Overlapping domain decomposition based exponential time differencing methods for semilinear parabolic equations

DOI10.1007/s10543-020-00817-0zbMath1460.65115OpenAlexW3036011591WikidataQ115604950 ScholiaQ115604950MaRDI QIDQ2660594

Thi-Thao-Phuong Hoang, Lili Ju, Xiao Li

Publication date: 31 March 2021

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-020-00817-0

zbMATH Keywords

convergence analysissemilinear parabolic equationoverlapping domain decompositionwaveform relaxationparallel Schwarz iterationlocalized exponential time differencing

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Parallel numerical computation (65Y05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Semilinear parabolic equations (35K58)

Related Items (4)

Fully discrete error analysis of first‐order low regularity integrators for the Allen‐Cahn equation ⋮ Efficient Exponential Integrator Finite Element Method for Semilinear Parabolic Equations ⋮ Low regularity integrators for semilinear parabolic equations with maximum bound principles ⋮ Localized Exponential Time DifferencingMethod for Shallow Water Equations: Algorithms and Numerical Study

Uses Software

• SERK2

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exponential time differencing for stiff systems
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• High order explicit methods for parabolic equations
• Overlapping localized exponential time differencing methods for diffusion problems
• Nonoverlapping localized exponential time differencing methods for diffusion problems
• Fast explicit integration factor methods for semilinear parabolic equations
• Characteristic exponents and diagonally dominant linear differential systems
• Fast high-order compact exponential time differencing Runge-Kutta methods for second-order semilinear parabolic equations
• Strong Stability-Preserving High-Order Time Discretization Methods
• Time-Dependent Problems and Difference Methods
• Exponential integrators
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
• Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
• Phase transitions and generalized motion by mean curvature
• Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation
• Analytical inversion of symmetric tridiagonal matrices
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Strong Stability Preserving Integrating Factor Runge--Kutta Methods
• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
• Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection
• Thin film epitaxy with or without slope selection
• SERK2v2: A new second‐order stabilized explicit Runge‐Kutta method for stiff problems
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

This page was built for publication: Overlapping domain decomposition based exponential time differencing methods for semilinear parabolic equations