve the Poisson equation for theoverall electrostatic potential using a…
Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with…
The methods which are actively used for electronic structure calculations of low-lying states of heavy- and superheavy-element compounds are briefly described. The advantages and disadvantages of calculations with the Dirac-Coulomb-Breit…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious…
Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modeling these statistics may require theoretical templates that go beyond second-order…
We present a simulation workflow for efficient investigations of the interplay between 3D lithium-ion electrode microstructures and electrochemical performance, with emphasis on lithium plating. Our approach addresses several challenges.…
The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…
We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate…
In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr\"odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the so-called bond order…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential…
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of…
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,…