相关论文: Optimal frequency resolution for spectral proper o…

Speckle photography can be used to monitor deformations of solid surfaces. The measuring characteristics, such as range or lateral resolution depend heavily on the optical recording and illumination set-up. This paper shows how, by the…

We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our…

In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods.…

Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physical instability and numerical instability. Optimization is a…

This paper presents a pseudo-spectral method for Dynamic Optimization Problems (DOPs) that allows for tight polynomial bounds to be achieved via flexible sub-intervals. The proposed method not only rigorously enforces inequality…

We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…

In this paper, we present a Localized Orthogonal Decomposition (LOD) in Petrov-Galerkin formulation for a two-scale Helmholtz-type problem. The two-scale problem is, for instance, motivated from the homogenization of the Helmholtz equation…

We investigate the stochastic gradient descent (SGD) method where the step size lies within a banded region instead of being given by a fixed formula. The optimal convergence rate under mild conditions and large initial step size is proved.…

Large Eddy Simulation is based on decomposition of turbulent flow structures to large energy containing scales and small subgrid scales. The present study captures all flow low energy modes of a sample shear layer using the proper…

We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of…

Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation group synchronization…

We performed a comparative study of extraction of large-scale flow structures in Rayleigh B\'enard convection using proper orthogonal decomposition (POD) and {\em Fourier analysis}. We show that the free-slip basis functions capture the…

A spectral method is considered for approximating the fractional Laplacian and solving the fractional Poisson problem in 2D and 3D unit balls. The method is based on the explicit formulation of the eigenfunctions and eigenvalues of the…

In this paper, we combine concepts of the generalized multiscale finite element method and mode decomposition methods to construct a robust local-global approach for model reduction of flows in high-contrast porous media. This is achieved…

The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…

In this paper we propose an accurate, and computationally efficient method for incorporating adaptive spatial resolution into weakly-compressible Smoothed Particle Hydrodynamics (SPH) schemes. Particles are adaptively split and merged in an…

This study presents a framework for estimating the full vibrational state of wind turbine blades from sparse deflection measurements. The identification is performed in a reduced-order space obtained from a Proper Orthogonal Decomposition…

Due to recent technological advances, large brain imaging data sets can now be collected. Such data are highly complex so extraction of meaningful information from them remains challenging. Thus, there is an urgent need for statistical…

Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…

Speed-of-sound (SoS) is an emerging ultrasound contrast modality, where pulse-echo techniques using conventional transducers offer multiple benefits. For estimating tissue SoS distributions, spatial domain reconstruction from relative…