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Title: Fully Nonlinear Equations with Applications to Grad Equations in Plasma Physics
Award ID(s):
1840314
NSF-PAR ID:
10401524
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Communications on Pure and Applied Mathematics
Volume:
76
Issue:
3
ISSN:
0010-3640
Page Range / eLocation ID:
604 to 615
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  2. Abstract We propose a uniform block-diagonal preconditioner for condensed $H$(div)-conforming hybridizable discontinuous Galerkin schemes for parameter-dependent saddle point problems, including the generalized Stokes equations and the linear elasticity equations. An optimal preconditioner is obtained for the stiffness matrix on the global velocity/displacement space via the auxiliary space preconditioning technique (Xu (1994) The Auxiliary Space Method and Optimal Multigrid Preconditioning Techniques for Unstructured Grids, vol. 56. International GAMM-Workshop on Multi-level Methods (Meisdorf), pp. 215–235). A spectrally equivalent approximation to the Schur complement on the element-wise constant pressure space is also constructed, and an explicit computable exact inverse is obtained via the Woodbury matrix identity. Finally, the numerical results verify the robustness of our proposed preconditioner with respect to model parameters and mesh size. 
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