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Discontinuous Galerkin Methods for Modeling Hurricane Storm Surge
Abstract Storm surge due to hurricanes and tropical storms can result in significant loss of life, property damage, and long-term damage to coastal ecosystems and landscapes. Computer modeling ofExpand
Discontinuous Galerkin Methods with Nodal and Hybrid Modal/Nodal Triangular, Quadrilateral, and Polygonal Elements for Nonlinear Shallow Water Flow
Abstract We present a comprehensive assessment of nodal and hybrid modal/nodal discontinuous Galerkin (DG) finite element solutions on a range of unstructured meshes to nonlinear shallow water flowExpand
Solving differential equations using deep neural networks
TLDR
The resulting DNN framework for PDEs enables straightforward system prototyping and natural integration of large data sets (be they synthetic or experimental), all while simultaneously enabling single-pass exploration of an entire parameter space. Expand
Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations
TLDR
A family of generalized slope limiters in two dimensions for Runge-Kutta discontinuous Galerkin (RKDG) solutions of advection-diffusion systems are studied and a series of coupled p-enrichment schemes are introduced. Expand
A Hybridized Discontinuous Galerkin Method for the Nonlinear Korteweg–de Vries Equation
TLDR
A hybridized discontinuous Galerkin (HDG) method for solving nonlinear Korteweg–de Vries type equations that shows optimal convergence at order $$k+1$$k-1 in both linear and nonlinear cases, which improves upon previously employed techniques. Expand
Foundations of the blended isogeometric discontinuous Galerkin (BIDG) method
TLDR
The BIDG method contrasts with existing high-order accurate DG methods over curvilinear meshes in that the underlying geometry is exactly preserved at every mesh refinement level, allowing for intricate and complicated real-world mesh design to be streamlined and automated using computer-aided design (CAD) software. Expand
Solving Irregular and Data-enriched Differential Equations using Deep Neural Networks
TLDR
The resulting DNN framework for PDEs seems to demonstrate almost fantastical ease of system prototyping, natural integration of large data sets (be they synthetic or experimental), all while simultaneously enabling single-pass exploration of the entire parameter space. Expand
A parallel and adaptive hybridized discontinuous Galerkin method for anisotropic nonhomogeneous diffusion
Abstract The diffusion equation in anisotropic and nonhomogeneous media arises in the study of flow through porous media with sharp material interfaces. We discuss the solution of this problem by aExpand
A discontinuous Galerkin method for viscous compressible multifluids
TLDR
A generalized discontinuous Galerkin method for a multicomponent compressible barotropic Navier–Stokes system of equations, which has a functional viscosity ν which depends on the pressure p = p ( ρ , μ i ) of the flow, with the density ρ and the local concentration μ i. Expand
FanStore: Enabling Efficient and Scalable I/O for Distributed Deep Learning
TLDR
FanStore is presented, a transient runtime file system that optimizes DL I/O on existing hardware/software stacks that provides a POSIX-compliant interface with native hardware throughput in an efficient and scalable manner. Expand
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