An optimization based domain decomposition method for partial differential equations. (English) Zbl 0941.65123
The authors present an optimization-based domain decomposition algorithm for solving boundary value problems. Finite element approximations to solutions of the optimality system are defined and analyzed. A parallelizable gradient method for the solution of the optimality system is studied.
Some of the potential good features of the domain decomposition algorithm discussed in the paper are: (i) different finite element discretizations based on different grid sizes and different degree polynomials may be used in each subdomain; (ii) problems with discontinuous media which lead to partial differential equations with discontinuous coefficients can be easily treated.
Results from some numerical experiments showing the good numerical properties of the proposed algorithm can be found. In their concluding remarks the authors declare that the method can be extended to nonlinear problems and that details concerning the development, analysis and implementation of such an extension is subject of a forthcoming paper.
Some of the potential good features of the domain decomposition algorithm discussed in the paper are: (i) different finite element discretizations based on different grid sizes and different degree polynomials may be used in each subdomain; (ii) problems with discontinuous media which lead to partial differential equations with discontinuous coefficients can be easily treated.
Results from some numerical experiments showing the good numerical properties of the proposed algorithm can be found. In their concluding remarks the authors declare that the method can be extended to nonlinear problems and that details concerning the development, analysis and implementation of such an extension is subject of a forthcoming paper.
Reviewer: K.Georgiev (Sofia)
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
| 65Y05 | Parallel numerical computation |
Keywords:
finite element methods; domain decomposition; optimization techniques; parallel computation; algorithm; gradient method; discontinuous coefficients; numerical experimentsReferences:
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