Related papers: Numerical Methods for Multilattices
A numerical simulation algorithm for lattice QCD is described, in which the short- and long-distance effects of the sea quarks are treated separately. The algorithm can be regarded, to some extent, as an implementation at the quantum level…
In this paper, we study different discrete data clustering methods, which use the Model-Based Clustering (MBC) framework with the Multinomial distribution. Our study comprises several relevant issues, such as initialization, model…
A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…
Hypo-elastoplasticity is a framework suitable for modeling the mechanics of many hard materials that have small elastic deformation and large plastic deformation. In most laboratory tests for these materials the Cauchy stress is in…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
We propose a framework for simulating the real-time dynamics of quantum field theories (QFTs) using continuous-variable quantum computing (CVQC). Focusing on ($1+1$)-dimensional $\varphi^4$ scalar field theory, the approach employs the…
Recently developed analytic methods in the framework of the Field Correlator Method are reviewed in this series of four lectures and results of calculations are compared to lattice data and experiment. Recent lattice data demonstrating the…
We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained optimization problem with virtual Dirichlet controls on the…
The focus of this paper is on the analysis of the Conjugate Gradient method applied to a non-symmetric system of linear equations, arising from a Fast Fourier Transform-based homogenization method due to (Moulinec and Suquet, 1994).…
Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for…
Lattice and special nonlattice multilevel constellations constructed from binary codes, such as Constructions A, C, and D, have relevant applications in Mathematics (sphere packing) and in Communication (multi-stage decoding and efficient…
To mitigate the substantial computational costs associated with modeling the mechanical behavior of large-scale architected lattice structures, this work introduces a concurrent multiscale approach: the Generalized Non-local Quasicontinuum…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
Despite the numerous successful applications of lattice QCD in nuclear and particle theory, fundamental algorithmic challenges remain. Among those, relevant for numerical studies of QCD on a space-time torus, is topological freezing--a form…
The Lattice Boltzmann method (LBM) is a well-established mesoscopic approach for simulating fluid dynamics by evolving particle distribution functions on discrete lattices. While the LBM is highly parallelizable on classical hardware, its…
The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix-vector product that involves the sign function of the hermitian Wilson matrix. In this paper we…
We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We…
Due to the sign problem, it is exponentially difficult to study QCD on the lattice at finite chemical potential. We propose a method --an overlap improving multi-parameter reweighting technique-- to alleviate this problem. We apply this…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…