Multigrid methods for cubic spline solution of two point (and 2D) boundary value problems

DOI10.1016/j.apnum.2014.04.004zbMath1336.65120OpenAlexW1984045033MaRDI QIDQ268831

Vincenzo Pennati, Marco Donatelli, Matteo Molteni, Stefano Serra Capizzano

Publication date: 15 April 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2014.04.004

zbMATH Keywords

finite elementsnumerical examplesnumerical experimentscubic splinesmultigrid methodsspectral analysisToeplitz matricessymbolsecond-order two point boundary value problem

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (3)

Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem ⋮ Optimizing a multigrid Runge-Kutta smoother for variable-coefficient convection-diffusion equations ⋮ Spectral Analysis and Spectral Symbol of $d$-variate $\mathbb Q_{\boldsymbol p}$ Lagrangian FEM Stiffness Matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A \(V\)-cycle multigrid for multilevel matrix algebras: proof of optimality
• Higher order method for singular boundary-value problems by using spline function
• Spline finite difference methods for singular two point boundary value problems
• A new fourth-order cubic spline method for second-order nonlinear two- point boundary-value problems
• Multi-iterative methods
• Multigrid methods with web-splines
• Convergence analysis of two-grid methods for elliptic Toeplitz and PDEs matrix-sequences
• Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
• A unifying approach to some old and new theorems on distribution and clustering
• Preconditioning cubic spline collocation discretizations of elliptic equations
• Cubic spline solution of singularly perturbed boundary value problems with significant first derivatives
• Multigrid methods for block Toeplitz matrices with small size blocks
• An algebraic generalization of local Fourier analysis for grid transfer operators in multigrid based on Toeplitz matrices
• Asymptotic Results on the Spectra of Block Toeplitz Preconditioned Matrices
• Iterative Solution Methods
• V-cycle Optimal Convergence for Certain (Multilevel) Structured Linear Systems
• Trivariate spline approximations of 3D Navier-Stokes equations
• A note on the spectral distribution of toeplitz matrices
• Spline solution of non-linear singular boundary value problems
• Distribution results on the algebra generated by Toeplitz sequences: A finite-dimensional approach

This page was built for publication: Multigrid methods for cubic spline solution of two point (and 2D) boundary value problems