Estimation of execution parameters takes centre stage in automatic offloading of complex biomedical workflows to cloud and high performance facilities. Since ordinary users have no or very limited knowledge of the performance characteristics of particular tasks in the workflow, the scheduling system has to have the capabilities to select appropriate amount of compute resources, e.g., compute nodes, GPUs, or processor cores and estimate the execution time and cost. The presented approach considers a fixed set of executables that can be used to create custom workflows, and collects performance data of successfully computed tasks. Since the workflows may differ in the structure and size of the input data, the execution parameters can only be obtained by searching the performance database and interpolating between similar tasks. This paper shows it is possible to predict the execution time and cost with a high confidence. If the task parameters are found in the performance database, the mean interpolation error stays below 2.29%. If only similar tasks are found, the mean interpolation error may grow up to 15%. Nevertheless, this is still an acceptable error since the cluster performance may vary on order of percent as well.
In a simple undirected graph, we introduce a special connectedness induced by a set of paths of length 2. We focus on the 8-adjacency graph (with the vertex set ℤ^2 ) and study the connectedness induced by a certain set of paths of length 2 in the graph. For this connectedness, we prove a digital Jordan curve theorem by determining the Jordan curves, i.e., the circles in the graph that separate ℤ^2 into exactly two connected components. These Jordan curves are shown to have an advantage over those given by the Khalimsky topology on ℤ^2 .
The rapid development of novel procedures in medical ultrasonics, including treatment planning in therapeutic ultrasound and image reconstruction in photoacoustic tomography, leads to increasing demand for large-scale ultrasound simulations. However, routine execution of such simulations using traditional methods, e.g., finite difference time domain, is expensive and often considered intractable due to the computational and memory requirements. The k-space corrected pseudospectral time domain method used by the k-Wave toolbox allows for significant reductions in spatial and temporal grid resolution. These improvements are achieved at the cost of all-to-all communication, which are inherent to the multi-dimensional fast Fourier transforms. To improve data locality, reduce communication and allow efficient use of accelerators, we recently implemented a domain decomposition technique based on a local Fourier basis. In this paper, we investigate whether it is feasible to run the distributed k-Wave implementation on the Salomon cluster equipped with 864 Intel Xeon Phi (Knight’s Corner) accelerators. The results show the immaturity of the KNC platform with issues ranging from limited support of Infiniband and LustreFS in Intel MPI on this platform to poor performance of 3D FFTs achieved by Intel MKL on the KNC architecture. Yet, we show that it is possible to achieve strong and weak scaling comparable to CPU-only platforms albeit with the runtime 1.8× to 4.3× longer. However, the accounting policy for Salomon’s accelerators is far more favorable and thus their employment reduces the computational cost significantly.
The behavior of a parallel application can be presented in many ways, but performance visualization tools usually focus on communication graphs and runtime of processes or threads in specific (groups of) functions. A different approach is required when searching for the optimal configuration of tunable parameters, for which it is necessary to run the application several times and compare the resource consumption of these runs. We present RADAR visualizer, a tool that was originally developed to analyze such measurements and to detect the optimal configuration for each instrumented part of the code. In this case, the optimum was defined as the minimum energy consumption of the whole application, but any other metric can be defined. RADAR visualizer presents the application behavior in several graphical representations and tables including the amount of savings that can be reached. Together with our MERIC library, we provide a complete toolchain for HPC application behavior monitoring, data analysis, and graphical representation. The final part is performing dynamic tuning (applying optimal settings for each region during the application runtime) for the production runs of the analyzed application.
It is expected that with the appearance of exascale supercomputers the mean time between failure in supercomputers will decrease. Classical checkpoint-restart approaches are too expensive at that scale. Local-failure local-recovery (LFLR) strategies are an option that promises to leverage the costs, but actually implementing it into any sufficiently large simulation environment is a challenging task. In this paper we discuss how LFLR methods can be incorporated in a PDE framework, focussing at the linear solvers as the innermost component. We discuss how Krylov solvers can be modified to support LFLR, and present numerical tests. We exemplify our approach by reporting on the implementation of these features in the Dune framework, present C++ software abstractions, which simplify the incorporation of LFLR techniques and show how we use these in our solver library. To reduce the memory costs of full remote backups, we further investigate the benefits of lossy compression and in-memory checkpointing.
