Neumann-Neumann type domain decomposition of elliptic problems on metric graphs
In this paper we develop a Neumann-Neumann type domain decomposition method for elliptic problems on metric graphs. We describe the iteration in the continuous and discrete setting and rewrite the latter as a preconditioner for the Schur complement system. Then we formulate the discrete iteration as...
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| creator | Kovács, Mihály Vághy, Mihály András |
| description | In this paper we develop a Neumann-Neumann type domain decomposition method
for elliptic problems on metric graphs. We describe the iteration in the
continuous and discrete setting and rewrite the latter as a preconditioner for
the Schur complement system. Then we formulate the discrete iteration as an
abstract additive Schwarz iteration and prove that it convergences to the
finite element solution with a rate that is independent of the finite element
mesh size. We show that the condition number of the Schur complement is also
independent of the finite element mesh size. We provide an implementation and
test it on various examples of interest and compare it to other
preconditioners. |
| doi_str_mv | 10.48550/arxiv.2402.05707 |
| format | Article |
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for elliptic problems on metric graphs. We describe the iteration in the
continuous and discrete setting and rewrite the latter as a preconditioner for
the Schur complement system. Then we formulate the discrete iteration as an
abstract additive Schwarz iteration and prove that it convergences to the
finite element solution with a rate that is independent of the finite element
mesh size. We show that the condition number of the Schur complement is also
independent of the finite element mesh size. We provide an implementation and
test it on various examples of interest and compare it to other
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for elliptic problems on metric graphs. We describe the iteration in the
continuous and discrete setting and rewrite the latter as a preconditioner for
the Schur complement system. Then we formulate the discrete iteration as an
abstract additive Schwarz iteration and prove that it convergences to the
finite element solution with a rate that is independent of the finite element
mesh size. We show that the condition number of the Schur complement is also
independent of the finite element mesh size. We provide an implementation and
test it on various examples of interest and compare it to other
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for elliptic problems on metric graphs. We describe the iteration in the
continuous and discrete setting and rewrite the latter as a preconditioner for
the Schur complement system. Then we formulate the discrete iteration as an
abstract additive Schwarz iteration and prove that it convergences to the
finite element solution with a rate that is independent of the finite element
mesh size. We show that the condition number of the Schur complement is also
independent of the finite element mesh size. We provide an implementation and
test it on various examples of interest and compare it to other
preconditioners.</abstract><doi>10.48550/arxiv.2402.05707</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | Neumann-Neumann type domain decomposition of elliptic problems on metric graphs |
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