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The Dpg-Star Method, Leszek Demkowicz, Jay Gopalakrishnan, Brendan Keith
The Dpg-Star Method, Leszek Demkowicz, Jay Gopalakrishnan, Brendan Keith
Portland Institute for Computational Science Publications
This article introduces the DPG-star (from now on, denoted DPG*) finite element method. It is a method that is in some sense dual to the discontinuous Petrov– Galerkin (DPG) method. The DPG methodology can be viewed as a means to solve an overdetermined discretization of a boundary value problem. In the same vein, the DPG* methodology is a means to solve an underdetermined discretization. These two viewpoints are developed by embedding the same operator equation into two different saddle-point problems. The analyses of the two problems have many common elements. Comparison to othermethods in the literature round out the newly …
Mathematical Modeling Of Corona Virus In The United Arab Emirates, Alya Saif Ahmad Alshehhi
Mathematical Modeling Of Corona Virus In The United Arab Emirates, Alya Saif Ahmad Alshehhi
Theses
The Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is a viral in-fectious disease that can be transmitted to humans through interaction with infected ani-mals or humans. The Middle East respiratory syndrome (MERS) is still one of the main public health concerns in the Gulf region including United Arab Emirates. The fact that diseases have been imported into other parts of the world show the possibility of has a MERS pandemic. In this work, we are aiming to study a mathematical model of the MERS transmission among the UAE population and camels. The goal is to determine what are the paths of …
A Spacetime Dpg Method For The Wave Equation In Multiple Dimensions, Jay Gopalakrishnan, Paulina Sepulveda
A Spacetime Dpg Method For The Wave Equation In Multiple Dimensions, Jay Gopalakrishnan, Paulina Sepulveda
Portland Institute for Computational Science Publications
A spacetime discontinuous Petrov-Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The wellposedness of this formulation is established using a previously presented abstract framework. One of the main tasks in the verification of the conditions of this framework is proving a density result. This is done in detail for a simple domain in arbitrary dimensions. The DPG method based on the weak formulation is then studied theoretically and numerically. Error estimates and numerical results are presented for triangular, rectangular, tetrahedral, and hexahedral meshes of …
Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie
Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie
Mathematics and Statistics Faculty Publications and Presentations
The advantage of using algebraic geometry over enumeration for describing sets related to attractors in large dynamic networks from biology is advocated. Examples illustrate the gains.
Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng
Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng
Theses and Dissertations
Solutions to the one-dimensional and two-dimensional nonlinear Schrodinger (NLS) equation are obtained numerically using methods based on radial basis functions (RBFs). Periodic boundary conditions are enforced with a non-periodic initial condition over varying domain sizes. The spatial structure of the solutions is represented using RBFs while several explicit and implicit iterative methods for solving ordinary differential equations (ODEs) are used in temporal discretization for the approximate solutions to the NLS equation. Splitting schemes, integration factors and hyperviscosity are used to stabilize the time-stepping schemes and are compared with one another in terms of computational efficiency and accuracy. This thesis shows …
Numerical Simulation For A Rising Bubble Interacting With A Solid Wall: Impact, Bounce, And Thin Film Dynamics, Changjuan Zhang, Jie Li, Li-Shi Luo, Tiezheng Qian
Numerical Simulation For A Rising Bubble Interacting With A Solid Wall: Impact, Bounce, And Thin Film Dynamics, Changjuan Zhang, Jie Li, Li-Shi Luo, Tiezheng Qian
Mathematics & Statistics Faculty Publications
Using an arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out numerical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between numerical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using …