Journal
NUMERISCHE MATHEMATIK
Volume 141, Issue 4, Pages 967-1008Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00211-018-1011-1
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Funding
- Austrian Science Fund (FWF) [P27005, F65]
- CONICYT through FONDECYT project [P11170050]
- Austrian Science Fund (FWF) [P27005] Funding Source: Austrian Science Fund (FWF)
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We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as well as the local mesh-refinement. Besides convergence with optimal algebraic rates, we also prove almost optimal computational complexity. In particular, we provide an additive Schwarz preconditioner which can be computed in linear complexity and which is optimal in the sense that the condition numbers of the preconditioned systems are uniformly bounded. As model problem serves the 2D or 3D Laplace operator and the associated weakly-singular integral equation with energy space (H) over tilde (-1/2)(Gamma). The main results also hold for the hyper-singular integral equation with energy space H-1/2(Gamma).
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