Isogeometric analysis for phase-field models of geometric PDEs and high-order PDEs on stationary and evolving surfaces
From MaRDI portal
Publication:2173603
DOI10.1016/j.cma.2019.03.043zbMath1441.65023OpenAlexW2936322123WikidataQ114196937 ScholiaQ114196937MaRDI QIDQ2173603
Navid Valizadeh, Timon Rabczuk
Publication date: 17 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2019.03.043
mean curvature flowCahn-Hilliard equationphase-field modelisogeometric analysisWillmore flowevolving surface
Numerical computation using splines (65D07) Nonlinear parabolic equations (35K55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Computer-aided design (modeling of curves and surfaces) (65D17)
Related Items (18)
Numerical modeling of phase separation on dynamic surfaces ⋮ Nonlocal operator method for the Cahn-Hilliard phase field model ⋮ Numerical simulation of binary fluid-surfactant phase field model coupled with geometric curvature on the curved surface ⋮ Subdivision based isogeometric analysis for geometric flows ⋮ An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split ⋮ Phase-field Navier-Stokes model for vesicle doublets hydrodynamics in incompressible fluid flow ⋮ Fast isogeometric solvers for hyperbolic wave propagation problems ⋮ A shallow physics-informed neural network for solving partial differential equations on static and evolving surfaces ⋮ Space-time methods based on isogeometric analysis for time-fractional Schrödinger equation ⋮ Mesoscale simulations of spherulite growth during isothermal crystallization of polymer melts via an enhanced 3D phase-field model ⋮ A localized extrinsic collocation method for Turing pattern formations on surfaces ⋮ Phase-field-lattice Boltzmann method for dendritic growth with melt flow and thermosolutal convection-diffusion ⋮ Isogeometric analysis of insoluble surfactant spreading on a thin film ⋮ Adaptive higher-order phase-field modeling of anisotropic brittle fracture in 3D polycrystalline materials ⋮ Isogeometric analysis for a phase-field constrained optimization problem of morphological evolution of vesicles in electrical fields ⋮ The Cahn-Hilliard equation with generalized mobilities in complex geometries ⋮ Isogeometric analysis of hydrodynamics of vesicles using a monolithic phase-field approach ⋮ Modeling and numerical simulation of surfactant systems with incompressible fluid flows on surfaces
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Curvature driven interface evolution
- Isogeometric analysis of the advective Cahn-Hilliard equation: spinodal decomposition under shear flow
- An adaptive meshfree method for phase-field models of biomembranes. II: A Lagrangian approach for membranes in viscous fluids
- Phase-field approximations of the Willmore functional and flow
- Isogeometric analysis of free-surface flow
- Computationally efficient solution to the Cahn-Hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem
- Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations
- A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant
- Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
- Discrete quadratic curvature energies
- A general framework for surface modeling using geometric partial differential equations
- Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
- PDE's on surfaces -- a diffusive interface approach
- Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches
- Solving PDEs in complex geometries: a diffuse domain approach
- Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
- An adaptive level set approach for incompressible two-phase flows
- A level set approach for computing solutions to incompressible two-phase flow
- On the variational theory of cell-membrane equilibria
- A generalized-\(\alpha\) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method
- Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics
- A PDE-based fast local level set method
- A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
- On the use of local maximum entropy approximants for Cahn-Hilliard phase-field models in 2D domains and on surfaces
- Colliding interfaces in old and new diffuse-interface approximations of Willmore-flow
- PetIGA: a framework for high-performance isogeometric analysis
- Isogeometric analysis of geometric partial differential equations
- Phase-field model of cellular migration: three-dimensional simulations in fibrous networks
- Isogeometric analysis of the Cahn-Hilliard equation -- a convergence study
- A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface
- Discrete surface modelling using partial differential equations
- Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
- Isogeometric analysis of high order partial differential equations on surfaces
- Isogeometric analysis of the Cahn-Hilliard phase-field model
- Nonlinear manifold learning for meshfree finite deformation thin-shell analysis
- A phase field formulation of the Willmore problem
- A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
- Computation of geometric partial differential equations and mean curvature flow
- A finite element-based level set method for structural optimization
- A Stable and Efficient Method for Treating Surface Tension in Incompressible Two-Phase Flow
- Phase transitions and generalized motion by mean curvature
- The Motion of a Surface by Its Mean Curvature. (MN-20)
- Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
- Propagation of fronts in a nonlinear fourth order equation
- Mean curvature flow by the Allen–Cahn equation
- Computational Fluid–Structure Interaction
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- YZβ discontinuity capturing for advection‐dominated processes with application to arterial drug delivery
- Finite element methods for surface PDEs
- A free-boundary model for diffusion-induced grain boundary motion
This page was built for publication: Isogeometric analysis for phase-field models of geometric PDEs and high-order PDEs on stationary and evolving surfaces
