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Showing 1 to 20 of 25 for “"Neumann Boundary Conditions"”.
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Comparison Theorems in Elliptic Partial Differential Equations with Neumann Boundary Conditions
<p>In this thesis, we study how the solution of a PDE changes when the data are rearranged. Specifically, we prove comparison theorems on spherical shells, spheres, and hemispheres, showing that under rearrangement of the data, the solution's convex mean increases. We also obtain similar weighted …
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Finite Element Approximations of Burgers' Equation with Robin's Boundary Conditions
… study of Burgers' equation with Robin's boundary conditions. The goal is to determine the behavior of the solutions in the limiting cases of Dirichlet and Neumann boundary conditions. We develop and test two separate finite element and Galerkin schemes. The Galerkin/Conservation method is …
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Finite element approximations of Burgers' equation
… is a numerical study of Burgers' equation with Neumann boundary conditions. The goal is to determine the long term behavior of solutions. We develop and test two separate finite element and Galerkin schemes and then use those schemes to compute the response to various initial conditions and …
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Laplace's equation on perturbed domains
… to several test cases. Both Dirichlet and Neumann boundary conditions are considered. We verify our methods by constructing exact solutions for the perturbed geometries.
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A Numerical Study of Burgers' Equation With Robin Boundary Conditions
… equation on a finite spatial domain with various boundary conditions. We first conduct experiments to confirm the numerical solutions observed by other researchers for Neumann boundary conditions. Then we consider the case where the non-homogeneous Robin boundary conditions approach …
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Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2
… admissible functions to satisfy Dirichlet boundary conditions on a portion of the fixed boundary with positive one-dimensional Hausdorff measure and Neumann boundary conditions on the rest of the fixed boundary. In this thesis we consider the behavior of minimizers in a neighborhood of some …
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Deep Learning-based Numerical Methods for Stochastic Partial Differential Equations and Applications
… In particular, the forward SPDEs may allow for Neumann boundary conditions. We also prove the convergence analysis of the proposed algorithms. The numerical results indicate that the performance of the algorithm is quite effective for solving the SPDEs, even in high-dimensional cases. The …
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Regularity of Neumann solutions to an elliptic free boundary problem
… properties of solutions to an elliptic free boundary problem, near a Neumann fixed boundary. Consider a nonnegative function u which minimizes the functional ... on a bounded, convex domain ... This function u is harmonic in its positive phase and satisfies ... along the free boundary ... , …
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Uniform heating of thin ceramic slabs in a multimode microwave cavity
… and to determine the stability of solutions for Neumann boundary conditions. The choices of parameters in the equation that lead to uniform heating of the ceramic slab have been characterized.
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Asymptotic behavior of the solutions to a family of PDE's arising from the chemotaxis equations of Keller and Segal
… is considered on [0,1] x [0,T] with homogeneous Neumann boundary conditions. The operators which lead to global solutions and those that lead to solutions which blow up in finite time are considered as a function of rho, using an application of the methods of Hillen and Potapov [Math. Methods …
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Mathematical and Numerical Analysis of a Pair of Coupled Cahn-Hilliard Equations with a Logarithmic Potential
… a logarithmic potential and with homogeneous Neumann boundary conditions. This pair of coupled equations arises in a phase separation model of thin film of binary liquid mixture. Global existence and uniqueness of a weak solution to the problem is proved using Faedo-Galerkin method. Higher …
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Modeling flow encountering abrupt topography using hybridizable discontinuous Galerkin projection methods
… the pressure Poisson equation with homogeneous Neumann boundary conditions everywhere along the boundary. Extensive numerical results using physically realistic ocean flows are presented to verify the HDG projection methods, including the formation of internal wave beams over a shallow but …
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Taming of Complex Dynamical Systems
… nonlinearities and to Burgers’ Equation with Neumann boundary conditions. Numerical results are presented to illustrate the ideas.
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A parallel second order Cartesian method for elliptic interface problems and its application to tumor growth model
… allowing to express the interface transmission conditions. The method is described and the details of its parallelization, performed with the PETSc library, are provided. Numerical validations of the method follow with comparisons to other related methods in literature. A numerical study of the …
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Reduced basis method for 2nd order wave equation : application to one-dimensional seismic problem
… of pressure change with time. With Dirichlet and Neumann boundary conditions, the pressure distribution is solved for a total of 500 time steps, which is slighter more than a periodic cycle. Our focus is on the dependence of the output, the average surface pressure as it varies with time, on the …
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Ab Initio Computation of Radiative Properties of Monatomic Hydrogen
… works found thus far assume Dirichlet or von Neumann boundary conditions for the eigenvalue problem. At best this presumes a priori knowledge of the solution. In general, it is incorrect. The novel boundary condition treatment used here admits simultaneous solution for several wave functions, …
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Periodic orbit analysis of the Helmholtz equation in two-dimensional enclosures
… [3] is given. SPOT is extended to impedance boundary conditions. SPOT is implemented in the quarter stadium, quadrupole, circle and eccentric annulus enclosures with Dirichlet, Neumann and impedance boundary conditions. Concave enclosures with Dirichlet or Neumann boundary conditions were …
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Asymptotic methods in applied waveguide problems
… is also developed. Both Dirichlet and Neumann boundary conditions are considered. The applicability conditions of this approximation are investigated and the resulting accuracy is discussed. Numerical simulations supporting the validity of these asymptotic approximations are presented …
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Attitude Dynamics of Debris Resulting From Upper Stage Fragmentation in Low Earth Orbit
… Ohm's law is set up a Poisson problem with Neumann boundary conditions. The electrical potential, solution of Poisson problem and calculated by a finite element solver, defines the density current in the body and thus determines the torque applied on the debris.</p> <p>The results presented …
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A new hybrid numerical scheme for simulating fault ruptures with near fault bulk inhomogeneities
"The Finite Difference (FD) and the Boundary Integral (BI) Method have been used extensively to model spontaneously propagating shear cracks in a variety of engineering and geophysical applications. While FD has a large computational cost as it requires the discretization of the whole volume of …
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