A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

DOI10.1016/j.jcp.2017.11.007zbMath1380.65328OpenAlexW2767765402MaRDI QIDQ1700874

Alice Raeli, Angelo Iollo, Michel Bergmann

Publication date: 22 February 2018

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

Full work available at URL: https://hal.inria.fr/hal-01662050/file/RaeliBergmannIollo%20%281%29.pdf

zbMATH Keywords

quadtreefinite difference methodoctreehierarchical Cartesian gridvariable coefficient Poisson equation

Mathematics Subject Classification ID

PDEs with low regular coefficients and/or low regular data (35R05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (12)

A reconstruction-based Chebyshev-collocation method for the Poisson equation: an accurate treatment of the Gibbs-Wilbraham phenomenon on irregular interfaces ⋮ Second Order ADER Scheme for Unsteady Advection-Diffusion on Moving Overset Grids with a Compact Transmission Condition ⋮ Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface ⋮ ADER scheme for incompressible Navier-Stokes equations on overset grids with a compact transmission condition ⋮ Arbitrary-Lagrangian-Eulerian finite volume IMEX schemes for the incompressible Navier-Stokes equations on evolving chimera meshes ⋮ A RBF-based technique for 3D convection-diffusion-reaction problems in an anisotropic inhomogeneous medium ⋮ A parallel multilevel domain decomposition method for source identification problems governed by elliptic equations ⋮ A novel least squares finite volume scheme for discontinuous diffusion on unstructured meshes ⋮ A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems ⋮ An Asymptotic-Preserving All-Speed Scheme for Fluid Dynamics and Nonlinear Elasticity ⋮ A novel B-spline method to analyze convection-diffusion-reaction problems in anisotropic inhomogeneous medium ⋮ An Eulerian finite-volume approach of fluid-structure interaction problems on quadtree meshes

Uses Software

• Gerris
• p4est

Cites Work

• Parallel level-set methods on adaptive tree-based grids
• Level-set, penalization and Cartesian meshes: A paradigm for inverse problems and optimal design
• A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids
• Spatially adaptive techniques for level set methods and incompressible flow
• A penalization method to take into account obstacles in incompressible viscous flows
• A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
• Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries.
• A substructuring method for phase change modelling in hybrid media
• An octree-based solver for the incompressible Navier-Stokes equations with enhanced stability and low dissipation
• Solving elliptic problems with discontinuities on irregular domains -- the Voronoi interface method
• Boundary layer for a penalization method for viscous incompressible flow
• Algorithms and data structures for massively parallel generic adaptive finite element codes
• p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
• An Adaptive Mesh Projection Method for Viscous Incompressible Flow
• Simple and Efficient Traversal Methods for Quadtrees and Octrees

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