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Articles 1 - 6 of 6
Full-Text Articles in Applied Mathematics
Numerical Methods For Optimal Transport And Optimal Information Transport On The Sphere, Axel G. R. Turnquist
Numerical Methods For Optimal Transport And Optimal Information Transport On The Sphere, Axel G. R. Turnquist
Dissertations
The primary contribution of this dissertation is in developing and analyzing efficient, provably convergent numerical schemes for solving fully nonlinear elliptic partial differential equation arising from Optimal Transport on the sphere, and then applying and adapting the methods to two specific engineering applications: the reflector antenna problem and the moving mesh methods problem. For these types of nonlinear partial differential equations, many numerical studies have been done in recent years, the vast majority in subsets of Euclidean space. In this dissertation, the first major goal is to develop convergent schemes for the sphere. However, another goal of this dissertation is …
Nystrom Methods For High-Order Cq Solutions Of The Wave Equation In Two Dimensions, Erli Wind-Andersen
Nystrom Methods For High-Order Cq Solutions Of The Wave Equation In Two Dimensions, Erli Wind-Andersen
Dissertations
An investigation of high order Convolution Quadratures (CQ) methods for the solution of the wave equation in unbounded domains in two dimensions is presented. These rely on Nystrom discretizations for the solution of the ensemble of associated Laplace domain modified Helmholtz problems. Two classes of CQ discretizations are considered: one based on linear multistep methods and the other based on Runge-Kutta methods. Both are used in conjunction with Nystrom discretizations based on Alpert and QBX quadratures of Boundary Integral Equation (BIE) formulations of the Laplace domain Helmholtz problems with complex wavenumbers. CQ in conjunction with BIE is an excellent candidate …
Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson
Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson
UNLV Theses, Dissertations, Professional Papers, and Capstones
Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …
A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Janani Gamage
A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Janani Gamage
Mathematics & Statistics Theses & Dissertations
Interface problems have many applications in physics. In this dissertation, we develop a direct method for solving three-dimensional elliptic interface problems and study their application in solving parabolic interface problems. As many of the physical applications of interface problems can be approximated with partial differential equations (PDE) with piecewise constant coefficients, our derivation of the model is focused on interface problems with piecewise constant coefficients but have a finite jump across the interface. The critical characteristic of the method is that our computational framework is based on a finite difference scheme on a uniform Cartesian grid system and does not …
Mathematical And Statistical Modeling With Deep Neural Networks, Albert Romero
Mathematical And Statistical Modeling With Deep Neural Networks, Albert Romero
Theses and Dissertations
General adversarial networks (GANs) are a form of machine learning that includes two neural networks competing in a zero-sum game. One network produces artificial, while the other tries to distinguish artificial data from real. The Wasserstein general adversarial network with gradient penalty (WGAN-GP) variant of this technique is used to produce solutions for ordinary and partial differential equations.
Novel Techniques For Solving Goursat Partial Differential Equations In The Linear And Nonlinear Regime, Tahir Naseem
Novel Techniques For Solving Goursat Partial Differential Equations In The Linear And Nonlinear Regime, Tahir Naseem
International Journal of Emerging Multidisciplinaries: Mathematics
The Goursat problem, which is related to hyperbolic partial differential equations, occurs in a variety of branches of physics and engineering. We studied the solution of the Goursat partial differential equation utilizing the reduced differential transform (RDT) and Adomian decomposition (AD) techniques in this inquiry. The problem's analytical solution is found in series form, which converges to exact solutions. The approaches' reliability and efficiency were evaluated using the Goursat problems (linear and non-linear). Additionally, the accuracy of the findings obtained demonstrates the reduced differential approach's superiority over the Adomian decomposition method and other numerical methods previously applied to the Goursat …