Marta Jarošová

Projector preconditioning and transformation of basis in FETI-DP algorithms for contact problems

AbstractTwo strategies, using edge averages, for FETI-DP (dual-primal finite element tearing and interconnecting) methods for contact problems are considered. The first one is a preconditioning technique by a conjugate projector, where the Lagrange multipliers corresponding to the variables of the coinciding edges are aggregated. The second one is an explicit transformation of basis introducing edge averages as new, additional primal variables. It is shown that both methods iterate in the same space and thus have the same rate of convergence. The theoretical result is confirmed by the solution of a model boundary variational inequality.

Implementation of K-means segmentation algorithm on Intel Xeon Phi and GPU

In our paper actual problems of medical image processing are being solved.We present acceleration of the image segmentation algorithm and show its further possible utilization for 3D model reconstructions of human body organs.Our attention has been drawn to utilization of modern and popular Intel Xeon Phi accelerators which offer many integrated cores for computational purposes. The paper presents speed up of the k-means algorithm for image segmentation. This speed up is achieved by effective parallelization. For parallel implementation we focus on Many Integrated Core (MIC) architecture with Intel Xeon Phi coprocessors. The MIC implementation is compared with GPU, CPU and sequential implementation. To demonstrate parallel capabilities of k-means algorithm, segmentation of CT images of human body are used. Results of this work will be used for development of the software application for automatic 3D model reconstruction of heart and liver.

Efficient methods for solving the Stokes problem with slip boundary conditions

The paper deals with the Stokes flow with the threshold slip boundary conditions. A finite element approximation of the problem leads to the minimization of a non-differentiable energy functional subject to two linear equality constraints: the impermeability condition on the slip part of the boundary and the incompressibility of the fluid. Eliminating the velocity components, one gets the smooth dual functional in terms of three Lagrange multipliers. The first Lagrange multiplier regularizes the problem. Its components are subject to simple bounds. The other two Lagrange multipliers treat the impermeability and the incompressibility conditions. The last Lagrange multiplier represents the pressure in the whole domain. The solution to the dual problem is computed by an active set strategy and a path-following variant of the interior-point method. Numerical experiments illustrate computational efficiency.

Implementation of the efficient communication layer for the highly parallel total FETI and hybrid total FETI solvers

Implementation, performance, and scalability results of communication layer for Total FETI and Hybrid Total FETI solver.In HTFETI several neighboring subdomains aggregated into clusters. This reduces the size of coarse problem and improves scalability.Optimization of nearest neighbor communication - global gluing matrix.Implementation of communication hiding and avoiding techniques inside the communication layerBenchmarks - elastic 3D cube up to 1.6 billion DOF and realistic car engine benchmark.Large test executed on Total FETI to see the real potential of communication layer on smaller clusters. This paper describes the implementation, performance, and scalability of our communication layer developed for Total FETI (TFETI) and Hybrid Total FETI (HTFETI) solvers. HTFETI is based on our variant of the Finite Element Tearing and Interconnecting (FETI) type domain decomposition method. In this approach a small number of neighboring subdomains is aggregated into clusters, which results in a smaller coarse problem. To solve the original problem TFETI method is applied twice: to the clusters and then to the subdomains in each cluster.The current implementation of the solver is focused on the performance optimization of the main CG iteration loop, including: implementation of communication hiding and avoiding techniques for global communications; optimization of the nearest neighbor communication - multiplication with a global gluing matrix; and optimization of the parallel CG algorithm to iterate over local Lagrange multipliers only.The performance is demonstrated on a linear elasticity 3D cube and real world benchmarks.

Acceleration of Blender Cycles Path-Tracing Engine Using Intel Many Integrated Core Architecture

This paper describes the acceleration of the most computationally intensive kernels of the Blender rendering engine, Blender Cycles, using Intel Many Integrated Core architecture (MIC). The proposed parallelization, which uses OpenMP technology, also improves the performance of the rendering engine when running on multi-core CPUs and multi-socket servers. Although the GPU acceleration is already implemented in Cycles, its functionality is limited. Our proposed implementation for MIC architecture contains all features of the engine with improved performance. The paper presents performance evaluation for three architectures: multi-socket server, server with MIC (Intel Xeon Phi 5100p) accelerator and server with GPU accelerator (NVIDIA Tesla K20m).

