Browsing by Author "Dawson, Clint"

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    Enhancing Research in Natural Hazards Engineering Through the DesignSafe Cyberinfrastructure
    (Frontiers Media S.A., 2020) Rathje, Ellen M.; Dawson, Clint; Padgett, Jamie E.; Pinelli, Jean-Paul; Stanzione, Dan; Arduino, Pedro; Brandenberg, Scott J.; Cockerill, Tim; Esteva, Maria; Haan, Fred L. Jr.; Kareem, Ahsan; Lowes, Laura; Mosqueda, Gilberto
    The DesignSafe cyberinfrastructure (www.designsafe-ci.org) is part of the NSF-funded Natural Hazard Engineering Research Infrastructure (NHERI) and provides cloud-based tools to manage, analyze, understand, and publish critical data for research to understand the impacts of natural hazards. The DesignSafe Data Depot provides private and public disk space to support research collaboration and data publishing through a web interface. The DesignSafe Reconnaissance Portal uses a map interface to provide easy access to data collected to investigate the effects of natural hazards, and the DesignSafe Workspace provides cloud-based tools for simulation, data analytics, and visualization; as well as access to high performance computing (HPC). This paper provides an overview of the DesignSafe cyberinfrastructure and describes specific examples of the use of DesignSafe in research for natural hazards. These examples include electronic data reports that use Jupyter notebooks to allow researchers to interrogate data interactively within the web portal, computational workflows that integrate ensembles of HPC-based simulations and surrogate modeling, and the publication of field research data after natural hazard events that utilize a variety of DesignSafe tools. The paper also provides an overall assessment of current DesignSafe impact and usage, demonstrating how DesignSafe is enhancing research in natural hazards.
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    Error Estimates for Godunov Mixed Methods for Nonlinear Parabolic Equations
    (1988-05) Dawson, Clint
    Many computational fluids problems are described by nonlinear parabolic partial differential equations. These equations generally involve advection (transport) and a small diffusion term, and in some cases, chemical reactions. In almost all cases they must be solved numerically, which means approximating steep fronts, and handling time-scale effects caused by the advective and reactive processes. We present a time-splitting algorithm for solving such parabolic problems in one space dimension. This algorithm, referred to as the Godunov-mixed method, involves splitting the differential equation into its advective, diffusive, and reactive components, and solving each piece sequentially. Advection is approximated by a Godunov-type procedure, and diffusion by a mixed finite element method. Reactions split into an ordinary differential equation, which is handled by integration in time. The particular scheme presented here combines the higher-order Godunov MUSCL algorithm with the lowest-order mixed method. This splitting approach is capable of resolving steep fronts and handling the time-scale effects caused by rapid advection and instantaneous reactions. The scheme as applied to various boundary value problems satisfies maximum principles. The boundary conditions considered include Dirichlet, Neumann and mixed boundary conditions. These maximum principles mimic discretely the classical maximum principles satisfied by the true solution. The major results of this thesis are discrete L$\sp\infty$(L$\sp2$) and L$\sp\infty$(L$\sp1$) error estimates for the method assuming various combinations of the boundary conditions mentioned above. These estimates show that the scheme is essentially first-order in space and time in both norms; however, in the L$\sp1$ estimates, one sees a much weaker dependence on the lower bound of the diffusion coefficient than is usually derived in standard energy estimates. All of these estimates hold for uniform and non-uniform grid. Error estimates for a lower-order Godunov-mixed method for a fully nonlinear advection-diffusion-reaction problem are also considered. First-order estimates in L$\sp1$ are derived for this problem.
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    Error estimates for Godunov mixed methods for nonlinear parabolic equations
    (1988) Dawson, Clint; Wheeler, Mary F.
    Many computational fluids problems are described by nonlinear parabolic partial differential equations. These equations generally involve advection (transport) and a small diffusion term, and in some cases, chemical reactions. In almost all cases they must be solved numerically, which means approximating steep fronts, and handling time-scale effects caused by the advective and reactive processes. We present a time-splitting algorithm for solving such parabolic problems in one space dimension. This algorithm, referred to as the Godunov-mixed method, involves splitting the differential equation into its advective, diffusive, and reactive components, and solving each piece sequentially. Advection is approximated by a Godunov-type procedure, and diffusion by a mixed finite element method. Reactions split into an ordinary differential equation, which is handled by integration in time. The particular scheme presented here combines the higher-order Godunov MUSCL algorithm with the lowest-order mixed method. This splitting approach is capable of resolving steep fronts and handling the time-scale effects caused by rapid advection and instantaneous reactions. The scheme as applied to various boundary value problems satisfies maximum principles. The boundary conditions considered include Dirichlet, Neumann and mixed boundary conditions. These maximum principles mimic discretely the classical maximum principles satisfied by the true solution. The major results of this thesis are discrete L$\sp\infty$(L$\sp2$) and L$\sp\infty$(L$\sp1$) error estimates for the method assuming various combinations of the boundary conditions mentioned above. These estimates show that the scheme is essentially first-order in space and time in both norms; however, in the L$\sp1$ estimates, one sees a much weaker dependence on the lower bound of the diffusion coefficient than is usually derived in standard energy estimates. All of these estimates hold for uniform and non-uniform grid. Error estimates for a lower-order Godunov-mixed method for a fully nonlinear advection-diffusion-reaction problem are also considered. First-order estimates in L$\sp1$ are derived for this problem.
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    Mixed Finite Element Methods as Finite Difference Methods for Solving Elliptic Equations on Triangular Elements
    (1993-11) Arbogast, Todd; Dawson, Clint; Keenan, Phil
    Several procedures of mixed finite element type for solving elliptic partial differential equations are presented. The efficient implementation of these approaches using the lowest-order Raviart-Thomas approximating spaces defined on triangular elements is discussed. A quadrature rule is given which reduces a mixed method to a finite difference method on triangles. This approach substantially reduces the complexity of the mixed finite element matrix, but may also lead to a loss of accuracy in the solution. An enhancement of this method is derived which combines numerical quadrature with Lagrange multipliers on certain element edges. The enhanced method regains the accuracy of the solution, with little additional cost if the geometry is sufficiently smooth. Numerical examples in two dimensions are given comparing the accuracy of the various methods.