Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 24 for “"semi-discrete"”.
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Overcoming Computational Complexity Barriers for Optimal Transport in Discrete and Semi-Discrete Settings
… given a $d$-dimensional continuous (resp. discrete) probability distribution $mu$ defined over a support $Asubsetmathbb{R}^d$ and a discrete distribution $nu$ defined over a support $Bsubsetmathbb{R}^d$, the semi-discrete (resp. discrete) optimal transport problem asks for computing a …
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Solution of fully-coupled shallow water equations and contaminant transport using a primitive variable Riemann solver and a semi-discrete SUPG method
… variables rather than conserved variables, and a semi-discrete Streamline Upwind Petrov-Galerkin (SUPG) method in finite element context are applied to compare the performance of these two numerical models. The Riemann-solver scheme is based on the unstructured finite volume discretization using …
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Numerical solutions for a class of singular integrodifferential equations
… we are able to establish convergence for a semi-discrete scheme. We use an ordinary differential equation solver for the semi-discrete scheme and then improve the result by using a fully discretized scheme. We report our numerical findings and comment on the rates of convergence.
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Moment Matching and Modal Truncation for Linear Systems
… the forward Euler scheme. In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are virtually insignificant. Eliminating such modes dramatically improves the stable time-step without sacrificing output accuracy. This is accomplished by modal …
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Mathematical and Numerical Analysis of a Pair of Coupled Cahn-Hilliard Equations with a Logarithmic Potential
… on the initial data is presented. Numerically, semi-discrete and fully-discrete piecewise linear finite element approximations to the continuous problem are proposed for which existence, uniqueness and various stability estimates of the approximate solutions are proved. Semi-discrete and …
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The Application of Improved Numerical Techniques to 1-D Micellar/Polymer Flooding Simulation
… something equivalent to a salinity gradient. The semi-discrete method was applied to a 1-D micellar/polymer flooding simulator. By using a semi-discrete method, the time step size can be controlled and varied to be as large as pos-sible without sacrificing accuracy. The stability limit can also be …
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A Class of Stable, Efficient Navier-Stokes Solvers
… Using the nice identity, we prove that the semi-discrete iterative scheme for the steady-state SE converges ("semi-discrete" means that the spatial variable are kept continuous). This identity will also be crucial for our proofs of the stability and error estimates of the time-dependent …
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Numerical Investigations of Magnetohydrodynamic Hypersonic Flows
… work is provided through the implementation of a semi-discrete central scheme in-house code toward the solution of the Orszag-Tang vortex system.
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Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality
… approximations considered are the following: 1. Semi-discrete approximations, in which only the spatial domain is discretised by finite elements; 2. fully discrete approximations, in which the spatial domain is again discretised by finite elements and, in addition, the time domain is discretised …
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Deep generative models via explicit Wasserstein minimization
… the network is a continuous distribution (the “semi-discrete” setting), then the Wasserstein distance is realized by a deterministic optimal transport mapping; (b) given an optimal transport mapping between a generator network and a target distribution, the Wasserstein distance may be decreased …
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Numerical Simulations Of Black Hole Binaries: Second Order Spectral Methods
… as is typical in first-order formulations. Semi-discrete stability of the new method is proved using energy arguments for the scalar wave equation in flat space, and the generalization to the scalar wave on a curved background is derived. Evolutions of the second order Einstein equations in …
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Approximations and Object-Oriented Implementation for a Parabolic Partial Differential Equation
… system of equations. For the second method, a semi-discrete method is used which transforms the partial differential equation into a system of ordinary differential equations. The goal of this work is to investigate the influence of boundary conditions, domain geometry, and initial condition on …
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High Cycle Fatigue Simulation using Extended Space-Time Finite Element Method Coupled with Continuum Damage Mechanics
… method based on Finite Element Method (FEM) and semi-discrete schemes for fatigue design and analysis. Semi-discrete schemes are known to suffer from either the time-step constraints or lack of convergence due to the oscillatory nature of the fatigue loading condition. As such, simulating loading …
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Investigation of infinite-dimensional dynamical system models applicable to granular flows
… from the BSR model. In addition, an innovative semi-discrete numerical scheme for obtaining approximate solutions is described in detail and the questions of consistency, convergence, stability and accuracy of the scheme are treated at considerable length. It is shown how this numerical scheme …
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Intercalation dynamics in lithium-ion batteries
… treatment of the reaction rates; I develop a semi-discrete finite volume method for numerical simulations; and I include a careful asymptotic treatment of the dynamical regimes found in different limits of the governing equations. Further, I will present several new findings relevant to …
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Characterization of nonlinearity parameters in an elastic material with quadratic nonlinearity with a complex wave field
… laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. In the one-dimensional cases, it is shown that the analytical and numerical solutions are in good agreement with each other, as well as how different …
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Time-dependent adjoint-based optimization of photonic crystals and metamaterials using a stabilized finite element method
In the current research, a time-dependent discrete adjoint algorithm for optimization of electromagnetic problems is developed. The proposed algorithm improves the efficiency for gradient-based optimization. The time-dependent Maxwell equations are discretized using a semi-discrete Petrov-Galerkin …
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Statistical aspects of optimal transport
… the rate of approximation of entropic OT in the semi-discrete case, and complement these results by considering the problem of trajectory reconstruction, proposing two practical methods based off both un-regularized and entropic OT.
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Modeling, Discontinuous Galerkin Approximation and Simulation of the 1-D Compressible Navier Stokes Equations
… the temporal derivatives are zero. We develop a semi-discrete model by applying a linear discontinuous Galerkin method in the spatial dimension. The resulting finite dimensional model is a differential algebraic equation (DAE) which is solved using standard integrators. We investigate two methods …
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On the discrete nonlinear Schrödinger equation with PT-Symmetry
… the inverse scattering method for the nonlocal semi-discrete nonlinear Schrödinger equation (known as Ablowitz-Ladik equation) with parity-time symmetry proposed in Ablowitz and Musslimani’s paper. This includes the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data …
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