Related papers: A Multi-Vector Interface Quasi-Newton Method with …
We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of…
In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of…
The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to incorporate local curvature information. Since the true…
We present a first step towards a multigrid method for solving the min-cost flow problem. Specifically, we present a strategy that takes advantage of existing black-box fast iterative linear solvers, i.e. algebraic multigrid methods. We…
Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…
An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure)…
Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the…
Simulating compositional multiphase flow in porous media is a challenging task, especially when phase transition is taken into account. The main problem with phase transition stems from the inconsistency of the primary variables such as…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
In this paper we propose a novel and general approach to design semi-implicit methods for the simulation of fluid-structure interaction problems in a fully Eulerian framework. In order to properly present the new method, we focus on the…
This work focuses on the derivation and the analysis of a novel, strongly-coupled partitioned method for fluid-structure interaction problems. The flow is assumed to be viscous and incompressible, and the structure is modeled using linear…
Coupled hydro-mechanical processes are of great importance to numerous engineering systems, e.g., hydraulic fracturing, geothermal energy, and carbon sequestration. Fluid flow in fractures is modeled after a Poiseuille law that relates the…
Designing efficient quasi-Newton methods is an important problem in nonlinear optimization and the solution of systems of nonlinear equations. From the perspective of the matrix approximation process, this paper presents a unified framework…
A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…
This paper addresses the challenge of solving large-scale nonlinear equations with H\"older continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within explicit superlinear convergence rate, which outperforms…
In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…
The cost of a partitioned fluid-structure interaction scheme is typically assessed by the number of coupling iterations required per time step, while ignoring the Newton loops within the nonlinear sub-solvers. In this work, we discuss why…