Efficient high-order immersed interface methods for heat equations with interfaces

DOI10.1007/s10483-014-1851-6zbMath1298.65124OpenAlexW1490986592MaRDI QIDQ468580

Zhou-shun Zheng, Jian-kang Liu

Publication date: 7 November 2014

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10483-014-1851-6

zbMATH Keywords

Richardson extrapolation methodimmersed interface method (IIM)alternative direction implicit (ADI) schemehigh-order compact (HOC) scheme

Mathematics Subject Classification ID

Heat equation (35K05) 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)

Related Items (7)

A hybrid semi-Lagrangian cut cell method for advection-diffusion problems with Robin boundary conditions in moving domains ⋮ Immersed boundary smooth extension: a high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods ⋮ Very high-order accurate polygonal mesh finite volume scheme for conjugate heat transfer problems with curved interfaces and imperfect contacts ⋮ Immersed boundary smooth extension (IBSE): a high-order method for solving incompressible flows in arbitrary smooth domains ⋮ High‐order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing ⋮ Fully discrete least-squares spectral element method for parabolic interface problems ⋮ A dimension splitting method for time dependent PDEs on irregular domains

Uses Software

• IIMPACK

Cites Work

• Unnamed Item
• Mathematical model and computer simulation of three dimensional thin film elliptic interface problems
• A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions
• On the accuracy of finite difference methods for elliptic problems with interfaces.
• The immersed interface method for two-dimensional heat-diffusion equations with singular own sources
• Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
• An interpolation matched interface and boundary method for elliptic interface problems
• A second order virtual node method for elliptic problems with interfaces and irregular domains
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• A three-dimensional computational method for blood flow in the heart. I: Immersed elastic fibers in a viscous incompressible fluid
• Theoretical and numerical analysis on a thermoelastic system with discontinuities
• Computational methods for continuum models of platelet aggregation
• A note on immersed interface method for three-dimensional elliptic equations
• High order ADI method for solving unsteady convection-diffusion problems
• An immersed boundary method with direct forcing for the simulation of particulate flows
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• Flow patterns around heart valves: A numerical method
• Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• A Fast Iterative Algorithm for Elliptic Interface Problems
• Modeling elastic shells immersed in fluid
• The Immersed Interface/Multigrid Methods for Interface Problems
• Convergence analysis of the immersed interface method
• The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions
• The Immersed Interface Method
• The immersed interface method for the Navier-Stokes equations with singular forces

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