A correction function-based kernel-free boundary integral method for elliptic PDEs with implicitly defined interfaces

DOI10.1016/j.jcp.2023.112545arXiv2309.05965OpenAlexW4387953150MaRDI QIDQ6202130

Wenjun Ying, Han Zhou

Publication date: 21 February 2024

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2309.05965

zbMATH Keywords

jump conditionselliptic PDEscompact finite difference methodinterface problemsCartesian grid-based method

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)

Cites Work

• A kernel-free boundary integral method for implicitly defined surfaces
• A correction function method for Poisson problems with interface jump conditions
• A finite element method for interface problems in domains with smooth boundaries and interfaces
• A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions
• A numerical method for solving variable coefficient elliptic equation with interfaces
• A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
• Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
• An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane
• Boundary integral solutions of coupled Stokes and Darcy flows
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Numerical analysis of blood flow in the heart
• A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
• Numerical solution of the incompressible Navier-Stokes equations
• A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow.
• A partial differential equation approach to multidimensional extrapolation.
• New Cartesian grid methods for interface problems using the finite element formulation
• Immersed boundary smooth extension (IBSE): a high-order method for solving incompressible flows in arbitrary smooth domains
• High order solution of Poisson problems with piecewise constant coefficients and interface jumps
• The ghost fluid method for deflagration and detonation discontinuities
• Three-dimensional elliptic solvers for interface problems and applications
• Boundary integral equations as applied to an oscillating bubble near a fluid-fluid interface
• A fast Poisson solver for complex geometries
• A boundary condition capturing method for Poisson's equation on irregular domains
• Partition of unity extension of functions on complex domains
• An immersed finite element method for elliptic interface problems in three dimensions
• A fourth-order kernel-free boundary integral method for implicitly defined surfaces in three space dimensions
• Imposing jump conditions on nonconforming interfaces for the correction function method: a least squares approach
• An augmented matched interface and boundary (MIB) method for solving elliptic interface problem
• Matched interface and boundary method for elasticity interface problems
• Immersed boundary smooth extension: a high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods
• A kernel-free boundary integral method for elliptic boundary value problems
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• The finite element method for elliptic equations with discontinuous coefficients
• Flow patterns around heart valves: A numerical method
• A Method for Computing Nearly Singular Integrals
• A discontinuous Galerkin method for elliptic interface problems with application to electroporation
• The immersed boundary method
• Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
• A Fast Adaptive Multipole Algorithm for Particle Simulations
• An Integral Equation Approach to the Incompressible Navier--Stokes Equations in Two Dimensions
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
• A Fast Iterative Algorithm for Elliptic Interface Problems
• A Jump Condition Capturing Finite Difference Scheme for Elliptic Interface Problems
• A Grid-Based Boundary Integral Method for Elliptic Problems in Three Dimensions
• A fast marching level set method for monotonically advancing fronts.
• A finite element method for crack growth without remeshing
• A Cartesian Grid-Based Boundary Integral Method for an Elliptic Interface Problem on Closely Packed Cells
• Fast High Order Accurate Solution of Laplace’s Equation on Irregular Regions
• A Kernel-Free Boundary Integral Method for Variable Coefficients Elliptic PDEs
• The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions
• Numerical Solution of the Navier-Stokes Equations
• A fast algorithm for particle simulations
• The immersed interface method for the Navier-Stokes equations with singular forces
• A boundary condition capturing method for incompressible flame discontinuities.

This page was built for publication: A correction function-based kernel-free boundary integral method for elliptic PDEs with implicitly defined interfaces