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Fast solvers of integral and pseudodifferential equations on closed curves

Authors:	J Saranen G Vainikko

Institution:	University of Oulu, Department of Mathematical Sciences, 90570 Oulu Finland ; Institut of Mathematics, Helsinki University of Technology, 02150 Espoo, Finland

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 ${\O}(N\log N)$ arithmetical operations.

Keywords:	Boundary integral equation trigonometric Galerkin method fast algorithms

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