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An approach to accelerating a parallel domain decomposition (DD) solver by graphics processing units (GPUs) is investigated. The solver is based on the Balancing Domain Decomposition Method by Constraints (BDDC), which is a nonoverlapping DD technique. Two kinds of local matrices are required by BDDC. First, dense matrices corresponding to local Schur complements of interior unknowns are constructed by the sparse direct solver. These are further used as part of the local saddle-point problems within BDDC. In the next step, the local matrices are copied to GPUs. Repeated multiplications of local vectors with the dense matrix of the Schur complement are performed for each subdomain. In addition, factorizations and backsubstitutions with the dense saddle-point subdomain matrices are also performed on GPUs. Detailed times of main components of the algorithm are measured on a benchmark Poisson problem. The method is also applied to an unsteady problem of incompressible flow, where the Krylov subspace iterations are performed repeatedly in each time step. The results demonstrate the potential of the approach to speed up realistic simulations up to 5 times with a preference towards large subdomains. [ABSTRACT FROM AUTHOR]

A general multi-purpose data structure for an efficient representation of conforming unstructured homogeneous meshes for scientific computations on CPU and GPU-based systems is presented. The data structure is provided as open-source software as part of the TNL library (https://tnl-project.org/). The abstract representation supports almost any cell shape and common 2D quadrilateral, 3D hexahedron and arbitrarily dimensional simplex shapes are currently built into the library. The implementation is highly configurable via templates of the C++ language, which allows avoiding the storage of unnecessary dynamic data. The internal memory layout is based on state-of-the-art sparse matrix storage formats, which are optimized for different hardware architectures in order to provide high-performance computations. The proposed data structure is also suitable for meshes decomposed into several subdomains and distributed computing using the Message Passing Interface (MPI). The efficiency of the implemented data structure on CPU and GPU hardware architectures is demonstrated on several benchmark problems and a comparison with another library. Its applicability to advanced numerical methods is demonstrated with an example problem of two-phase flow in porous media using a numerical scheme based on the mixed-hybrid finite element method (MHFEM). We show GPU speed-ups that rise above 20 in 2D and 50 in 3D when compared to sequential CPU computations, and above 2 in 2D and 9 in 3D when compared to 12-threaded CPU computations. [ABSTRACT FROM AUTHOR]

Starting from the matrix elements of a nucleon-nucleon potential operator provided in a basis of spherical harmonic oscillator functions, we present an algorithm for expressing a given potential operator in terms of irreducible tensors of the SU(3) and SU(2) groups. Further, we introduce a GPU-based implementation of the latter and investigate its performance compared with a CPU-based version of the same. We find that the CUDA implementation delivers speedups of 2.27x – 5.93x. [ABSTRACT FROM AUTHOR]

In this paper we propose a method for locally adjusted optical flow-based registration of multimodal images, which uses the segmentation of object of interest and its representation by the signed-distance function (OF method). We deal with non-rigid registration of the image series acquired by the Modiffied Look-Locker Inversion Recovery (MOLLI) magnetic resonance imaging sequence, which is used for a pixel-wise estimation of relaxation time. The spatial registration of the images within the series is necessary to compensate the patient's imperfect breath-holding. The evolution of intensities and a large variation of image contrast within the MOLLI image series, together with the myocardium of left ventricle (the object of interest) typically not being the most distinct object in the scene, makes the registration challenging. The paper describes all components of the proposed OF method and their implementation. The method is then compared to the performance of a standard mutual information maximization-based registration method, applied either to the original image (MIM) or to the signed-distance function (MIM). Several experiments with synthetic and real MOLLI images are carried out. On synthetic image with a single object, MIM performed the best, while OF and MIM provided better results on synthetic images with more than one object and on real images. When applied to signed-distance function of two objects of interest, MIM provided a larger registration error, but more homogeneously distributed, compared to OF. For the real MOLLI image series with left ventricle pre-segmented using a level-set method, the proposed OF registration performed the best, as is demonstrated visually and by measuring the increase of mutual information in the object of interest and its neighborhood. [ABSTRACT FROM AUTHOR]

We apply the importance-truncation procedure in the framework of the ab initio symmetry-adapted no-core shell model. We study efficacy of this new method for the description of energies and E2 transitions of the ground-state rotational band in 12C. We demonstrate that the coupling SU(3)-scheme basis with the perturbative relevance estimate leads to a dramatic reduction in dimensionality of the nuclear eigenvalue problem. [ABSTRACT FROM AUTHOR]

The article provides a brief overview of a one-dimensional model of two-phase ow in the geometry of a circulating uidized bed combustor exhibiting vertical variability of cross-section. The model is based on numerical solution of conservation laws for mass, momentum and energy of gas and solid components of the uidized-bed system by means of the finite-volume method in space and of a multistep higher-order solver in time. The presented computational results reproduce characteristic behavior of uidized beds in the given geometry. [ABSTRACT FROM AUTHOR]

We present the CUDA implementation of the parallel multigrid solver for the linear complementarity problem. As a smoother, the Projected SOR method is used. We describe implementation of all parts of the multigrid cycle on GPU. We explain, what specific properties of the GPU must be taken into account during the parallelization. The efficiency of the final algorithm is demonstrated on the constrained level-set method used in image segmentation. For this task, the speed-up up to 3 was achieved on Nvidia GeForce GTX 480 compared to more expensive 12 core AMD Opteron. [ABSTRACT FROM AUTHOR]

The necessity of using non-Newtonian models for hemodynamics in geometries mimicking large vessels is investigated. Phase-contrast magnetic resonance imaging (PC-MRI) measurements are performed on a specially-designed phantom representing the aorta while using several types of fluids. These measurements are compared against the results of the lattice Boltzmann method (LBM) computational fluid dynamics (CFD) simulator in 3D. On the phantom side, two types of non-Newtonian fluids (water-based solutions of glycerine with xanthan gum and sucrose with xanthan gum) and Newtonian fluid (clear water) are used in the experiments; three different acrylic plates are inserted to represent aortic stenosis of varying degrees; and two constant flow regimes with high and low flow rates are used. The CFD simulations in the geometry and inflow boundary conditions corresponding to each experiment are performed both with non-Newtonian and Newtonian approaches. Additionally, the accuracy of the PC-MRI flow measurements is assessed and discussed with respect to the known PC-MRI flow underestimation due to turbulence. Based on the type of stenosis and inflow rate, the results indicate that the Newtonian models produce comparable results with the experimentally acquired data, which is in favor of overall less expensive Newtonian models. [ABSTRACT FROM AUTHOR]