Related papers: A Low-rank Method for Parameter-dependent Fluid-st…
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations…
Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…
A unified fluid-structure interaction (FSI) formulation is presented for solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the generalized-alpha scheme are used for the spatial and temporal discretization. The membrane…
This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…
This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively…
A variational formulation based on velocity and stress is developed for linear fluid-structure interaction (FSI) problems. The well-posedness and energy stability of this formulation are established. To discretize the problem, a…
We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…
Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…
(Rephrased) Non-conformance decision-making processes in high-precision manufacturing of engineering structures are often delayed due to numerical simulations that are needed for analyzing the defective parts and assemblies. Interfaces…
Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six--dimensional phase space, making simulations of…
In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on…
Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…
We present an implementation of a fully variational formulation of an immersed method for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use…
In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is used, whereby gradient information is computed via a dual problem. To…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface $\Gamma \subset \mathbb{R}^3$ without boundary. This formulation leads to a coupled system of two second order scalar surface partial…
Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…