Solving of multi-connected curvilinear boundary value problems by the fast PIES. (English) Zbl 1507.65282
Summary: This paper presents the fast parametric integral equations system (PIES) in solving two-dimensional (2D) multi-connected curvilinear potential boundary value problems. The fast PIES is a combination of the fast multipole technique with a modified binary tree and original PIES. It was successfully employed for exploring the efficiency of the method applied in modelling and solving single-connected 2D potential problems. The fast PIES allows reducing the time of numerical computations (CPU time), as well as RAM utilization. However, application to the multi-connected problems requires appropriate changes in the fast multipole computations due to the small distance between some segments in internal parts of the boundary. The method is demonstrated with the examples of curvilinear potential problems dealing with perforated plates (plates with many circular holes).
MSC:
| 65N99 | Numerical methods for partial differential equations, boundary value problems |
Software:
pi-BEMReferences:
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