An object-oriented framework for hp-adaptive discontinuous galerkin methods

dc.contributor.advisor Castillo, Paul E. Velazquez-Suarez, Esov S. College of Engineering en_US
dc.contributor.committee Ierkic, Henrick Mario
dc.contributor.committee Ramos, Rafael A.
dc.contributor.committee Steinberg, Lev
dc.contributor.department Department of Electrical and Computer Engineering en_US
dc.contributor.representative Alemar, Jose D. 2019-02-12T16:03:44Z 2019-02-12T16:03:44Z 2006
dc.description.abstract In this work, we consider second order elliptic problems arising in the modeling of single phase flows in porous media in 2D and in the analysis of transverse electromagnetic modes in wave guides using a discontinuous Galerkin (DG) method, the so-called Local Discontinuous Galerkin (LDG) method. We designed and developed an object oriented framework for performing DG computations on unstructured meshes that allows the use of arbitrary degree in the polynomial approximations and non conformal meshes with an arbitrary number of hanging nodes per edge. We present numerical studies of an automatic mesh adaptation technique and a semi-algebraic multilevel preconditioner for the LDG method. DG methods may be viewed as high-order extensions of the classical finite volume method. Since no inter-element continuity is imposed, they can be defined on very general meshes, including non-conforming meshes, making these methods suitable for h-adaptivity. Our adaptive algorithm starts with an initial, conformal spatial discretization of the domain where the numerical solution of the partial differential equation is obtained using the LDG method. In each step, the error of the solution is estimated and the mesh is modified successively by performing two local operations: refining a fraction of the cells where the estimated error is greater and agglomerating a fraction of the cells where the estimated error is smallest. This procedure is repeated until the solution reaches a desired accuracy. It has been recently shown that the spectral condition number of the stiffness matrix exhibits an asymptotic behavior of O(h?2) on structured and unstructured meshes, where h is the mesh size, making the use of effective preconditioners a practical requirement. We present a semi-algebraic multilevel preconditioner for the LDG method and show through several numerical experiments that its performance does not degrade as the number of unknowns augments. The performance of these techniques is explored on problems with high jumps in the coefficients, which is the typical scenario of problems arising in practical applications. en_US
dc.description.graduationSemester Fall en_US
dc.description.graduationYear 2006 en_US
dc.language.iso English en_US
dc.rights.holder (c) 2006 Esov S. Velazquez Suarez en_US
dc.rights.license All rights reserved en_US
dc.subject hp-Adaptive en_US
dc.subject Galerkin methods en_US
dc.title An object-oriented framework for hp-adaptive discontinuous galerkin methods en_US
dc.type Dissertation en_US
dspace.entity.type Publication Computing and Information Sciences and Engineering en_US Ph.D. en_US
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
200.83 MB
Adobe Portable Document Format