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Showing 1 to 12 of 12 for “"Elliptic Equation"”.
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A perturbation solution of linear elliptic equation
The first boundary value problem for eΔu + a(x,y,e)ux + b(x,y,e)uy +c(x,y,e)u = d(x,y,e) for small e. This problem with coefficients independent of e was treated by Norman Levinson and appeared in Annals of Mathematics, Vol. 51, No. 2, March, 1950 [TRUNCATED].
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Homogenization of Partial Differential Equations with Random, Large Potential
Partial differential equations with highly oscillatory, random coefficients describe many applications in applied science and engineering such as porous media and composite materials. Homogenization of PDE states that the solution of the initial model converges to the solution to a macro model, …
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Convergence of complete Ricci-βat manifolds
… is given as the gradient βow of a solution to an elliptic equation. We use an estimate of Colding-Minicozzi of a functional that measures the distance to the tangent cone. In the second part of this thesis, we prove a matrix Harnack inequality for the Laplace equation on manifolds with suitable …
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Adams inequalities with exact growth condition : on Rn and the Heisenberg group
… than] n, higher order gradients and homogeneous elliptic differential operators. Next we give an application to a quasilinear elliptic equation, and prove the existence of ground state solution of this equation. Lastly, we extend our result to the Heisenberg group. By applying the same technique …
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Minimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimation
… guide. We demonstrate this approach for the 1D elliptic equation or the elliptic partial differential equation and observe how this method works in cases with significant and without any expert bias. In the case of significant expert bias, the method substantially reduces the bias and, in the …
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Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems
… method to reduce the two-dimensional Helmholtz equation with complex scattering surface into a successive sequence of the transmission problems with a plane interface. Then, we use Fourier-Spectral method in the periodic structure problem and Hermite-Spectral method in the unbounded rough …
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Model Reduction and Domain Decomposition Methods for Uncertainty Quantification
… the computational cost of solving a Stochastic Elliptic Equation (SEE) via a Monte Carlo sampling method. The approach takes advantage of a lower stochastic dimension at the subdomain level to construct a PC expansion of a reduced linear system that is later used to compute samples of the …
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Recovery Techniques For Finite Element Methods And Their Applications
… to the exact gradient for both second order elliptic equation and Stokes equation. The gradient recovery technique can be used in a posteriori error</p> <p>estimates for Crouzeix-Raviart element, which is relatively simple to implement and problem independent.</p> <p>Our second target is to …
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Preconditioning of Karush--Kuhn--Tucker Systems arising in Optimal Control Problems
… problems governed by partial differential equations. The KKT matrix is symmetric, nonsingular, and indefinite. For the solution of the linear systems generalizations of the conjugate gradient method, MINRES and SYMMLQ, are used. The performance of these iterative solution methods depends on …
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Numerical Methods for All Mach Number flows for Gas Dynamics
… to solve the all-Mach number flow for the Euler equations of gas dynamics on staggered grid is presented in this thesis. The system is discretized to second order in space on staggered grid, in a fashion similar to the Nessyahu-Tadmor central scheme for 1D model and Jang-Tadmor central scheme for …
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Collective behaviour of active particles with mean-field interaction
… derive a macroscopic partial differential equation (PDE) from a nonlinear interacting stochastic particle system used to model ants and use the PDE to provide a phase diagram for the collective behaviour of the particle model. The PDE model sustains ants forming bidirectional lanes and ants …
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Stime sul bordo per soluzioni di equazioni ellittiche singolari
Nella prima parte di questa tesi viene studiata l’equazione Δu + f(u) = 0 in un dominio regolare (che soddisfa la proprietà della sfera interna e della sfera esterna) e limitato di RN, dove f(t) è una funzione regolare positiva, decrescente, e che tende a infinito per t che tende a zero. Nella …