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Showing 1 to 20 of 64 for “"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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Approximate inference : decomposition methods with applications to networks
… defined on a graph G. Our algorithm is based on decomposition of G into appropriately chosen small components; then computing estimates locally in each of these components and then producing a good global solution. We show that if either G excludes some finite-sized graph as its minor (e.g. …
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Model Reduction and Domain Decomposition Methods for Uncertainty Quantification
… 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 random variables associated to the …
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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
… 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-∝ solver …
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Decomposition methods for large scale stochastic and robust optimization problems
We propose new decomposition methods for use on broad families of stochastic and robust optimization problems in order to yield tractable approaches for large-scale real world application. We introduce a new type of a Markov decision problem named the Generalized Rest less Bandits Problem that …
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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
… 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 volume is applied for the spacial …
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Dynamic Programming Decomposition Methods For Capacity Allocation And Network Revenue Management Problems
In this thesis, we develop decomposition-based approximate dynamic programming methods for problems in capacity allocation and network revenue management. Noting that the dynamic programming formulation of these problems suffers from the “curse of dimensionality”, we demonstrate that a set of …
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Accurate, efficient, and stable domain decomposition methods for analysis of electromechanical problems
… basis functions or even different numerical methods. Various numerical examples are presented to validate the proposed algorithm and demonstrate its performance and applications.
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Theory and Practice of Large-scale Logistics: Offline Contextual Bandits and Decomposition Methods
… in misspecified settings. Unlike standard methods that fail when reward models are poorly specified, ESR provably yields policies that asymptotically achieve optimal performance while remaining compatible with gradient-based optimization. The value of this approach is demonstrated through …
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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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Optimizing hysteretic power loss of magnetic ferrite nanoparticles
… remote heating. Several organometallic thermal decomposition methods were adapted to synthesize nanoparticles with anisotropy energies varying over 3 orders of magnitude and transferred into water using a high-temperature ligand exchange protocol. Furthermore, we compare nanoparticles of the …
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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 (BDDC) …
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The computation of matrix functions in particular, the matrix exponential
… In principle, there are many different methods to calculate the exponential of a matrix. In practice, some of the methods are preferable to others, but none of which is entirely satisfactory from either a theoretical or a computational point of view. Computations of the matrix …
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Quasi-potential analysis of multi-variate stochastic differential equations
… Finally, I introduce and implement vector field decomposition methods used to arrive at quasi-potentials from the literature for polynomial systems with demonstrations on example systems. The application of these methods to genetic switches fails and is discussed in Chapter 4.
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Strongly orthotropic continuum mechanics
… Material Principal Co-rotation and P–I–C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple …
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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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