Towards Domain Decomposition for Nonlocal Problems Export

@article{citeulike:5839177, abstract = {In this paper we present the first results on substructuring methods for nonlocal operators, specifically, an instance of the nonlocal p-Laplace operator. We present a nonlocal variational formulation of this operator, proving a nonlocal Poincar\'{e} inequality and upper bound to establish a spectral equivalence. We then introduce a nonlocal two-domain variational formulation utilizing nonlocal transmission conditions, and prove equivalence with the single-domain formulation. A nonlocal Schur complement is introduced. We establish condition number bounds for the nonlocal stiffness and Schur complement matrices. Supporting numerical experiments demonstrating the conditioning of the nonlocal single- and two-domain problems are presented.}, archivePrefix = {arXiv}, author = {Aksoylu, Burak and Parks, Michael L.}, citeulike-article-id = {5839177}, citeulike-linkout-0 = {http://arxiv.org/abs/0909.4504}, citeulike-linkout-1 = {http://arxiv.org/pdf/0909.4504}, day = {24}, eprint = {0909.4504}, keywords = {general-math}, month = {Sep}, posted-at = {2009-09-25 09:23:06}, priority = {2}, title = {Towards Domain Decomposition for Nonlocal Problems}, url = {http://arxiv.org/abs/0909.4504}, year = {2009} }

TY - JOUR ID - citeulike:5839177 L3 - citeulike-article-id:5839177 N2 - In this paper we present the first results on substructuring methods for nonlocal operators, specifically, an instance of the nonlocal p-Laplace operator. We present a nonlocal variational formulation of this operator, proving a nonlocal Poincar\'{e} inequality and upper bound to establish a spectral equivalence. We then introduce a nonlocal two-domain variational formulation utilizing nonlocal transmission conditions, and prove equivalence with the single-domain formulation. A nonlocal Schur complement is introduced. We establish condition number bounds for the nonlocal stiffness and Schur complement matrices. Supporting numerical experiments demonstrating the conditioning of the nonlocal single- and two-domain problems are presented. TI - Towards Domain Decomposition for Nonlocal Problems KW - general-math AU - Aksoylu, Burak AU - Parks, Michael PY - 2009/Sep/24/ UR - http://arxiv.org/abs/0909.4504 ER -