Related papers: Accelerated Matrix Element Method with Parallel Co…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
One major challenge for the legacy measurements at the LHC is that the likelihood function is not tractable when the collected data is high-dimensional and the detector response has to be modeled. We review how different analysis strategies…
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case…
We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential…
We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…
A major computational bottleneck in modern High Energy Physics event generators arises from the integration of the matrix element, which requires repeated evaluations at different phase-space points to cover all possible initial- and…
Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities.…
An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into…
Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is a challenging problem. Analytical solutions for these models are rarely available, which means that the likelihood is also intractable. In this case,…
The use of machine learning algorithms is an attractive way to produce very fast detector simulations for scattering reactions that can otherwise be computationally expensive. Here we develop a factorised approach where we deal with each…
Inference of latent feature models in the Bayesian nonparametric setting is generally difficult, especially in high dimensional settings, because it usually requires proposing features from some prior distribution. In special cases, where…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…