Lattice Green’s Functions for High-Order Finite Difference Stencils
DOI10.1137/23m1573872arXiv2309.13503MaRDI QIDQ6184511
James Gabbard, Wim M. van Rees
Publication date: 25 January 2024
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2309.13503
Finite difference methods applied to problems in fluid mechanics (76M20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Green's functions for elliptic equations (35J08) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)
Cites Work
- Unnamed Item
- A high order solver for the unbounded Poisson equation
- A parallel fast multipole method for elliptic difference equations
- Fast and accurate numerical methods for solving elliptic difference equations defined on lattices
- 70+ years of the Watson integrals
- Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region
- Fast immersed interface Poisson solver for 3D unbounded problems around arbitrary geometries
- A regularization method for solving the Poisson equation for mixed unbounded-periodic domains
- Non-singular Green's functions for the unbounded Poisson equation in one, two and three dimensions
- Computation of volume potentials on structured grids with the method of local corrections
- A fast multi-resolution lattice Green's function method for elliptic difference equations
- A method of immersed layers on Cartesian grids, with application to incompressible flows
- A Fourier-based elliptic solver for vortical flows with periodic and unbounded directions
- Compact finite difference schemes of arbitrary order for the Poisson equation in arbitrary dimensions
- A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains
- Analytic inversion of the five-point Poisson operator
- An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies
- FFT, FMM, or Multigrid? A comparative Study of State-Of-the-Art Poisson Solvers for Uniform and Nonuniform Grids in the Unit Cube
- Asymptotic expansions of lattice Green's functions
- Planar potential flow on Cartesian grids
- High-performance symbolic-numerics via multiple dispatch
- Nemo/Hecke
- Simplified Impurity Calculation
- FLUPS: A Fourier-Based Library of Unbounded Poisson Solvers
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