Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
M Salvalaglio, KR Elder - Modelling and Simulation in Materials …, 2022 - iopscience.iop.org
Comprehensive investigations of crystalline systems often require methods bridging
atomistic and continuum scales. In this context, coarse-grained mesoscale approaches are …
atomistic and continuum scales. In this context, coarse-grained mesoscale approaches are …
A review on computational modelling of phase-transition problems
Phase-transition problems are ubiquitous in science and engineering. They have been
widely studied via theory, experiments and computations. This paper reviews the main …
widely studied via theory, experiments and computations. This paper reviews the main …
[图书][B] Numerical models for differential problems
A Quarteroni, S Quarteroni - 2009 - Springer
Alfio Quarteroni Third Edition Page 1 MS&A – Modeling, Simulation and Applications 16
Numerical Models for Di erential Problems Alfio Quarteroni Third Edition Page 2 MS&A Volume …
Numerical Models for Di erential Problems Alfio Quarteroni Third Edition Page 2 MS&A Volume …
Linearly first-and second-order, unconditionally energy stable schemes for the phase field crystal model
In this paper, we develop a series of linear, unconditionally energy stable numerical
schemes for solving the classical phase field crystal model. The temporal discretizations are …
schemes for solving the classical phase field crystal model. The temporal discretizations are …
Stabilized second‐order convex splitting schemes for Cahn–Hilliard models with application to diffuse‐interface tumor‐growth models
X Wu, GJ Van Zwieten… - International journal for …, 2014 - Wiley Online Library
We present unconditionally energy‐stable second‐order time‐accurate schemes for diffuse‐
interface (phase‐field) models; in particular, we consider the Cahn–Hilliard equation and a …
interface (phase‐field) models; in particular, we consider the Cahn–Hilliard equation and a …
A fully-discrete decoupled finite element method for the conserved Allen–Cahn type phase-field model of three-phase fluid flow system
In this article, we develop and analyze a novel fully discrete decoupled finite element
method to solve a flow-coupled ternary phase-field model for the system consisting of three …
method to solve a flow-coupled ternary phase-field model for the system consisting of three …
The variational collocation method
H Gomez, L De Lorenzis - Computer Methods in Applied Mechanics and …, 2016 - Elsevier
We propose the variational collocation method for the numerical solution of partial
differential equations. The conceptual basis is the establishment of a direct connection …
differential equations. The conceptual basis is the establishment of a direct connection …
Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics
A Tagliabue, L Dede, A Quarteroni - Computers & Fluids, 2014 - Elsevier
In this paper, we consider the numerical approximation of high order Partial Differential
Equations (PDEs) by means of NURBS-based Isogeometric Analysis (IGA) in the framework …
Equations (PDEs) by means of NURBS-based Isogeometric Analysis (IGA) in the framework …
A mathematical model coupling tumor growth and angiogenesis
We present a mathematical model for vascular tumor growth. We use phase fields to model
cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and …
cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and …
An isogeometric collocation approach for Bernoulli–Euler beams and Kirchhoff plates
In this paper, IGA collocation methods are for the first time introduced for the solution of thin
structural problems described by the Bernoulli–Euler beam and Kirchhoff plate models. In …
structural problems described by the Bernoulli–Euler beam and Kirchhoff plate models. In …