AI summary · arXiv: 2301.06503v1 · math.NA
A Computationally Efficient Vectorized Implementation of Localizing Gradient Damage Method in MATLAB
The essentials
- Subrato Sarkar presents a computationally efficient vectorized implementation of the localizing gradient damage method (LGDM) in MATLAB.
- LGDM is a fracture modeling method implemented using MATLAB for its simple and easy-to-learn coding interface.
- The vectorized implementation addresses the computational inefficiency of MATLAB-developed codes for large-scale simulations.
- LGDM is chosen as the fracture modeling method due to its thermodynamically consistent formulation built upon the micromorphic framework.
- The non-linear coupled field formulation of LGDM allows for testing the computational efficiency of the vectorized MATLAB implementation in a non-linear finite element setting.
- The results show that the vectorized MATLAB implementation significantly saves computational resources and time compared to non-vectorized implementations parallelized with MATLAB parfor.
- Numerical problems in 1D, 2D, and 3D are solved on a consumer-grade PC to validate the effectiveness of the vectorized implementation.
- Supplementary materials including sample source codes are provided, which can be valuable resources for researchers working on similar coupled field models.
Key points written by AI: they may contain errors, check them against the paper.
Ask questions about this paper to our AI assistant
How to chat with this paper? Illustrated guide
You can also chat with multiple papers at once here.
⚠The license of the paper does not allow us to build upon its content and the AI assistant only knows about the paper metadata rather than the full article.
Keep this conversation — a free account saves your questions and answers, your collections of papers and your alerts.
Create a free accountTools for this paper
Advanced tools Premium
For researchers who follow a field closely: citation alerts, journal-club slides, version comparison and Zotero export. Discover Premium
Papers around this one
See them on a mapRanked by how close their title and abstract are to this paper’s. Select some to read them together.
Closest papers
-
A robust monolithic solver for phase-field fracture integrated with fracture energy based arc-length method and under-relaxationRitukesh Bharali, Somdatta Goswami, Cosmin Anitescu et al. · 2021 · Numerical Analysis · AI summary available
Abstract
The phase-field fracture free-energy functional is non-convex with respect to the displacement and the phase field. This results in a poor performance of the conventional monolithic solvers like the Newton-Raphson method. In order to circumvent this issue, researchers opt for the alternate minimization (staggered) solvers. Staggered solvers are robust for the phase-field based fracture simulations as the displacement and the phase-field sub-problems are convex in nature. Nevertheless, the staggered solver requires very large number of iterations (of the order of thousands) to converge. In this work, a robust monolithic solver is presented for the phase-field fracture problem. The solver adop…
-
A robust solution strategy for the Cahn-Larché equationsErlend Storvik, Jakub Wiktor Both, Jan Martin Nordbotten et al. · 2022 · Numerical Analysis · AI summary available
Abstract
In this paper we propose a solution strategy for the Cahn-Larch\'e equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a Ginzburg-Landau type energy functional. The system can be seen as a combination of the Cahn-Hilliard regularized interface equation and linearized elasticity, and is non-linearly coupled, has a fourth order term that comes from the Cahn-Hilliard subsystem, and is non-convex and nonlinear in both the phase-field and displacement variables. We propose a novel semi-implicit discretization in time that uses a standard convex-concave splitting method of the nonlinear double-well potential, as well as special treatment…
-
Provably stable numerical method for the anisotropic diffusion equation in toroidally confined magnetic fieldsDean Muir, Kenneth Duru, Matthew Hole et al. · 2023 · Numerical Analysis · AI summary available
Abstract
We present a novel numerical method for solving the anisotropic diffusion equation in toroidally confined magnetic fields which is efficient, accurate and provably stable. The continuous problem is written in terms of a derivative operator for the perpendicular transport and a linear operator, obtained through field line tracing, for the parallel transport. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing …
-
Thirty years of the finite volume method for solid mechanicsPhilip Cardiff, Ismet Demirdžić · 2018 · Numerical Analysis · AI summary available
Abstract
Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, which can be classified in a variety of ways, such as grid arrangement (cell-centred vs staggered vs vertex-centred), solution algorithm (implicit vs explicit), and stabilisation strategy (Rhie-Chow vs Jameson-Schmidt-Turkel vs Godunov upwinding). This article gives an overview, historical perspective, comparison and critical analysis of the different approaches where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given. The article finish…
