We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with transport cost homogeneous of degree one. Our algorithm is built on multilev...
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We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with transport cost homogeneous of degree one. Our algorithm is built on multilevel primal-dual algorithms. Several numerical examples and a complexity analysis are provided to demonstrate its computational speed. On some commonly used image examples of size 512 x 512, the proposed algorithm gives solutions within 0.2 similar to 1.5 seconds on a single CPU, which is much faster than the state-of-the-art algorithms.
In this paper, we are concerned with the weighted plane wave least-squares (PWLS) method for three-dimensional Helmholtz equations, and develop the multi-level adaptive BDDC algorithms for solving the resulting discre...
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In this paper, we are concerned with the weighted plane wave least-squares (PWLS) method for three-dimensional Helmholtz equations, and develop the multi-level adaptive BDDC algorithms for solving the resulting discrete system. In order to form the adaptive coarse components, the local generalized eigenvalue problems for each common face and each common edge are carefully designed. The condition number of the two-level adaptive BDDC preconditioned system is proved to be bounded above by a user-defined tolerance and a constant which is dependent on the maximum number of faces and edges per subdomain and the number of subdomains sharing a common edge. The efficiency of these algorithms is illustrated on a benchmark problem. The numerical results show the robustness of our two-level adaptive BDDC algorithms with respect to the wave number, the number of subdomains and the mesh size, and illustrate that our multi-level adaptive BDDC algorithm can reduce the scale of the coarse problem and can be used to solve large wave number problems efficiently. (C) 2020 Elsevier B.V. All rights reserved.
We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications. The Collection is widely used by the numerical linear algebra commun...
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We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications. The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms. It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats. Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs). We provide software for accessing and managing the Collection, from MATLAB(TM), Mathematica(TM), Fortran, and C, as well as an online search capability. Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task.
This special issue contains a selection of papers from the Sixth International Workshop on the Numerical Solution of Markov Chains, held in Williamsburg, Virginia on September 16-17, 2010. The papers cover a broad ran...
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This special issue contains a selection of papers from the Sixth International Workshop on the Numerical Solution of Markov Chains, held in Williamsburg, Virginia on September 16-17, 2010. The papers cover a broad range of topics including perturbation theory for absorbing chains, bounding techniques, steady-state and transient solution methods, multilevel algorithms, preconditioning, and applications. Copyright (C) 2011 John Wiley & Sons, Ltd.
We present Glimmer, a new multilevel algorithm for multidimensional scaling designed to exploit modern graphics processing unit (GPU) hardware. We also present GPU-SF, a parallel force-based subsystem used by Glimmer....
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We present Glimmer, a new multilevel algorithm for multidimensional scaling designed to exploit modern graphics processing unit (GPU) hardware. We also present GPU-SF, a parallel force-based subsystem used by Glimmer. Glimmer organizes input into a hierarchy of levels and recursively applies GPU-SF to combine and refine the levels. The multilevel nature of the algorithm makes local minima less likely, while the GPU parallelism improves the speed of computation. We propose a robust termination condition for GPU-SF based on a filtered approximation of the normalized stress function. We demonstrate the benefits of Glimmer in terms of speed, normalized stress, and visual quality against several previous algorithms for a range of synthetic and real benchmark data sets. We also show that the performance of Glimmer on GPUs is substantially faster than a CPU implementation of the same algorithm.
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