Datacenters are at the heart of the AI, Industry 4.0 and cloud revolution. A datacenter contains a large number of computing nodes hosted in a large temperature-controlled room. Due to the increasing total power and power density of computing nodes, the overall datacenter compute capacity is often capped by peak power consumption and temperature bottlenecks. To preserve the homogeneous performance assumption between all the nodes, complex cooling solution are required, but they might not be sufficient. In this work, we analysed and characterised the thermal properties of a Tier0 datacenter deploying advanced hybrid cooling technologies: specifically, we studied the spatial and temporal heterogeneity during production and cooling emergency hazards. This paper gives first quantitative evidence of thermal bottlenecks in real-life production workload, showing the presence of significant spatial thermal heterogeneity which could be exploited by thermal-aware job scheduling and datacenter-room run-time workload adaptation and distribution.
We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered directional multi-level approximation of the Helmholtz kernel can be applied even on high-frequency levels efficiently. We provide a detailed analysis of the almost linear asymptotic complexity of the presented method. Our numerical experiments are in good agreement with the provided theory.
Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain’s boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices corresponding to the integral operators requires efficient algorithms. This article describes two approaches that allow us to solve boundary element equations on surface meshes consisting of several millions of triangles while preserving the optimal convergence rates of the Galerkin discretization.
Amorphous solids, like metallic glasses, exhibit an excess of low frequency vibrational states reflecting the break-up of sound due to the strong structural disorder inherent to these materials. Referred to as the boson peak regime of frequencies, how the corresponding eigenmodes relate to the underlying atomic-scale disorder remains an active research topic. In this paper we investigate the use of a polynomial filtered eigensolver for the computation and study of low frequency eigenmodes of a Hessian matrix located in a specific interval close to the boson peak regime. A distributed-memory parallel implementation of a polynomial filtered eigensolver is presented. Our implementation, based on the Trilinos framework, is then applied to a Hessian matrix of an atomistic bulk metallic glass structure derived from a molecular dynamics simulation for the computation of eigenmodes close to the boson peak. In addition, we study the parallel scalability of our implementation on multicore nodes. Our resulting calculations successfully concur with previous atomistic results, and additionally demonstrate a broad cross-over of boson peak frequencies within which sound is seen to break-up.
Cranial orthoses are used to correct an abnormal children head shape, and such they have to be designed individually. Customization of those orthoses is currently fully manual task. A software tool should make this process semi-automatic with only small intervention from the user and speed up the whole process. In the future, this tool will be part of the process chain from 3D scanning of the patient head to the 3D printing of the final product. This will allow to produce the orthosis anywhere, without necessity to have expensive devices on one place. For high quality of 3D printing, 3D computer models with high-resolution meshes must be used. We have started development of our tool by rapid testing of methodology. For this purpose we used open source software Blender. Although Blender’s functions we used are more robust, they are also unnecessary computationally more expensive. For this reason we have implemented the necessary transformation functions using radial basis functions (RBF) which can be easily modified to include rigid body movements.
This paper introduces two tools for manual energy evaluation and runtime tuning developed at IT4Innovations in the READEX project. The MERIC library can be used for manual instrumentation and analysis of any application from the energy and time consumption point of view. Besides tracing, MERIC can also change environment and hardware parameters during the application runtime, which leads to energy savings. MERIC stores large amounts of data, which are difficult to read by a human. The RADAR generator analyses the MERIC output files to find the best settings of evaluated parameters for each instrumented region. It generates a report and a MERIC configuration file for application production runs.
Despite the fact that biotechnology with microalgae is attracting a lot of research interest since 1950s, a reliable computational tool for simulation of microalgal bioreactors is still lacking. In this work, a unified multidisciplinary modeling framework for microalgae culture systems is presented. Our framework consists of the model of microalgae growth in form of advection-diffusion-reaction system within a phenomenological model of photosynthesis and photoinhibition. The fluid dynamics is described by the Navier-Stokes equations and the irradiance field inside a reactor closes the equation system. The main achievement resides in successful integration of computational fluid dynamics code ANSYS Fluent and reaction kinetics, which makes our approach reliable and simple to implement. As a case study, the simulation of microalgae growth in a Couette-Taylor bioreactor is presented. The bioreactor operation leads to hydrodynamically induced fluctuating light conditions and the flashing light enhancement phenomenon, known from experiments. The presented model thus exhibits features of a real system.
