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Showing 1 to 20 of 121 for “"Domain decomposition"”.
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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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Boundary method-based domain decomposition on multiprocessors
… equation on irregular as well as regular domains. The method, called the boundary method-based domain decomposition or BMDD, combines the attractiveness of the domain decomposition technique in parallel solution of the boundary value problem with the advantage of a boundary method. Unlike …
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Domain Decomposition Preconditioners for Hermite Collocation Problems
… partial differential equations on square domains with mixed boundary conditions. The first method, called <i>edge preconditioning</i>, is based on a decomposition of the domain in parallel strips, and the second, called <i>edge-vertex preconditioning</i>, is based on a two-dimensional …
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Domain decomposition methods for time-harmonic elastic waves
… 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. These …
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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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The SAS Domain Decomposition Method for Structural Analysis
A new domain decomposition method for the efficient and parallelizable numerical handling of plate bending and three dimensional elasticity problem is developed via the discovery of two special classes of matrices. The first class of matrices, say $A\in{\cal C}\sp{n\times n}$, has the relation A = …
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Domain decomposition for hexahedral mesh generation using singularity lines
… automatically a hexahedral mesh for a 3D domain of arbitrary complexity is a challenging problem that has puzzled the research community considerably. As opposed to tetrahedral mesh generation, there is no existing algorithm that can operate with the push of a button and produce the result …
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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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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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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 for Monte Carlo particle transport simulations of nuclear reactors
… of the method. In this thesis, a robust domain decomposition algorithm is proposed to alleviate this, along with models and analysis to support its use for full-scale reactor analysis. Algorithms were implemented in the full-physics Monte Carlo code OpenMC, and tested for a …
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Domain decomposition and high order discretization of elliptic partial differential equations
… has led to a recent burgeoning of research into domain decomposition algorithms. Domain decomposition is a procedure which employs subdivision of the solution domain into smaller regions of convenient size or shape and, although such partitionings have proven to be quite effective on serial …
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ADMM Based Methods for Time-Domain Decomposition Formulations of Optimal Control Problems
… of multipliers (ADMM)-based methods for time-domain decomposition (TDD) formulations of linear-quadratic partial differential equation (PDE)-constrained optimization problems. The solution of such optimization problems is computing time and memory intensive. TDD formulations split the …
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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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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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Polynomial reduction with full domain decomposition preconditioner for spectral element poisson solvers
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms
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