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Mathematics of Computation

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Fast solvers of integral and pseudodifferential equations on closed curves

Authors: J. Saranen and G. Vainikko
Journal: Math. Comp. 67 (1998), 1473-1491
MSC (1991): Primary 65R20; Secondary 65N35, 45E10
MathSciNet review: 1489973
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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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Additional Information

J. Saranen
Affiliation: University of Oulu, Department of Mathematical Sciences, 90570 Oulu Finland

G. Vainikko
Affiliation: Institut of Mathematics, Helsinki University of Technology, 02150 Espoo, Finland

Keywords: Boundary integral equation, trigonometric Galerkin method, fast algorithms
Received by editor(s): January 11, 1995
Received by editor(s) in revised form: July 22, 1996
Article copyright: © Copyright 1998 American Mathematical Society