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Filtering by: Creator Au, Whitlow W. L. Remove constraint Creator: Au, Whitlow W. L. Advisor Peszynska, Malgorzata Remove constraint Advisor: Peszynska, Malgorzata Rights Statement In Copyright Remove constraint Rights Statement: In Copyright

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  • Model Adaptivity and Numerical Solutions Using Sensitivity Analysis

    Creator:
    Kennedy, Kenneth M.
    Abstract:
    In this work we consider the dependence of solutions to a partial differential equations system on its data. The problem of interest is a coupled model of nonlinear flow and transport in porous media, with applications, e.g. to environmental modeling. The model of flow we consider is known as the...
    Resource Type:
    Dissertation
    Full Text:
    form Lu+N (u) = f, (2.0.1) where u is the unknown that is sought, L is the linear part of the model

  • Stochastic analysis of flow and transport in porous media

    Creator:
    Vasylkivska, Veronika S.
    Abstract:
    Random fields are frequently used in computational simulations of real-life processes. In particular, in this work they are used in modeling of flow and transport in porous media. Porous media as they arise in geological formations are intrinsically deterministic but there is significant uncertainty involved in determination of their properties...
    Resource Type:
    Dissertation
    Full Text:
    . Showalter, Dr. Nathan L. Gibson and Dr. Margaret L. Niess for agreeing to serve on my graduate committee

  • Mathematical treatment and simulation of methane hydrates and adsorption models

    Creator:
    Medina, Francis Patricia
    Abstract:
    In this dissertation we develop mathematical treatment for two important applications: (i) evolution of methane in coalbeds with the associated phenomena of adsorption, and (ii) formation of methane hydrates in seabed. We use simplified models for (i) and (ii) since we are more interested in qualitative properties of the solutions...
    Resource Type:
    Dissertation
    Full Text:
    methane hydrate problem. First, let V and W be linear spaces over R and consider the set L(V,W ) of

  • A heterogeneous flow numerical model based on domain decomposition methods

    Creator:
    Zhang, Yi
    Abstract:
    In this study, a heterogeneous flow model is proposed based on a non-overlapping domain decomposition method. The model combines potential flow and incompressible viscous flow. Both flow domains contain a free surface boundary. The heterogeneous domain decomposition method is formulated following the Dirichlet-Neumann method. Both an implicit scheme and an...
    Resource Type:
    Masters Thesis
    Full Text:
    ), (v, q)) = (f ,v) , ∀(v, q) ∈ W0. We also define the linear map L : W → W such that L(w) , (−µ∆u+ a

  • Explorations of Optimization Methods for Deep Learning with Examples from Various Applications

    Creator:
    Zhang, Nachuan
    Abstract:
    This paper explores some optimization methods such as the gradient descent method, Gauss-Newton method, and stochastic gradient method. Some examples of minimizing objective functions are given to validate the theories. Then we introduce a simple example of artificial neural networks, define its structure, and apply the optimization methods to it....
    Resource Type:
    Capstone Project
    Full Text:
    add weight matrices and bias vectors on the network. We use W [l] ∈ Rnl×nl−1 to denote the matrix of

  • Modeling and simulation of reaction-diffusion problem applied to biofilm growth

    Creator:
    Armstrong, Jessica S.
    Abstract:
    One method for CO2 sequestration is to store the liquid form of CO2 in small cement wells in the ground. An issue with this method is the susceptibility of cement to fracture and thus release the CO2. One proposition is to fill these cracks with biofilm of the bacteria Sporosarcina...
    Resource Type:
    Honors College Thesis
    Full Text:
    Robert L. Higdon Ph.D., Committee Member, representing Mathematics Mina E. Ossiander Ph.D, Committee

  • Hybrid Multiscale Methods with Applications to Semiconductors, Porous Media, and Materials Science

    Creator:
    Costa, Timothy B.
    Abstract:
    In this work we consider two multiscale applications with tremendous computational complexity at the lower scale. First, we examine a model for charge transport in semicon- ductor structures with heterojunction interfaces. Due to the complex physical phenomena at the interface, the model at the design scale is unable to adequately...
    Resource Type:
    Dissertation
    Full Text:
    constant C > 0 such that for each v ∈ V and w ∈W we have |Av(w)| ≤ C‖v‖V ‖w‖W . (2.1.18) We denote L(V,W

  • Analysis of domain decomposition methods for the simulation of charge transport in semiconductor structures with heterojunctions

    Creator:
    Costa, Timothy B.
    Abstract:
    Charge transport in a semiconductor structure with heterojunction is described by a multiscale partial differential equation model. This model can be used, e.g., for the design of more efficient solar cells. Phenomena at the heterojunction must be resolved at the angstrom scale while the size of the device is that...
    Resource Type:
    Masters Thesis
    Full Text:
    = w|Ωi , wΓi = limx→Γwi, and [w]Γ = wΓ2 − wΓ1 denotes the jump of w. We denote by νi the outward

  • Operator Splitting for a Wildfire Model in a Heterogeneous Environment with a Surrogate Wind Velocity Field

    Creator:
    Pantuso, Nicholas M.
    Abstract:
    Living in the Pacific Northwest, we are acutely aware of the dangers posed by wildfires. Largely due to the worsening effects of climate change, this danger is only increasing. Along with causing property and economic damage to those communities affected by wildfires, exposure to the smoke generated by wildfires can...
    Resource Type:
    Masters Thesis
    Full Text:
    , our problem is simplified to dQ dt = ∇ · (k∇Q)− v⃗ · ∇Q+ f(S,Q) + fext, (x, t) ∈ (0, L)× (0, T

  • Nonlinear finite difference schemes for the Klausmeier system

    Creator:
    McClellan, Natalia A.
    Abstract:
    In this work we consider a model for pattern-producing vegetation in semi-arid regions of the world proposed by Klausmeier. It is a coupled nonlinear diffusion-advection evolutionary PDE system describing the vegetation density and water amount. The model was studied extensively by J.Sherratt who took into consideration the field data for...
    Resource Type:
    Masters Thesis
    Full Text:
    ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.5 The l∞-norm of errors in W (in comparison to the ODE45 solution) for differ- ent time