کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4598821 | 1631107 | 2016 | 16 صفحه PDF | دانلود رایگان |
In this work we analyse the Steklov–Poincaré (or interface Schur complement) matrix arising in a domain decomposition method in the presence of anisotropy. Our problem is formulated such that three types of anisotropy are being considered: refinements with high aspect ratios, uniform refinements of a domain with high aspect ratio and anisotropic diffusion problems discretized on uniform meshes. Our analysis indicates a condition number of the interface Schur complement with an order ranging from O(1)O(1) to O(h−2)O(h−2). By relating this behaviour to an underlying scale of fractional Sobolev spaces, we propose optimal preconditioners which are spectrally equivalent to fractional matrix powers of a discrete interface Laplacian. Numerical experiments to validate the analysis are included; extensions to general domains and non-uniform meshes are also considered.
Journal: Linear Algebra and its Applications - Volume 488, 1 January 2016, Pages 168–183