The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing

From MaRDI portal
Publication:5112636

DOI10.1137/19M1305914zbMath1447.65057arXiv1912.09263OpenAlexW3024213355WikidataQ115525562 ScholiaQ115525562MaRDI QIDQ5112636

Zhengguang Liu, Xiao-Li Li

Publication date: 2 June 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.09263



Related Items

A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation, Mass-, Energy-, and Momentum-Preserving Spectral Scheme for Klein-Gordon-Schrödinger System on Infinite Domains, Efficiency energy-preserving cosine pseudo-spectral algorithms for the sine-Gordon equation with Neumann boundary conditions, A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system, Linear and fully decoupled scheme for a hydrodynamics coupled phase-field surfactant system based on a multiple auxiliary variables approach, Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations, Energy-conserving and time-stepping-varying ESAV-Hermite-Galerkin spectral scheme for nonlocal Klein-Gordon-Schrödinger system with fractional Laplacian in unbounded domains, Arbitrary high-order linearly implicit energy-preserving algorithms for Hamiltonian PDEs, Stabilized exponential-SAV schemes preserving energy dissipation law and maximum bound principle for the Allen-Cahn type equations, Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy functionals, Positivity-preserving and unconditionally energy stable numerical schemes for MEMS model, Arbitrary high-order exponential integrators conservative schemes for the nonlinear Gross-Pitaevskii equation, Two efficient spectral methods for the nonlinear fractional wave equation in unbounded domain, Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine-Gordon equation with damping, Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows, A general class of linear unconditionally energy stable schemes for the gradient flows, An efficient energy-stable pseudospectral method for simulating vortex dynamics of the Ginzburg-Landau-Schrödinger equation, Efficient and accurate exponential SAV algorithms with relaxation for dissipative system, On convergence of a novel linear conservative scheme for the two-dimensional fractional nonlinear Schrödinger equation with wave operator, Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential, Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations, A general class of linear unconditionally energy stable schemes for the gradient flows. II., Energy stable schemes for the Klein-Gordon-Zakharov equations, Three decoupled, second-order accurate, and energy stable schemes for the conserved Allen-Cahn-type block copolymer (BCP) model, Explicit high accuracy energy-preserving Lie-group sine pseudo-spectral methods for the coupled nonlinear Schrödinger equation, A structure-preserving, upwind-SAV scheme for the degenerate Cahn-Hilliard equation with applications to simulating surface diffusion, The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn–Hilliard equation, The exponential SAV approach for the time-fractional Allen-Cahn and Cahn-Hilliard phase-field models, A novel relaxed scalar auxiliary variable approach for gradient flows, Fully decoupled linear BDF2 scheme for the penalty incompressible Ericksen-Leslie equations, Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation, Low regularity integrators for semilinear parabolic equations with maximum bound principles, Mass-, and energy preserving schemes with arbitrarily high order for the Klein-Gordon-Schrödinger equations, Energy dissipation-preserving GSAV-Fourier-Galerkin spectral schemes for space-fractional nonlinear wave equations in multiple dimensions, A linearly implicit energy-preserving exponential time differencing scheme for the fractional nonlinear Schrödinger equation, Unconditionally energy-stable linear convex splitting algorithm for the \(L^2\) quasicrystals, An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations, A computationally optimal relaxed scalar auxiliary variable approach for solving gradient flow systems, A highly efficient and accurate new SAV approach for the modified phase field crystal model, Unconditional convergence of conservative spectral Galerkin methods for the coupled fractional nonlinear Klein-Gordon-Schrödinger equations, Unconditional stability of first and second orders implicit/explicit schemes for the natural convection equations, A novel class of explicit energy-preserving splitting methods for charged-particle dynamics, Linear multi-step methods and their numerical stability for solving gradient flow equations, High-order schemes for the fractional coupled nonlinear Schrödinger equation, A Unified Design of Energy Stable Schemes with Variable Steps for Fractional Gradient Flows and Nonlinear Integro-differential Equations, Energy dissipation and maximum bound principle preserving scheme for solving a nonlocal ternary Allen-Cahn model, Asymptotically compatible energy of two variable-step fractional BDF2 schemes for the time fractional Allen-Cahn model, Fully decoupled, linear, and energy-preserving GSAV difference schemes for the nonlocal coupled sine-Gordon equations in multiple dimensions, Efficient numerical simulation of Cahn-Hilliard type models by a dimension splitting method, Unnamed Item, Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system, Two linearly implicit energy preserving exponential scalar auxiliary variable approaches for multi-dimensional fractional nonlinear Schrödinger equations, High-order time-accurate, efficient, and structure-preserving numerical methods for the conservative Swift-Hohenberg model, Explicit high-order energy-preserving exponential time differencing method for nonlinear Hamiltonian PDEs, A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator, New efficient time-stepping schemes for the Navier-Stokes-Cahn-Hilliard equations, Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model, A family of effective structure-preserving schemes with second-order accuracy for the undamped sine-Gordon equation, Novel energy stable schemes for Swift-Hohenberg model with quadratic-cubic nonlinearity based on the \(H^{-1}\)-gradient flow approach, On a nonlinear energy-conserving scalar auxiliary variable (SAV) model for Riesz space-fractional hyperbolic equations, Generalized SAV approaches for gradient systems, High-order explicit conservative exponential integrator schemes for fractional Hamiltonian PDEs, Efficient energy preserving Galerkin-Legendre spectral methods for fractional nonlinear Schrödinger equation with wave operator, The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes, Step-by-step solving schemes based on scalar auxiliary variable and invariant energy quadratization approaches for gradient flows, New efficient and unconditionally energy stable schemes for the Cahn-Hilliard-Brinkman system, Original variables based energy-stable time-dependent auxiliary variable method for the incompressible Navier-Stokes equation, On efficient semi-implicit auxiliary variable methods for the six-order Swift-Hohenberg model, Linearly implicit and second-order energy-preserving schemes for the modified Korteweg-de Vries equation, Explicit exactly energy-conserving methods for Hamiltonian systems, Dissipation-preserving rational spectral-Galerkin method for strongly damped nonlinear wave system involving mixed fractional Laplacians in unbounded domains



Cites Work