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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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 | References | Similar Articles | Additional Information

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.


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Additional Information

J. Saranen
Affiliation: University of Oulu, Department of Mathematical Sciences, 90570 Oulu Finland
Email: jsaranen@cc.oulu.fi

G. Vainikko
Affiliation: Institut of Mathematics, Helsinki University of Technology, 02150 Espoo, Finland
Email: gennadi.vainikko@hut.fi

DOI: http://dx.doi.org/10.1090/S0025-5718-98-00997-1
PII: S 0025-5718(98)00997-1
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