chebyshev collocation spectral method Research Articles (Page 3)

In this paper we analyze a preconditioning technique for the solution of Chebyshev spectral collocation equations with Dirichlet boundary conditions. We obtain bounds on the eigenvalues for the Helmholtz equation. These eigenvalue bounds are obtained as a consequence of estimates on the field of values ${{(\tilde A_{N^2 } U,U)_{I_2 } } / {(\tilde Q_{N^2 } U,U)_{I_2 } }}$, where $\tilde A_{N^2 } $ is the weighted collocation matrix and $\tilde A_{N^2 } $ is the preconditioner. The preconditioner $\tilde Q_{N^2 } $ is robust in the sense that it provides bounds on the $H_{0,w}^1 $ condition number of $\tilde Q_{N^2 }^{ - 1} \tilde L_{N^2 } $ when $\tilde L_{N^2 } $ is the weighted collocation matrix associated with the general elliptic operator $Lu: = - \Delta u + a_1 u_x + a_2 u_y + a_0 u$.

Journal Article SPANWISE MODULATION OF STREAMWISE ROLLS IN ROTATING CHANNEL FLOW Get access THOMAS J. BRIDGES, THOMAS J. BRIDGES Department of Mathematics, University of SurreyGuildford, Surrey GU2 5XH Search for other works by this author on: Oxford Academic Google Scholar ALISON J. COOPER ALISON J. COOPER Mathematics Institute, University of WarwickCoventry CV4 7AL Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Mechanics and Applied Mathematics, Volume 48, Issue 2, May 1995, Pages 257–284, https://doi.org/10.1093/qjmam/48.2.257 Published: 01 May 1995 Article history Received: 12 January 1994 Revision received: 15 June 1994 Published: 01 May 1995

Four and six-element conforming domain decomposition techniques are developed for Chebyshev spectral collocation methods for Poisson problems in rectangular domains. The applicability of the methods is demonstrated on standard test problems.

Numerical methods for hypersonic boundary layer stability

Chebyshev spectral collocation methods for laminar flow through a channel contraction

The Chebyshev spectral collocation method for the Euler gas-dynamic equations is described. It is used with shock fitting to compute several two-dimensional, gas-dynamic flows. Examples include a shock-acoustic wave interaction, a shock/vortex interaction, and the classical blunt body problem. With shock fitting, the spectral method has a clear advantage over second order finite differences in that equivalent accuracy can be obtained with far fewer grid points.