A fast direct algorithm for implementing a high-order finite element method on rectangles as applied to boundary value problems for the Poisson equation

DOI10.1134/S1064562417020089zbMath1371.65123OpenAlexW2592641931MaRDI QIDQ2399511

I. A. Zlotnik, Alexander Zlotnik

Publication date: 24 August 2017

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562417020089

zbMATH Keywords

algorithmfinite element methodeigenvalue problemfast discrete Fourier transformPoisson-type equations

Mathematics Subject Classification ID

Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for discrete and fast Fourier transforms (65T50) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (3)

Fast Fourier solvers for the tensor product high-order FEM for a Poisson type equation ⋮ A ``converse stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation ⋮ Numerical simulation of gravity anomaly based on the unstructured element grid and finite element method

Cites Work

• Matrix decomposition algorithms for elliptic boundary value problems: A survey
• Matrix decomposition algorithms for the \(C^{0}\)-quadratic finite element Galerkin method
• Finite element method with discrete transparent boundary conditions for the time-dependent 1D Schrödinger equation
• The Methods of Cyclic Reduction, Fourier Analysis and the FACR Algorithm for the Discrete Solution of Poisson’s Equation on a Rectangle
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