Related papers: Fast stray field computation on tensor grids
Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element…
In this paper, we propose a new method for computing the stray-field and the corresponding energy for a given magnetization configuration. Our approach is based on the use of inverted finite elements and does not need any truncation. After…
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the…
We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order…
The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN, whereas the geometrically more versatile finite…
The simulation of electrical discharges has been attracting a great deal of attention. In such simulations, the electric field computation dominates the computational time. In this paper, we propose a fast tree algorithm that helps to…
We present a finite-difference method for the topology optimization of permanent magnets that is based on the FFT accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and…
We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost O(N log N), compared to the standard brute force approach which…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…
In micromagnetic simulations, the demagnetization field is by far the computationally most expensive field component and often a limiting factor in large multilayer systems. We present an exact method to calculate the demagnetization field…
We propose and justify a new approach for fast calculation of the electrostatic interaction energy of clusters of charged particles in constrained energy minimization in the framework of rigid protein-ligand docking. Our ``blind search''…
Finding efficient tensor contraction paths is essential for a wide range of problems, including model counting, quantum circuits, graph problems, and language models. There exist several approaches to find efficient paths, such as the…
The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Improvements both on a numerical and computational basis can relief problems related to this bottleneck. This work presents an efficient…
We propose a novel technique for faster deep neural network training which systematically applies sample-based approximation to the constituent tensor operations, i.e., matrix multiplications and convolutions. We introduce new sampling…
We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…
We present quantitative means for assessing the numerical accuracy of static magnetic field calculations in finite-element models. Our calculations use the three-dimensional Opera simulation software suite of Dassault Syst`emes. Our need to…
In this paper we present a method to accurately compute the energy of the magnetostatic interaction between linearly (or uniformly, as a special case) magnetized polyhedrons. The method has applications in finite element micromagnetics, or…
The approximate computation of all gravitational forces between $N$ interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than $\mathcal{O}(N)$ operations. FMM groups…