In this thesis, we study Prandtl's boundary layer theory for 2D, stationary, incompressible Navier-Stokes flows posed on domains with boundaries. The boundary layer hypothesis posed …
This thesis consists of two topics on discontinuous Galerkin (DG) finite element methods for time-dependent problems. In the first part of the thesis, we analyze …
In this work, we develop and analyze solvers and preconditioners designed for the implicit time integration of discontinuous Galerkin (DG) discretizations. The discontinuous Galerkin method …
Colloidal membranes are an example of a novel bioinspired soft material with rich properties that stem from the interplay of geometry and molecular order. A …
Despite the enormous amount of biological variation and technical uncertainty in sequence data, most phylogenetic workflows propagate a single point estimate throughout the numerous analysis …
Computational simulation pervades science and engineering, enabling new insights about complex physical phenomena. The advent of exascale computer systems, which will enable simulation at an …
This dissertation presents two topics on numerical solutions solving hyperbolic equations from both theoretical and practical points of view. In the first part, we introduce …
Neutrally buoyant, non-Brownian particles in a low Reynolds number pressure-driven flow display an irreversible net particle migration towards the center of the channel, resulting in …
We investigate two different topics in discrete mathematics: the geometry of piecewise-linear surfaces and the long-term behavior of discrete dynamical systems. A regular polygon surface …
For most eukaryotic organisms, protein coding sequences are only a small portion of the genome. Much of the genome is made up of transposable elements, …