%0 Conference Paper %1 citeulike:13617679 %A Bjørstad, Petter E. %A Widlund, Olof B. %B Elliptic Problem Solvers II %C New York %D 1984 %E Birkhoff, Garrett %E Schoenstadt, Arthur L. %I Academic Press %K 65n55-pdes-bvps-multigrid-methods-domain-decomposition 65n30-pdes-bvps-finite-elements 65-06-numerical-analysis-proceedings-conferences-collections-etc %R 10.1016/B978-0-12-100560-3.50023-8 %T Solving Elliptic Problems on Regions Partitioned into Substructures %U http://dx.doi.org/10.1016/B978-0-12-100560-3.50023-8 %X This chapter discusses the iterative methods for the solution of finite element approximations for elliptic equations defined on regions regarded as unions of subregions. In the design of methods for which the interaction between subproblems, that is, discrete elliptic problems on the subregions, is computed by a conjugate gradient method whereas the subproblems are solved by a direct method. This approach differs from the standard one in industry in which a direct method is used throughout the entire solution process. The whole problem is reduced to finding accurate values of the solution on the interfaces, that is, the curves or surfaces that separate the subregions. The chapter discusses the case of a plane region cut into two pieces. The region is equally well being subdivided into several subregions and the ideas can also be applied recursively. %@ 0121005607

@inproceedings{citeulike:13617679, abstract = {{This chapter discusses the iterative methods for the solution of finite element approximations for elliptic equations defined on regions regarded as unions of subregions. In the design of methods for which the interaction between subproblems, that is, discrete elliptic problems on the subregions, is computed by a conjugate gradient method whereas the subproblems are solved by a direct method. This approach differs from the standard one in industry in which a direct method is used throughout the entire solution process. The whole problem is reduced to finding accurate values of the solution on the interfaces, that is, the curves or surfaces that separate the subregions. The chapter discusses the case of a plane region cut into two pieces. The region is equally well being subdivided into several subregions and the ideas can also be applied recursively.}}, added-at = {2017-06-29T07:13:07.000+0200}, address = {New York}, author = {Bj{\o}rstad, Petter E. and Widlund, Olof B.}, biburl = {https://www.bibsonomy.org/bibtex/223a824af90ccf5575707d339c19e8bc2/gdmcbain}, booktitle = {Elliptic Problem Solvers {II}}, citeulike-article-id = {13617679}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/B978-0-12-100560-3.50023-8}, doi = {10.1016/B978-0-12-100560-3.50023-8}, editor = {Birkhoff, Garrett and Schoenstadt, Arthur L.}, interhash = {0a1529e8bc541ce919e7a20474b3b93e}, intrahash = {23a824af90ccf5575707d339c19e8bc2}, isbn = {0121005607}, keywords = {65n55-pdes-bvps-multigrid-methods-domain-decomposition 65n30-pdes-bvps-finite-elements 65-06-numerical-analysis-proceedings-conferences-collections-etc}, location = {Naval Postgraduate School, Monterey, Calif.}, posted-at = {2015-05-18 00:41:17}, priority = {2}, publisher = {Academic Press}, timestamp = {2019-04-03T06:51:55.000+0200}, title = {{Solving Elliptic Problems on Regions Partitioned into Substructures}}, url = {http://dx.doi.org/10.1016/B978-0-12-100560-3.50023-8}, year = 1984 }