Related papers: A Multi-Vector Interface Quasi-Newton Method with …
We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…
Quasi-Newton algorithms are among the most popular iterative methods for solving unconstrained minimization problems, largely due to their favorable superlinear convergence property. However, existing results for these algorithms are…
This paper is concerned with the partitioned iterative formulation to simulate the fluid-structure interaction of a nonlinear multibody system in an incompressible turbulent flow. The proposed formulation relies on a three-dimensional (3D)…
Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to…
Distributed computing is critically important for modern statistical analysis. Herein, we develop a distributed quasi-Newton (DQN) framework with excellent statistical, computation, and communication efficiency. In the DQN method, no…
Variable projection methods prove highly efficient in solving separable nonlinear least squares problems by transforming them into a reduced nonlinear least squares problem, typically solvable via the Gauss-Newton method. When solving…
Three-field Fluid-Structure Interaction (FSI) formulations for fluid and solid are applied and compared to the standard two field-one field formulation for fluid and solid, respectively. Both formulations are applied in a non linear setting…
Considered herein is a modified Newton method for the numerical solution of nonlinear equations where the Jacobian is approximated using a complex-step derivative approximation. We show that this method converges for sufficiently small…
Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new quasi-Newton method for minimax problems, which we call $J$-symmetric quasi-Newton method.…
In order to avoid the evaluation of the Jacobian matrix and its inverse, the present author recently introduced the pseudo-Jacobian matrix with a general applicability of any nonlinear systems of equations. By using this concept, this paper…
In this paper, we consider a monolithic approach to handle coupled fluid-structure interaction problems with different hyperelastic models in an all-at-once manner. We apply Newton's method in the outer iteration dealing with nonlinearities…
In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit…
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system of nonlinear equations. In the Interior Point context,…
We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in…
This work concerns the simulation of compressible multi-material fluid flows and follows the method FVCF-NIP described in the former paper Braeunig et al (Eur. J. Mech. B/Fluids, 2009). This Cell-centered Finite Volume method is totally…
In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on…
Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due…
We introduce an Eulerian approach for problems involving one or more soft solids immersed in a fluid, which permits mechanical interactions between all phases. The reference map variable is exploited to simulate finite-deformation…
This paper presents a numerical method for the simulation of fluid-structure interaction specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic Cosserat rods. Because of their high…
For capillary driven flow the interface curvature is essential in the modelling of surface tension via the imposition of the Young--Laplace jump condition. We show that traditional geometric volume of fluid (VOF) methods, that are based on…