Abstract
In this paper, we present a modification of the clustering procedure for the fast Boundary Element Method (BEM), based on hierarchical techniques for the matrix decomposition and Adaptive Cross Approximation (ACA). An initial segmentation of the surface elements is shown to be a reasonable tool to prevent problematic blocks which appear on surfaces with edges. It leads to significantly easier control of the Partial ACA algorithm and our numerical results show perfect convergence of all numerical quantities corresponding to the theory of BEM. In particular, third order convergence is reached for the gradient of the solution inside the domain.
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Notes
- 1.
Angle between the normal vectors to the triangles, see [8].
- 2.
Rjasanow, S. and Weißer, S.: Surface Segmentation (Version 1.0). Saarland University, Saarbrücken, Germany (2018). See https://github.com/s-weisser/surface-segmentation.
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Rjasanow, S., Weißer, S. (2019). ACA Improvement by Surface Segmentation. In: Apel, T., Langer, U., Meyer, A., Steinbach, O. (eds) Advanced Finite Element Methods with Applications. FEM 2017. Lecture Notes in Computational Science and Engineering, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-030-14244-5_14
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