This study deals with the problem of optimal setting of experimental design variables, which controls the accuracy of the numerical process of determining model parameters from data. Our approach, although case independent, is formulated as an inverse problem of a diffusion coefficient estimation using the FRAP (Fluorescence Recovery After Photobleaching) experimental technique. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this idea, we optimize an experimental design factor being the initial concentration of some particles. Numerical experiments on a 2D finite domain show that the discretized optimal initial condition attains only two values representing the existence or non-existence of diffusive particles. The number of jumps between these values determines the connectivity (or the bleaching pattern) and is dependent on the value of a diffusion coefficient, e. g., the annulus shaped initial condition is better than a disc for some specific range of model parameters.
Stencil calculations and matrix-free Krylov subspace solvers represent important components of many scientific computing applications. In these solvers, stencil applications are often the dominant part of the computation; an efficient parallel implementation of the kernel is therefore crucial to reduce the time to solution. Inspired by polynomial preconditioning, we remove upper bounds on the arithmetic intensity of the Krylov subspace building block by replacing the matrix with a higher-degree matrix polynomial. Using the latest state-of-the-art stencil compiler programs with temporal blocking, reduced memory bandwidth usage and, consequently, better utilization of SIMD vectorization and thus speedup on modern hardware, we are able to obtain performance improvements for higher polynomial degrees than simpler cache-blocking approaches have yielded in the past, demonstrating the new appeal of polynomial techniques on emerging architectures. We present results in a shared-memory environment and an extension to a distributed-memory environment with local shared memory.
Two proportionality based gradient methods for the solution of large convex bound constrained quadratic programming problems, MPRGP (Modified Proportioning with Reduced Gradient Projections) and P2GP (Proportionality-based Two-phase Gradient Projection) are presented and applied to the solution of auxiliary problems in the inner loop of an augmented lagrangian algorithm called SMALBE (Semi-monotonic Augmented Lagrangian for Bound and Equality constraints). The SMALBE algorithm is used to generate the Lagrange multipliers for the equality constraints. The performance of the algorithms is tested on the solution of the discretized contact problems by means of TFETI (Total Finite Element Tearing and Interconnecting).
The contribution focuses on the estimation of material parameters on subdomains with given material interfaces in the Darcy flow problem. For the estimation, we use the Bayesian approach, which incorporates the natural uncertainty of measurements. The main interest of this contribution is to describe the posterior distribution of material parameters using samples generated by the Metropolis-Hastings method. This method requires a large number of direct problem solutions, which is time-consuming. We propose a combination of the standard direct solutions with sampling from the stochastic Galerkin method (SGM) solution. The SGM solves the Darcy flow problem with random parameters as additional problem dimensions. This leads to the solution in the form of a function of both random variables and space variables, which is computationally expensive to obtain, but the samples are very cheap. The resulting sampling procedure is applied to a model groundwater flow inverse problem as an alternative to the existing deterministic approach.
This paper deals with the novel PermonSVM machine learning tool. PermonSVM is a part of our PERMON toolbox. It implements the linear two-class Support Vector Machines. PermonSVM is built on top of PermonQP (PERMON module for quadratic programming) which in turn uses PETSc. The main advantage of PermonSVM is that it is parallel. The parallelism comes from a distribution of matrices and vectors. The MPRGP algorithm, implemented in PermonQP, is used as a solver of the quadratic programming problem arising from the dual SVM formulation. The scalability of MPRGP was proven in problems of mechanics with more than billion of unknowns solved on tens of thousands of cores. Apart from the scalability of our approach, we also investigate the relations between training rate, hyperplane margin, the value of the dual functional, and the norm of the projected gradient.
We introduce an efficient method for computing the Stekloff eigenvalues associated with the indefinite Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition repeatedly. We propose solving the discretized problem with Fast Fourier Transform (FFT) based on carefully designed extensions and restrictions operators. The proposed Fourier method, combined with proper eigensolver, results in an efficient and easy approach for computing the Stekloff eigenvalues.
Krylov subspace methods based on short recurrences such as CGL or MINRES represent an attractive way of solving large and sparse systems of linear algebraic equations. Loss of orthogonality in the underlying Lanczos process delays significantly their convergence in finite-precision computation, whose connection to exact computation is still not fully understood. In this paper, we exploit the idea of simultaneous comparison of finite-precision and exact computations for CGL and MINRES, by taking advantage of their relationship valid also in finite-precision arithmetic. In particular, we show that finite-precision CGL residuals and Lanczos vectors have to be aggregated over the intermediate iterations to form a counterpart to vectors from the exact computation. Influence of stagnation in exact MINRES computation is also discussed. Obtained results are supported by numerical experiments.
