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Showing 1 to 20 of 22 for “"domain decomposition methods"”.
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Domain decomposition methods for time-harmonic elastic waves
… difficult to solve both by direct and iterative methods. Domain decomposition methods are hybrid methods in the sense that they use an iterative coupling of smaller problems that are solved by direct methods,and rely on the splitting the global problem into local problems on smaller subdomains. …
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Model Reduction and Domain Decomposition Methods for Uncertainty Quantification
… likelihood that an inclusion is present in the domain. In Chapter 3, we use a Domain Decomposition (DD) approach to compute the Karhunen-Loeve (KL) modes of a random process through the use of local KL expansions at the subdomain level. Furthermore, we analyze the relationship between the local …
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Optimization Based Domain Decomposition Methods for Linear and Nonlinear Problems
Optimization based domain decomposition methods for the solution of partial differential equations are considered. The crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between …
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Defect correction based domain decomposition methods for some nonlinear problems
… correction schemes as a class of nonoverlapping domain decomposition methods offer several advantages in the ways they split a complex problem into several subdomain problems with less complexity. The schemes need a nonlinear solver to take care of the residual at the interface. The adaptive-∝ …
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Advancing domain decomposition methods and entity resolution with graph neural networks
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms
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Domain Decomposition Methods for Convection-Diffusion-Reaction Equations with Finite Volume Discretizations
… studied. Both overlapping and non-overlapping domain decom- position (DD) preconditioning methods are considered. With overlapping DD preconditioners, we work on a time dependent CDR model. The additive Runge-Kutta (ARK) scheme is used for the time discretization and the fourth-order finite …
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Accurate, efficient, and stable domain decomposition methods for analysis of electromechanical problems
… problem is decomposed into smaller subdomain problems and parallel computing schemes are then employed to reduce the computation time significantly. Second, the tree-cotree splitting (TCS) method is adopted to deal with the low-frequency breakdown problem, which often accompanies the …
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Unified conformal/nonconformal domain decomposition methods for solving large-scale multi-region electromagnetic problems
… boundary. First, two nonconformal FETI-DP methods are formulated, both of which implement the Robin-type transmission condition at the subdomain interfaces to preserve the fast convergence of the iterative solution of the global interface problem in the high-frequency region. The first …
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Stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition
Overlapping domain decomposition methods, otherwise known as overset or chimera methods, are useful approaches for simplifying the discretizations of partial differential equations in or around complex geometries. While in wide use, the methods are prone to numerical instability unless numerical …
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Domain decomposition preconditioners for higher-order discontinuous Galerkin discretizations
… accuracy at lower computational cost. Domain decomposition methods are studied for the parallel solution of the linear system arising at each iteration of the implicit scheme. A minimum overlapping additive Schwarz (ASM) preconditioner and a Balancing Domain Decomposition by Constraints …
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Adaptive Discontinuous Galerkin Methods Applied to Multiscale & Multiphysics Problems towards Large-scale Modeling & Joint Imaging
… the stability and accuracy of the DG methods and domain decomposition methods.</p>
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Domain decomposition based algorithms for some inverse problems
… are developed 011frameworks provided by domain decomposition methods and the numerical schemes use finite volume and finite difference discretisations. Three algorithms are developed in the context of a metal cutting problem. The algorithms require measurement data within the physical …
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Investigation of explicit finite-element time-domain methods and modeling of dispersive media and 3D high-speed circuits
In this dissertation, efficient time-domain domain decomposition algorithms are investigated, compared, and further enhanced, and a new domain decomposition method is proposed based on the knowledge of existing ones. First, several explicit domain decomposition methods, including the dual-field …
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A study on computational electromagnetics problems with applications to casimir force calculations
… be desirable to aid in their design. Recent methods have been developed that incorporate CEM techniques, notably the electric field integral equation (EFIE). Herein, we present three methods, one of a new devising, that make use of various CEM techniques. Our new method allows for the easy …
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Advances in Algorithms for Atmospheric Sciences
… approach to classical stabilization methods and test its sensitivity to model parameters on two-dimensional benchmark problems. The second project develops a distributed data assimilation scheme for ensemble Kalman filters (EnKFs), which improve the state estimate of the system using …
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Geometric Integrators for Hamiltonian PDEs
<p>We consider methods for systematic construction of algorithms for a class of time-dependent PDEs with Hamiltonian structure. These systems possess phase space geometry and constants of the motion that need to be preserved by the integration algorithm to reflect the qualitative features of the …
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Optimal shape design with domain decomposition
… the flow distribution in the computational domain or on its subset and sought the geometrical configuration that produced this flow. Based on this idea, we formulated a control problem, in which the optimization procedure minimizes the error between the target flow and the actual flow …
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Mathematical and computational aspects of solving mixed-domain problems using the finite element method
This work focuses on mixed-domain problems, where fields defined over different domains are governed by different partial differential equations and may be coupled. Multiphysics problems, where different regions are governed by different (interacting) physical laws, are examples of mixed-domain …
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Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters
… between boundary integral equation solvers and Domain Decomposition Methods (DDM) for frequency domain Helmholtz transmission problems in composite two-dimensional media is presented. Composite media are characterized by piece-wise constant material properties (i.e., index of refraction) and …
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