This work presents recent progress in phase-field-based fracture modeling in heterogeneous porous media. Existing algorithms that have been developed in the last years are extended to tackle three-dimensional configurations. Our solution technique is formulated in terms of a nested Newton loop that combines a primal-dual active set method (required for treating the crack irreversibility) and a ...

This paper describes a new technique to find the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this ...

We consider the simulation of three-dimensional transonic Euler flow using pseudo-transient Newton–Krylov methods [8,9]. The main computation involves solving a large, sparse linear system at each Newton (nonlinear) iteration. We develop a technique for adaptively selecting the linear solver method to match better the numeric properties of the linear systems as they evolve during the course of ...

Counterexample driven re nement is a promising technique to generate automatic abstractions for model checking software. A central problem in automating this approach is the re nement of models from spurious error traces. We present a solution to this problem for C programs. Our solution introduces compile time names for run time values, and handles all constructs in the C programming language....

A time-dependent, two-dimensional model of a semiconductor laser array is numerically studied by means of Θand Newton-Raphson methods. A parallel version of the BiCGSTAB algorithm for the solution of the linear equations resulting from the Newton-Raphson technique is presented. It is shown that the proposed method reduces by half the number of messages and, by means of communications overlappin...

The dogleg method is a classical trust-region technique for globalizing Newton’s method. While it is widely used in optimization, including large-scale optimization via truncatedNewton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexac...

This paper describes a new technique to nd the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this Ne...

We propose a Newton-CG primal proximal point algorithm for solving large scale log-determinant optimization problems. Our algorithm employs the essential ideas of the proximal point algorithm, the Newton method and the preconditioned conjugate gradient solver. When applying the Newton method to solve the inner sub-problem, we find that the log-determinant term plays the role of a smoothing term...

Quasi-Newton methods are widely used in practise for convex loss minimization problems. These methods exhibit good empirical performance on a wide variety of tasks and enjoy super-linear convergence to the optimal solution. For largescale learning problems, stochastic Quasi-Newton methods have been recently proposed. However, these typically only achieve sub-linear convergence rates and have no...

This paper describes a fall-back procedure for use with the Gauss-Newton method for nonlinear least-squares problems. While the basic Gauss-Newton algorithm is often successful, it is well-known that it can sometimes generate poor search directions and exhibit slow convergence. For dealing with such situations we suggest a new two-dimensional search strategy. Numerical experiments indicate that...