Local Fourier Analysis of p-Multigrid for High-Order Finite Element Operators

Multigrid methods are popular for solving linear systems derived from discretizing PDEs. Local Fourier analysis (LFA) is a technique investigating and tuning multigrid methods. P-multigrid high-order or spectral finite element methods, especially on unstructured meshes. In this paper, we introduce LFAToolkit.jl, new Julia package LFA of LFAToolkit.jl analyzes preconditioning techniques arbitrary second order PDEs supports mixed Specifically, develop p-multigrid with second-order using discretizations examine the performance Jacobi Chebyshev smoothing two-grid schemes aggressive p-coarsening. A natural extension framework h-multigrid difference that can be represented in language elements. With extension, replicate previous work convenient extensible abstraction. Examples one, two, three dimensions presented to validate our Laplacian elasticity.