Some Domain Decomposition Algorithms for Elliptic Problems
Some Domain Decomposition Algorithms for Elliptic Problems
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In our eReader you can find the full English version of the book. Read Some Domain Decomposition Algorithms for Elliptic Problems Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Some Domain Decomposition Algorithms for Elliptic Problems
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Our finite element space is represented a* the sum of N+1 subspaces y' = Vo' + r, " + ... + V/^ .
The first subspace ^o" is equal to V^^, the same coarse global space of contin- uous, p. Ecewise Lnear functions on the coarse mesh defined by the substruc tures Q, that we introduced in Section 2. The other subspaces are related to 10 the subdomains, in the same way a* in a traditional Schwarz algorithm, i. E. Yh _ V'» p)^^(fi^). The computation of the projection of an arbitrary func- tion onto th...e subspace V^ involves the solution of a standard finite element linear system of algebraic equations which is on the order of N. This coarse, global approximation of the elliptic equation is of the same type as the local problems associated with subdomadns. The only reaJ difference between the problem related to the first subspace and the others lies in the way that the right hatnd side of the Linear system is generated as weighted averages with weights determined by the basis functions associated with the coarse mesh.
What to read after Some Domain Decomposition Algorithms for Elliptic Problems?
You can find similar books in the "Read Also" column, or choose other free books by Maksymilian Dryja to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Our finite element space is represented a* the sum of N+1 subspaces y' = Vo' + r, " + ... + V/^ .
The first subspace ^o" is equal to V^^, the same coarse global space of contin- uous, p. Ecewise Lnear functions on the coarse mesh defined by the substruc tures Q, that we introduced in Section 2. The other subspaces are related to 10 the subdomains, in the same way a* in a traditional Schwarz algorithm, i. E. Yh _ V'» p)^^(fi^). The computation of the projection of an arbitrary func- tion onto th...e subspace V^ involves the solution of a standard finite element linear system of algebraic equations which is on the order of N. This coarse, global approximation of the elliptic equation is of the same type as the local problems associated with subdomadns. The only reaJ difference between the problem related to the first subspace and the others lies in the way that the right hatnd side of the Linear system is generated as weighted averages with weights determined by the basis functions associated with the coarse mesh.
What to read after Some Domain Decomposition Algorithms for Elliptic Problems?
You can find similar books in the "Read Also" column, or choose other free books by Maksymilian Dryja to read onlineMoreLess
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