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The stationary Darcy–Brinkman equations in the double-diffusive convection, which model the heat and mass transfer phenomena, are considered in this paper. Based on a suitable contractive operator, the existence and uniqueness of the problem are firstly proved by using the fixed point theorem. The regularities of the weak solution are also derived. Then, the Newton iterative method is studied for solving the nonlinear discrete system generated from the finite element approximation, including the stability and the optimal error estimates regarding the spatial mesh size and the iterative factor. The analysis indicates that the viscosity coefficient has more impact on the numerical algorithm than the thermal conductivity and the mass diffusivity coefficients. Finally, many numerical examples are shown to confirm the correctness of the theoretical prediction. [ABSTRACT FROM AUTHOR]

By ignoring some cell overlaps, global placement computes the best position for each cell to minimize the wirelength. It is an important stage in very large scale integration (VLSI) physical design, since circuit performance heavily depends on the placement results. In this paper, we propose an augmented Lagrangian method to solve the VLSI global placement problem. In the proposed method, a cautious dynamic density weight strategy is used to balance the wirelength objective and the density constraints, and an adaptive step size is used to obtain a trade-off between runtime and solution quality. The proposed method is tested on the IBM mixed-size benchmarks and the International Symposium on Physical Design 2006 placement contest benchmarks. Experimental results show that our global placement method outperforms the state-of-the-art placement approaches in terms of solution quality on most of the benchmarks. [ABSTRACT FROM AUTHOR]

Placement is the process of determining the exact locations of circuit elements within a chip. It is a crucial step in very large scale integration (VLSI) physical design, because it affects routability, performance, and power consumption of a design. In this paper, we develop a new analytical placer to solve the VLSI standard cell placement problem. The placer consists of two phases, multilevel global placement (GP) and detailed cell placement (DP). In the stage of GP, during the clustering stage, we use a nonlinear programming technique and a best-choice clustering algorithm to take a global view of the whole netlist and placement information, and then use an iterative local refinement technique during the declustering stage to further distribute the cells and reduce the wirelength. In the stage of DP, we develop a fast legalization algorithm to make the solution by global placement legal and use a cell order polishing to improve the legal solution. The proposed algorithm is tested on the IBM standard cell benchmark circuits and Peko suites. Experimental results show that our placer obtains high-quality results in a reasonable running time. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the nonlinearly constrained continuous global minimization problem. Based on the idea of the penalty function method, an auxiliary function, which has approximately the same global minimizers as the original problem, is constructed. An algorithm is developed to minimize the auxiliary function to find an approximate constrained global minimizer of the constrained global minimization problem. The algorithm can escape from the previously converged local minimizers, and can converge to an approximate global minimizer of the problem asymptotically with probability one. Numerical experiments show that it is better than some other well known recent methods for constrained global minimization problems. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the box constrained nonlinear integer programming problem. We present an auxiliary function, which has the same discrete global minimizers as the problem. The minimization of the function using a discrete local search method can escape successfully from previously converged discrete local minimizers by taking increasing values of a parameter. We propose an algorithm to find a global minimizer of the box constrained nonlinear integer programming problem. The algorithm minimizes the auxiliary function from random initial points. We prove that the algorithm can converge asymptotically with probability one. Numerical experiments on a set of test problems show that the algorithm is efficient and robust. [Copyright &y& Elsevier]

We present a new definition of filled function, named globally concavized filled function, for the box constrained continuous global minimization problem. A class of this kind of filled functions are constructed. These functions contain two easily determinable parameters, which are not dependent on the radius of the basin at the current local minimizer to make them be globally concavized filled functions. We design a randomized algorithm to solve the problem basing on these functions and prove that the algorithm can converge asymptotically with probability one to a global minimizer of the problem. Numerical experiments are presented to show the effectiveness and robustness of the algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we show that the unconstrained continuous global minimization problem cannot be solved by any algorithm, so we consider the box constrained continuous global minimization problem. We present a definition of filled function for the problem. Moreover, a new class of filled functions are constructed, which contains only one parameter. A randomized algorithm is designed to solve the box constrained continuous global minimization problem based on the filled function. Numerical experiments are presented to show the practicability of the algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents a Branch and Bound method for a nonconvex integer quadratic programming problem with a separable objective function over a bounded box. For this problem, a special branch method is constructed, which has a property that if a box has been partitioned into sub-boxes, then at least one sub-box can be deleted. We analyze the complexity of the algorithm, and prove that it is better than that of the complete enumeration method in the worst case if the solution space is large enough. [Copyright &y& Elsevier]

