A fourth-order compact implicit immersed interface method for 2D Poisson interface problems

DOI10.1016/j.camwa.2022.06.011OpenAlexW4283712252MaRDI QIDQ2159881

Miguel Uh Zapata, Reymundo Itzá Balam

Publication date: 2 August 2022

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2022.06.011

zbMATH Keywords

Poisson equationimmersed interface methodcompact schemeimplicit finite differencefourth-order accuracy

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (1)

A compact sixth-order implicit immersed interface method to solve 2D Poisson equations with discontinuities

Uses Software

• IIMPACK

Cites Work

• Unnamed Item
• Unnamed Item
• A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions
• A high-order immersed boundary method for acoustic wave scattering and low-Mach number flow-induced sound in complex geometries
• Multigrid method and fourth-order compact scheme for 2D Poisson equation with unequal mesh-size discretization
• A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem
• An interpolation matched interface and boundary method for elliptic interface problems
• Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D Poisson equation
• Immersed interface methods for moving interface problems
• A projection method-based model with the exact C-property for shallow-water flows over dry and irregular bottom using unstructured finite-volume technique
• A new method to deduce high-order compact difference schemes for two-dimensional Poisson equation
• A new weak Galerkin finite element method for elliptic interface problems
• High-order implicit finite difference schemes for the two-dimensional Poisson equation
• A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains
• An immersed boundary neural network for solving elliptic equations with singular forces on arbitrary domains
• A high order compact FD framework for elliptic BVPs involving singular sources, interfaces, and irregular domains
• A high-order immersed interface method free of derivative jump conditions for Poisson equations on irregular domains
• A new eighth-order implicit finite difference method to solve the three-dimensional Helmholtz equation
• A second-order boundary condition capturing method for solving the elliptic interface problems on irregular domains
• A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• A comparison of numerical models for one-dimensional Stefan problems
• Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
• High Order Compact Finite Difference Schemes for the Helmholtz Equation with Discontinuous Coefficients
• Simplified immersed interface methods for elliptic interface problems with straight interfaces
• The immersed boundary method
• High-order difference schemes for two-dimensional elliptic equations
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Convergence of the ghost fluid method for elliptic equations with interfaces
• Numerical Solution of Partial Differential Equations
• A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations
• Convergence analysis of the immersed interface method
• The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions
• High-order compact scheme finite difference discretization for Signorini's problem
• The Immersed Interface Method for Simulating Two-Fluid Flows
• Systematic Derivation of Jump Conditions for the Immersed Interface Method in Three-Dimensional Flow Simulation
• The Immersed Interface Method
• Higher-Order, Cartesian Grid Based Finite Difference Schemes for Elliptic Equations on Irregular Domains

This page was built for publication: A fourth-order compact implicit immersed interface method for 2D Poisson interface problems