-
Modeling martensitic transformation in shape memory alloys using multi-phase-field elasticity models based on partial rank-one energy relaxation on pairwise interfacesMohammad Sarhil, Oleg Shchyglo, Dominik Brands et al. · 2023 · Numerical Analysis · Not summarized yet
Abstract
To model the mechanically-driven phase transformations, e.g. martensitic transformation, using the phase-field theory, suitable models are needed for describing the mechanical fields of the individual non-vanishing phase-fields in the interface regions in order to obtain the mechanical driving forces of phase-field motion. Quantitative modeling requires satisfying the interfacial static equilibrium and kinematic compatibility conditions which have already been achieved in the literature for dual-phase-field materials by using the rank-one relaxation (or convexification) of the energy density. A direct generalization to the multi-phase-field case is not applicable without breaking these condi…
-
Convergence Analysis for Nonlinear GMRESYunhui He · 2025 · Numerical Analysis · AI summary available
Abstract
In this work, we revisit nonlinear generalized minimal residual method (NGMRES) applied to nonlinear problems. NGMRES is used to accelerate the convergence of fixed-point iterations, which can substantially improve the performance of the underlying fixed-point iterations. We consider NGMRES with a finite window size $m$, denoted as NGMRES($m$). However, there is no convergence analysis for NGMRES($m$) applied to nonlinear systems. We prove that for general $m>0$, the residuals of NGMRES($m$) converge r-linearly under some conditions. For $m=0$, we prove that the residuals of NGMRES(0) converge q-linearly.
-
On the implementation of the eXtended Finite Element Method (XFEM) for interface problemsThomas Carraro, Sven Wetterauer · 2015 · Numerical Analysis · AI summary available
Abstract
The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate quadrature rule; (ii) the shape functions for the extended part of the finite element formulation; (iii) the boundary and interface conditions. We show how to handle the XFEM formulation providing a code that demonstrates the solution of two exemplary interface problems for a strong and a weak discontinuity respectively. In the weak discontinuity case, the loss of conformity due to the blending effect and its remedy are discussed. Furthermore, the optimal convergen…
-
Gradual Variation Analysis for Groundwater FlowLi Chen · 2010 · Numerical Analysis · Not summarized yet
Abstract
Groundwater flow in Washington DC greatly influences the surface water quality in urban areas. The current methods of flow estimation, based on Darcy's Law and the groundwater flow equation, can be described by the diffusion equation (the transient flow) and the Laplace equation (the steady-state flow). The Laplace equation is a simplification of the diffusion equation under the condition that the aquifer has a recharging boundary. The practical way of calculation is to use numerical methods to solve these equations. The most popular system is called MODFLOW, which was developed by USGS. MODFLOW is based on the finite-difference method in rectangular Cartesian coordinates. MODFLOW can be vie…
Go further
How are these papers found?
We compare the title and abstract of this paper with those of every paper summarized on this site, and with the papers Semantic Scholar recommends, those it cites and those citing it (for a much-cited paper, its most recent citations and, from OpenAlex, the most cited ones). Among the prior work and the follow-ups, the papers that use each other in depth, a method it uses and the much-cited follow-ups come a little higher. The levels (very close, close, related) come from the similarity of the texts, not from a judgment of quality; * marks a paper without an abstract, compared by its title. The sentence under a paper is written by an AI from the two abstracts: check it in the papers. A paper marked not relevant by three readers leaves the list.
For now only among the papers summarized on this site: search again to add the prior work, the follow-ups and Semantic Scholar’s recommendations.
The previous summary was created more than a year ago and can be re-run (if necessary) by clicking on the Run button below.
⚠The license of this specific paper does not allow us to build upon its content and the summarizing tools will be run using the paper metadata rather than the full article. However, it still does a good job, and you can also try our tools on papers with more open licenses.
Disclaimer: The AI-based summarization tool and virtual assistant provided on this website may not always provide accurate and complete summaries or responses. We encourage you to carefully review and evaluate the generated content to ensure its quality and relevance to your needs.