This paper presents a time-discontinuous Galerkin space-time finite element method for the seismic analysis of dam-reservoir-soil system. For the reservoir domain an auxiliary variable q, a first-order time derivative...
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This paper presents a time-discontinuous Galerkin space-time finite element method for the seismic analysis of dam-reservoir-soil system. For the reservoir domain an auxiliary variable q, a first-order time derivative of hydrodynamic pressure is introduced as the primary unknown. Similarly, velocity is taken as the primary unknown in the solid domain. In this approach, secondary unknowns (displacement and pressure) are computed in a postprocessing step by consistent time integration of the primary unknowns. This arrangement leads to a system of linearly coupled algebraic equations, which is solved with a block-iterative algorithm. In each iteration of the algorithm, two smaller linear systems, ie, one for velocity field and another for the auxiliary field, are solved separately and coupling between these two fields is enforced through iterations. Afterwards, numerical performance of the proposed scheme is demonstrated by solving some benchmark dam-reservoir interaction problems. It is shown that very few iterations are required for the convergence. Lastly, the method is employed to analyze the effects of dynamic interactions on the response of concrete dam to the earthquake loading.
iterative reconstruction methods such as the expectation maximization maximum likelihood (EMML) method can be accelerated by using a resealed block-iterative (RBI) algorithm. It was demonstrated that the space-alterna...
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ISBN:
(纸本)0780384393
iterative reconstruction methods such as the expectation maximization maximum likelihood (EMML) method can be accelerated by using a resealed block-iterative (RBI) algorithm. It was demonstrated that the space-alternating generalized expectation-maximization (SAGE) algorithm is superior to the EMML due to the following facts: (1) The hidden data spaces can be appropriately chosen and then be used in SAGE algorithm to speed up the convergence rate. (2) SAGE algorithm updates the parameters sequentially which makes its M-step to be treated more easily. In this paper, we present a novel algorithm that combines the RBI algorithm with SAGE algorithm. The convergence property of RBI-SAGE is discussed, and the image quality is assessed with mean absolute error and chi-square error. The experimental results show that the proposed method is more effective than the SAGE algorithm even if the projection data includes statistic noise.
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are blo...
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We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in established methods. Flexible strategies are used to select the blocks of operators activated at each iteration. In addition, we allow lags in operator processing, permitting asynchronous implementation. The decomposition phase of each iteration of our methods is to generate points in the graphs of the selected monotone operators, in order to construct a half-space containing the Kuhn-Tucker set associated with the system. The coordination phase of each iteration involves a projection onto this half-space. We present two related methods: the first method provides weakly convergent primal and dual sequences under general conditions, while the second is a variant in which strong convergence is guaranteed without additional assumptions. Neither algorithm requires prior knowledge of bounds on the linear operators involved or the inversion of linear operators. Our algorithmic framework unifies and significantly extends the approaches taken in earlier work on primal-dual projective splitting methods.
We consider the numerical aspect of the multicommodity network equilibrium problem proposed by Rockafellar in 1995. Our method relies on the flexible monotone operator splitting framework recently proposed by Combette...
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We consider the numerical aspect of the multicommodity network equilibrium problem proposed by Rockafellar in 1995. Our method relies on the flexible monotone operator splitting framework recently proposed by Combettes and Eckstein. (c) 2021 Elsevier B.V. All rights reserved.
A convex programming approach to binary tomographic image reconstruction in noisy environments is proposed. Conventional constraints are mixed with new constraints on the sinogram. A convex objective is then minimized...
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Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training the layers of a neural network is a challenging task...
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We propose a novel approach to monotone operator splitting based on the notion of a saddle operator. Under investigation is a highly structured multivariate monotone inclusion problem involving a mix of set-valued, co...
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We propose a novel approach to monotone operator splitting based on the notion of a saddle operator. Under investigation is a highly structured multivariate monotone inclusion problem involving a mix of set-valued, cocoercive, and Lipschitzian monotone operators, as well as various monotonicity-preserving operations among them. This model encompasses most formulations found in the literature. A limitation of existing primal-dual algorithms is that they operate in a product space that is too small to achieve full splitting of our problem in the sense that each operator is used individually. To circumvent this difficulty, we recast the problem as that of finding a zero of a saddle operator that acts on a bigger space. This leads to an algorithm of unprecedented flexibility, which achieves full splitting, exploits the specific attributes of each operator, is asynchronous, and requires to activate only blocks of operators at each iteration, as opposed to activating all of them. The latter feature is of critical importance in large-scale problems. The weak convergence of the main algorithm is established, aswell as the strong convergence of a variant. Various applications are discussed, and instantiations of the proposed framework in the context of variational inequalities and minimization problems are presented.
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