Optimal Operator preconditioning for weakly singular operator over 3D screens

نویسندگان

  • R. Hiptmair
  • RALF HIPTMAIR
  • CARLOS JEREZ-HANCKES
چکیده

In this supplement to [14], we propose a new Calderón-type preconditioner for the weakly singular integral operator for −∆ on screens in R. We introduce a modified hypersingular operator, which is the exact inverse of the weakly singular operator on the unit disk. It forms the foundation for dual-mesh-based operator preconditioning. Applied to low-order boundary element Galerkin discretizations, it achieves h-independent bounded condition numbers. Heuristic extensions to general screens even with non-smooth boundaries are discussed. Their good performance is confirmed by numerical tests.

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تاریخ انتشار 2017