Open AccessSolving anisotropic heat equations by exponential shift-and-invert and polynomial Krylov subspace methods
Author(s) -
Mike A. Botchev
Publication year - 2022
Publication title -
preprint/preprinty ipm im. m.v. keldyša
Language(s) - English
Resource type - Journals
eISSN - 2071-2901
pISSN - 2071-2898
DOI - 10.20948/prepr-2022-4
Subject(s) - krylov subspace , mathematics , multigrid method , polynomial , discretization , exponential function , eigenvalues and eigenvectors , convergence (economics) , algebraic equation , mathematical analysis , linear system , partial differential equation , physics , quantum mechanics , nonlinear system , economics , economic growth
We assess performance of the exponential Krylov subspace methods for solving a class of parabolic problems with a strong anisotropy in coefficients. Different boundary conditions are considered, which have a direct impact on the smallest eigenvalue of the discretized operator and, hence, on the convergence behavior of the exponential Krylov subspace solvers. Restarted polynomial Krylov subspace methods and shift-and-invert Krylov subspace methods combined with algebraic multigrid are considered.