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Domain decomposition finite element/finite difference method for the conductivity reconstruction in a hyperbolic equation

Larisa Beilina (Institutionen för matematiska vetenskaper, matematik)
Communications in Nonlinear Science and Numerical Simulation (1007-5704). Vol. 37 (2016), p. 222-237.
[Artikel, refereegranskad vetenskaplig]

We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the computational domain: finite difference method is used on the structured part of the computational domain and finite elements on the unstructured part of the domain. Explicit discretizations for both methods are constructed such that the finite element and the finite difference schemes coincide on the common structured overlapping layer between computational subdomains. Then the resulting approach can be considered as a pure finite element scheme which avoids instabilities at the interfaces. We derive an energy estimate for the underlying hyperbolic equation with absorbing boundary conditions and illustrate efficiency of the domain decomposition method on the reconstruction of the conductivity function in three dimensions.

Nyckelord: Domain decomposition method, Hyperbolic equation, Energy estimate, Finite element method, Finite, Mathematics, Mechanics, Physics



Denna post skapades 2016-03-29. Senast ändrad 2016-05-19.
CPL Pubid: 233765

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik
Fysik

Chalmers infrastruktur