Spectral methods for hyperbolic initial boundary value problems on parallel computers

• Published in: Journal of computational and applied mathematics Vol. 134; no. 1; pp. 165 - 190
• Main Authors: Dutt, Pravir K., Bedekar, Smita
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2001; Elsevier
• Subjects: Domain decomposition methods; Energy estimates on multidomains; Error estimates for the analytic case; Exact sciences and technology; Exponential accuracy; Galerkin-Collocation method; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; p and h– p versions of FEM; Parallel pre-conditioners; Partial differential equations, boundary value problems; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Symmetric formulation; Well posedness of continuity boundary conditions; 65N35; Primary 65M06; 65MI5; Domain decomposition methods; Exponential accuracy; Well posedness of continuity boundary conditions; Parallel pre-conditioners; Energy estimates on multidomains; Error estimates for the analytic case; Symmetric formulation; p and h– p versions of FEM; 65M12; Galerkin-Collocation method; Energy analysis; Spectral method; Error estimation; Continuous; Initial value problem; Well posed problem; Parallel computer; Boundary condition; Finite element method; Accuracy; Boundary value problem; Hyperbolic equation; Galerkin method; Collocation method; Domain decomposition; Preconditioning; Symmetry

In this paper a parallel spectral algorithm is developed for hyperbolic initial boundary value problems in one space dimension. The Galerkin-Collocation method, which is spectrally accurate in both space and time, is parallelized by using domain decomposition. This procedure leads to a minimization...