Given a set of sensors distributed on the plane and a set of Point of Interests (POIs) on a line segment, a primary task of the mobile wireless sensor network is to schedule covering the POIs by the sensors, such that each POI is monitored by at least one sensor. For balancing the energy consumption, we study the min-max line barrier target coverage (LBTC) problem which aims to minimize the maximum movement of the sensors from their original positions to their final positions at which the coverage is composed. We first proved that when the radius of the sensors are non-uniform integers, even 1-dimensional LBTC (1D-LBTC), a special case of LBTC in which the sensors are distributed on the line segment instead of the plane, is NP -hard. The hardness result is interesting, since the continuous version of LBTC to cover a given line segment instead of the POIs is known polynomial solvable. Then we present an exact algorithm for LBTC with uniform radius and sensors distributed on the plane, via solving the decision version of LBTC. We argue that our algorithm runs in time O (n 2 log n) and produces an optimal solution to LBTC. The time complexity compares favorably to the state-of-art runtime O (n 3 log n) of the continuous version which aims to cover a line barrier instead of the targets. Last but not the least, we carry out numerical experiments to evaluate the practical performance of the algorithms, which demonstrates a practical runtime gain comparing with an optimal algorithm based on integer linear programming. [ABSTRACT FROM AUTHOR]

Mixed-cell-height circuits have become popular in advanced technologies for better power, area, routability, and performance tradeoffs. With technology and region constraints imposed by modern circuit designs, the mixed-cell-height legalization problem has become even more challenging. Additionally, an ideal legalization method should minimize both the average and maximum cell movements to preserve the quality of a given placement as much as possible. In this article, we present an effective and efficient mixed-cell-height legalization algorithm to consider technology and region constraints while minimizing the average and maximum cell movements. We first present a fence region handling technique to unify the fence regions and the default region. To obtain a desired cell assignment, we then propose a movement-aware cell reassignment method by iteratively reassigning cells in locally dense areas to their desired rows. After cell reassignment, a technology-aware legalization is presented to remove cell overlaps while satisfying the technology constraints. Finally, we propose a technology-aware refinement to further reduce the average and maximum cell movements without increasing the technology constraints violations. Compared with the champion of the 2017 CAD Contest at ICCAD and the state-of-the-art work, experimental results based on the 2017 CAD Contest at ICCAD benchmarks show that our algorithm achieves the best average and maximum cell movements and significantly fewer technology constraint violations, in a comparable runtime. The experimental results based on the modified 2015 ISPD Contest benchmarks also demonstrate the effectiveness of our algorithm in minimizing the average and maximum cell movements, compared with state-of-the-art mixed-cell-height legalizers. [ABSTRACT FROM AUTHOR]

Metal fill insertion has become an essential step in reducing dielectric thickness variation and improving pattern uniformity, which is important in mitigating process variations, thereby achieving better manufacturing yield. However, metal fills could induce coupling capacitance, which is not often considered in existing works that typically focus more on pattern density uniformity, incurring significant problems in timing closure. However, it is a great challenge to consider three types of capacitances (i.e., area, fringe, and lateral capacitances) with design rules and density constraints at the fill insertion stage simultaneously. This article presents an efficient timing-aware fill insertion algorithm for minimizing the total capacitance and fill amount, considering the density constraints. First, we present an initial metal fill insertion and design-rule-aware legalization to obtain an initial fill insertion solution quickly. Second, from critical conductors to powers/grounds in a circuit, we divide conductors into different equivalent paths and then construct a capacitance graph to reduce the capacitance of each equivalent path globally. Third, we propose a density-aware coupling capacitance optimization method and a fast Monte Carlo-based fill selection to further reduce the coupling capacitance between any pair of conductors. Finally, we present a density-aware fill deletion method to reduce the fill amount. We evaluate the performance of our algorithm on the benchmarks of the 2018 CAD Contest at ICCAD and its official contest evaluator. Compared with the first-place team of the contest and the state-of-the-artwork, experimental results show that our algorithm achieves the lowest total capacitance and the least fill amount in a comparable runtime. [ABSTRACT FROM AUTHOR]

Abstract: We propose a derivative-free implementation of Dekkers and Aarts’ continuous simulated annealing (SA). Essential in DFSA is the ’random direction’ local technique that we introduce. We study the convergence properties of the resulting algorithm and test its performance on a set of 50 problems. Numerical results are presented which show the robustness of the algorithm. Numerical comparisons with SA, two derivative-free simulated annealing algorithms and three population-based global optimization algorithms show that the derivative-free SA, DFSA, offers a reasonable alternative to some recent global optimization algorithms, especially for problems requiring a ‘direct search’ type algorithm. [Copyright &y& Elsevier]

Floorplanning is a crucial step in very large scale integration design flow. It provides valuable insights into the hardware decisions and estimates a floorplan with different cost metrics. In this paper, to handle a multi-objective thermal-aware non-slicing floorplanning optimization problem efficiently, an adaptive hybrid memetic algorithm is presented to optimize the area, the total wirelength, the maximum temperature and the average temperature of a chip. In the proposed algorithm, a genetic search algorithm is used as a global search method to explore the search space as much as possible, and a modified simulated annealing search algorithm is used as a local search method to exploit information in the search region. The global exploration and local exploitation are balanced by a death probability strategy. In this strategy, according to the natural mechanisms, each individual in the population is endowed with an actual age and a dynamic survival age. Experimental results on the standard tested benchmarks show that the proposed algorithm is efficient to obtain floorplans, with decreasing the average and the peak temperature. [ABSTRACT FROM AUTHOR]