相关论文: Recursive multilevel trust region method with appl…

Non-linear phase field models are increasingly used for the simulation of fracture propagation models. The numerical simulation of fracture networks of realistic size requires the efficient parallel solution of large coupled non-linear…

Many large-scale optimization problems arising in science and engineering are naturally defined at multiple levels of discretization or model fidelity. Multilevel methods exploit this hierarchy to accelerate convergence by combining coarse-…

We introduce a novel variant of the recursive multilevel trust-region (RMTR) method, called MASTR. The method is designed for solving non-convex bound-constrained minimization problems, which arise from the finite element discretization of…

We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is…

We propose a globally convergent multilevel training method for deep residual networks (ResNets). The devised method can be seen as a novel variant of the recursive multilevel trust-region (RMTR) method, which operates in hybrid…

This work presents a variational physics-informed deep learning framework for phase-field modelling of brittle crack propagation in anisotropic media. Previous Deep Ritz Method (DRM) approaches have focused on second-order, isotropic…

Phase-field fracture models are known to overestimate the crack area, a discrepancy that compromises the accuracy of fracture predictions. This issue stems from the diffuse crack representation and numerical artifacts, such as strain…

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The…

Fracture mechanics is crucial for many fields of engineering, as precisely predicting failure of structures and parts is required for efficient designs. The simulation of failure processes is, from a mechanical and a numerical point of…

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure.…

The phase-field model for fracture, despite its popularity and ease of implementation comes with its set of computational challenges. They are the non-convex energy functional, variational inequality due to fracture irreversibility, the…

This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…

This work addresses an efficient Global-Local approach supplemented with predictor-corrector adaptivity applied to anisotropic phase-field brittle fracture. The phase-field formulation is used to resolve the sharp crack surface topology on…

In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith's theory-which does not incorporate a strength criterion-these…

In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual…

We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a (probably nonconvex) smooth function and a (probably nonsmooth) convex function. The model…

In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive…

We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a…

We introduce two multifidelity trust-region methods based on the Magical Trust Region (MTR) framework. MTR augments the classical trust-region step with a secondary, informative direction. In our approaches, the secondary ``magical''…