Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model
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Publication:4560712
DOI10.1137/18M1166961zbMath1403.65045OpenAlexW2902106637WikidataQ128871552 ScholiaQ128871552MaRDI QIDQ4560712
Publication date: 7 December 2018
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/18m1166961
Nonlinear parabolic equations (35K55) Initial-boundary value problems for higher-order parabolic equations (35K35) Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Applications to the sciences (65Z05)
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Cites Work
- On the maximum principle preserving schemes for the generalized Allen-Cahn equation
- Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models
- A two phase field model for tracking vesicle-vesicle adhesion
- A phase field model for vesicle-substrate adhesion
- Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation
- Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches
- Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
- Unconditionally energy stable numerical schemes for phase-field vesicle membrane model
- The scalar auxiliary variable (SAV) approach for gradient flows
- A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
- Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model
- Decoupled energy stable schemes for phase-field vesicle membrane model
- Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models
- Analysis of a phase field Navier-Stokes vesicle-fluid interaction model
- Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
- Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy
- An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
- Axisymmetric Indentation of a Thin Incompressible Elastic Layer
- The Global Dynamics of Discrete Semilinear Parabolic Equations
- A diffuse-interface method for simulating two-phase flows of complex fluids
- Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
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