Fast solvers of integral and pseudodifferential equations on closed curves

Saranen, J.; Vainikko, G.

doi:10.1090/S0025-5718-98-00997-1

Fast solvers of integral and pseudodifferential equations on closed curves
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by J. Saranen and G. Vainikko PDF

Math. Comp. 67 (1998), 1473-1491 Request permission

Abstract:

On the basis of a fully discrete trigonometric Galerkin method and two grid iterations we propose solvers for integral and pseudodifferential equations on closed curves which solve the problem with an optimal convergence order $\|u_N-u\|_\lambda \leq c_{\lambda ,\mu }N^{\lambda -\mu }\|u\|_\mu$, $\lambda \leq \mu$ (Sobolev norms of periodic functions) in $\mathrm {O}(N\log N)$ arithmetical operations.

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