Related papers: Mini-step Strategy for Transient Analysis

Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating method, they have evolved into a rich family of algorithms that…

The prediction of the quasi-static response of industrial laminate structures requires to use fine descriptions of the material, especially when debonding is involved. Even when modeled at the mesoscale, the computation of these structures…

The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…

This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may…

We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…

Computed tomography is widely used to examine internal structures in a non-destructive manner. To obtain high-quality reconstructions, one typically has to acquire a densely sampled trajectory to avoid angular undersampling. However, many…

We propose a new methodology for parametric domain decomposition using iterative principal component analysis. Starting with iterative principle component analysis, the high dimension manifold is reduced to the lower dimension manifold.…

We present a sparse coding-based framework for motion style decomposition and synthesis. Dynamic Time Warping is firstly used to synchronized input motions in the time domain as a pre-processing step. A sparse coding-based decomposition has…

We consider the problem of finding the optimal diagonal preconditioner for a positive definite matrix. Although this problem has been shown to be solvable and various methods have been proposed, none of the existing approaches are scalable…

This paper introduces the method of dynamic mode decomposition (DMD) for robustly separating video frames into background (low-rank) and foreground (sparse) components in real-time. The method is a novel application of a technique used for…

We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained…

Domain decomposition is a technique used to reduce memory overhead on large neutron transport problems. Currently, the optimal load-balanced processor allocation for these domains is typically determined through small-scale simulations of…

Low complexity of a system model is essential for its use in real-time applications. However, sparse identification methods commonly have stringent requirements that exclude them from being applied in an industrial setting. In this paper,…

Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…

Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…

In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

Dynamic evolution behaviors of dimension-varying control systems often appear in the genetic regulatory network and the vehicle clutch system etc. An interesting and significant study on dimension-varying control systems is how to realize…

The characterization of intermittent, multiscale and transient dynamics using data-driven analysis remains an open challenge. We demonstrate an application of the Dynamic Mode Decomposition (DMD) with sparse sampling for the diagnostic…