Proportioning with second-order information for model predictive control

We propose an algorithm for the effective solution of quadratic programming (QP) problems arising from model predictive control (MPC). MPC is a modern multivariable control method which gives the solution for a QP problem at each sample instant. Our algorithm combines the active-set strategy with the proportioning test to decide when to leave the actual active set. For the minimization in the face, we use a direct solver implemented by the Cholesky factors updates. The performance of the algorithm is illustrated by numerical experiments, and the results are compared with the state-of-the-art solvers on benchmarks from MPC.

On conditioning of Schur complements of H-TFETI clusters for 2D problems governed by Laplacian

Bounds on the spectrum of the Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients in the analysis of many domain decomposition methods. Here we are interested in the analysis of floating clusters, i.e. subdomains without prescribed Dirichlet conditions that are decomposed into still smaller subdomains glued on primal level in some nodes and/or by some averages. We give the estimates of the regular condition number of the Schur complements of the clusters arising in the discretization of problems governed by 2D Laplacian. The estimates depend on the decomposition and discretization parameters and gluing conditions. We also show how to plug the results into the analysis of H-TFETI methods and compare the estimates with numerical experiments. The results are useful for the analysis and implementation of powerful massively parallel scalable algorithms for the solution of variational inequalities.

Detection of Orbital Floor Fractures by Principal Component Analysis

Principal component analysis (PCA) is a statistical method based on orthogonal transformation, which is used to convert possibly correlated datasets into linearly uncorrelated variables called principal components. PCA is one of the simplest methods based on the eigenvector analysis. This method is widely used in many fields, such as signal processing, quality control or mechanical engineering. In this paper, we present the use of PCA in area of medical image processing. In the medical image processing with subsequent reconstruction of 3D models, data from sources such as Computed Tomography (CT) or Magnetic Resonance Imagining (MRI) are used. Series of images representing axial slices of human body are stored in Digital Imaging and Communications in Medicine (DICOM) format. Physical properties of different body tissues are characterized by different shades of grey of each pixel correlated to the tissue density. Properties of each pixel are then used in image segmentation and subsequent creation of 3D model of human organs. Image segmentation splits digital image into regions with similar properties which are later used to create 3D model. In many cases accurate detections of edges of such objects are necessary. This could be for example the case of a tumour or orbital fracture identification. In this paper, identification of the orbital fracture using PCA method is presented as an example of application of the method in the area of medical image processing.

Implementation of hybrid total FETI (HTFETI) solver for multi-core architectures

We describe the implementation and the performance and scalability results of a hybrid FETI (Finite Element Tearing and Interconnecting) solver based on our variant of the FETI type domain decomposition method called Total FETI. In our approach a small number of neighboring subdomains is aggregated into clusters, which results into a smaller coarse problem. To solve the original problem Total FETI method is applied twice: to the clusters and then to the subdomains in each cluster.Current implementation of the solver is focused on the performance optimization of the main CG iteration loop, including: implementation of communication hiding and avoiding techniques for global communications; optimization of the nearest neighbor communication - multiplication with global gluing matrix; and optimization of the parallel CG algorithm to iterate over local Lagrange multipliers only.The performance is demonstrated on a linear elasticity synthetic 3D cube and real world benchmarks.

The stokes flow with friction

Efficient methods for solving the Stokes problem with a friction effect simulated by the slip boundary condition are developed. The dual formulation of the problem arising from the finite element approximation leads to the minimization of the strictly quadratic function with few unknowns constrained by simple bounds. Two solution algorithms highly efficient in contact solid mechanics are tested: the active set strategy and the path-following variant of the interior point method. Numerical experiments conclude the paper.