A fast spectral element solver combining static condensation and multigrid techniques

作者：Haupt L; Stiller J^*; Nagel W E

来源：Journal of Computational Physics, 2013, 255: 384-395.

DOI：10.1016/j.jcp.2013.07.035

• Spectral element method
• Static condensation
• Multigrid method
• Elliptic equations

We propose a spectral element multigrid method for the two-dimensional Helmholtz equation discretized on regular grids. Combining p-multigrid with static condensation the method achieves nearly linear complexity with an order-independent convergence rate for solving the condensed equations. For smoothing we consider two groups of edge-based relaxation schemes, the best of which attains a multigrid convergence rate of rho approximate to 0.014 to 0.028. Numerical experiments have been carried out that demonstrate the robustness of the approach for orders up to 32 and a total of 10(9) degrees of freedom. In comparison with a fast finite difference solver, the latter is clearly outperformed already for errors of one percent or lower.

• 出版日期2013-12-15