Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning

@article{Helsing2008CornerSF,
  title={Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning},
  author={Johan Helsing and Rikard Ojala},
  journal={J. Comput. Physics},
  year={2008},
  volume={227},
  pages={8820-8840}
}
We take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points. Use of non-standard integral equations, graded meshes, interpolatory quadrature, and compressed inverse preconditioning are techniques that are explored, developed, mixed, and tested on some familiar problems in materials science. The recursive compressed inverse… CONTINUE READING
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