Preconditioning mixed finite elements for tide models.
| dc.contributor.advisor | Kirby, Robert C. | |
| dc.creator | Kernell, Oliver Tate, 1990- | |
| dc.creator.orcid | 0000-0003-0816-7027 | |
| dc.date.accessioned | 2019-12-04T16:49:17Z | |
| dc.date.available | 2019-12-04T16:49:17Z | |
| dc.date.created | 2019-08 | |
| dc.date.issued | 2019-07-24 | |
| dc.date.submitted | August 2019 | |
| dc.date.updated | 2019-12-04T16:49:17Z | |
| dc.description.abstract | We describe finite element methods for the linearized rotating shallow water equations which govern tides. Symplectic Euler and Crank-Nicolson time-stepping strategies have good energy preservation properties, which is desirable for tide modeling, but require careful treatment of linear algebra. For symplectic Euler, we have to invert the Raviart-Thomas element mass matrix at every time step. Thus we give estimates for the eigenvalues of these mass matrices. Crank-Nicolson, being fully implicit, has a more complicated system of equations which requires inverting the entire system. For this, we present an effective block preconditioner using parameter-weighted norms in H(div). We give results that are nearly dependent of the given constants. Finally, we provide numerical results that confirm this theory. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | https://hdl.handle.net/2104/10780 | |
| dc.language.iso | en | |
| dc.rights.accessrights | Worldwide access | |
| dc.subject | Finite elements. Mixed methods. Preconditioning. Tide model. Rotating shallow water equations. | |
| dc.title | Preconditioning mixed finite elements for tide models. | |
| dc.type | Thesis | |
| dc.type.material | text | |
| thesis.degree.department | Baylor University. Dept. of Mathematics. | |
| thesis.degree.grantor | Baylor University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Ph.D. |
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