A low complexity scaling method for the Lanczos Kernel in fixed-point arithmetic

We consider the problem of enabling fixed-point implementation of linear algebra kernels on low-cost embedded systems, as well as motivating more efficient computational architectures for scientific applications. Fixed-point arithmetic presents additional design challenges compared to floating-point arithmetic, such as having to bound peak values of variables and control their dynamic ranges. Algorithms for solving linear equations or finding eigenvalues are typically nonlinear and iterative, making solving these design challenges a nontrivial task. For these types of algorithms, the bounding problem cannot be automated by current tools. We focus on the Lanczos iteration, the heart of well-known methods such as conjugate gradient and minimum residual. We show how one can modify the algorithm with a low-complexity scaling procedure to allow us to apply standard linear algebra to derive tight analytical bounds on all variables of the process, regardless of the properties of the original matrix. It is shown that the numerical behavior of fixed-point implementations of the modified problem can be chosen to be at least as good as a floating-point implementation, if necessary. The approach is evaluated on field-programmable gate array (FPGA) platforms, highlighting orders of magnitude potential performance and efficiency improvements by moving form floating-point to fixed-point computation

High level synthesis FPGA implementation of the Jacobi algorithm to solve the Eigen problem

We present a hardware implementation of the Jacobi algorithm to compute the eigenvalue decomposition (EVD). The computation of eigenvalues and eigenvectors has many applications where real time processing is required, and thus hardware implementations are often mandatory. Some of these implementations have been carried out with field programmable gate array (FPGA) devices using low level register transfer level (RTL) languages. In the present study, we used the Xilinx Vivado HLS tool to develop a high level synthesis (HLS) design and evaluated different hardware architectures. After analyzing the design for different input matrix sizes and various hardware configurations, we compared it with the results of other studies reported in the literature, concluding that although resource usage may be higher when HLS tools are used, the design performance is equal to or better than low level hardware designs. © 2015 Ignacio Bravo et al

Custom optimization algorithms for efficient hardware implementation

The focus is on real-time optimal decision making with application in advanced control systems. These computationally intensive schemes, which involve the repeated solution of (convex) optimization problems within a sampling interval, require more efficient computational methods than currently available for extending their application to highly dynamical systems and setups with resource-constrained embedded computing platforms. A range of techniques are proposed to exploit synergies between digital hardware, numerical analysis and algorithm design. These techniques build on top of parameterisable hardware code generation tools that generate VHDL code describing custom computing architectures for interior-point methods and a range of first-order constrained optimization methods. Since memory limitations are often important in embedded implementations we develop a custom storage scheme for KKT matrices arising in interior-point methods for control, which reduces memory requirements significantly and prevents I/O bandwidth limitations from affecting the performance in our implementations. To take advantage of the trend towards parallel computing architectures and to exploit the special characteristics of our custom architectures we propose several high-level parallel optimal control schemes that can reduce computation time. A novel optimization formulation was devised for reducing the computational effort in solving certain problems independent of the computing platform used. In order to be able to solve optimization problems in fixed-point arithmetic, which is significantly more resource-efficient than floating-point, tailored linear algebra algorithms were developed for solving the linear systems that form the computational bottleneck in many optimization methods. These methods come with guarantees for reliable operation. We also provide finite-precision error analysis for fixed-point implementations of first-order methods that can be used to minimize the use of resources while meeting accuracy specifications. The suggested techniques are demonstrated on several practical examples, including a hardware-in-the-loop setup for optimization-based control of a large airliner.Open Acces

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Error assessment in structural transient dynamics

This paper presents in a unified framework the most representative state-of-the-art techniques on a posteriori error assessment for second order hyperbolic problems, i.e., structural transient dynamics. For the sake of presentation, the error estimates are grouped in four types: recovery-based estimates, the dual weighted residual method, the constitutive relation error method and error estimates for timeline-dependent quantities of interest. All these methodologies give a comprehensive overview on the available error assessment techniques in structural dynamics, both for energy-like and goal-oriented estimates

Computer Science Research Institute 2004 annual report of activities.

This report summarizes the activities of the Computer Science Research Institute (CSRI) at Sandia National Laboratories during the period January 1, 2004 to December 31, 2004. During this period the CSRI hosted 166 visitors representing 81 universities, companies and laboratories. Of these 65 were summer students or faculty. The CSRI partially sponsored 2 workshops and also organized and was the primary host for 4 workshops. These 4 CSRI sponsored workshops had 140 participants--74 from universities, companies and laboratories, and 66 from Sandia. Finally, the CSRI sponsored 14 long-term collaborative research projects and 5 Sabbaticals

Application of PEEC modeling for the development of a novel multi-gigahertz test interface with fine pitch wafer level package

Ph.DDOCTOR OF PHILOSOPH

WOFEX 2021 : 19th annual workshop, Ostrava, 1th September 2021 : proceedings of papers

The workshop WOFEX 2021 (PhD workshop of Faculty of Electrical Engineer-ing and Computer Science) was held on September 1st September 2021 at the VSB – Technical University of Ostrava. The workshop offers an opportunity for students to meet and share their research experiences, to discover commonalities in research and studentship, and to foster a collaborative environment for joint problem solving. PhD students are encouraged to attend in order to ensure a broad, unconfined discussion. In that view, this workshop is intended for students and researchers of this faculty offering opportunities to meet new colleagues.Ostrav

Error assessment and adaptivity for structural transient dynamics

The finite element method is a valuable tool for simulating complex physical phenomena. However, any finite element based simulation has an intrinsic amount of error with respect to the exact solution of the selected physical model. Being aware of this error is of notorious importance if sensitive engineering decisions are taken on the basis of the numerical results. Assessing the error in elliptic problems (as structural statics) is a well known problem. However, assessing the error in structural transient dynamics is still ongoing research. The present thesis aims at contributing on error assessment techniques for structural transient dynamics. First, a new approach is introduced to compute bounds of the error measured in some quantity of interest. The proposed methodology yields error bounds with better quality than the already available approaches. Second, an efficient methodology to compute approximations of the error in the quantity of interest is introduced. The proposed technique uses modal analysis to compute the solution of the adjoint problem associated with the selected quantity of interest. The resulting error estimate is very well suited for time-dependent problems, because the cost of computing the estimate at each time step is very low. Third, a space-time adaptive strategy is proposed. The local error indicators driving the adaptive process are computed using the previously mentioned modal-based error estimate. The resulting adapted approximations are more accurate than the ones obtained with an straightforward uniform mesh refinement. That is, the adapted computations lead to lower errors in the quantity of interest than the non-adapted ones for the same number of space-time elements. Fourth, a new type of quantities of interest are introduced for error assessment in time-dependent problems. These quantities (referred as timeline-dependent quantities of interest) are scalar time-dependent outputs of the transient solution and are better suited to time-dependent problems than the standard scalar ones. The error in timeline-dependent quantities is eficiently assessed using the modal-based description of the adjoint solution. The thesis contributions are enclosed in five papers which are attached to the thesis document.El mètode dels elements finits és una eina valuosa per a simular fenòmens físics complexos. Tot i això, aquest mètode només proporciona aproximacions de la solució exacta del model físic considerat. Per tant, quantificar l'error comés en l'aproximació és important si la simulació numèrica s'utilitza per a prendre decisions que poden tenir importants conseqüències. Actualment, les eines que permeten avaluar aquest error són ben conegudes per a problemes estacionaris, però encara presenten importants limitacions per a problemes transitoris com la dinàmica d'estructures. L'objectiu d'aquest treball és contribuir a millorar les tècniques existents per estimar l'error en dinàmica d'estructures i proposar-ne de noves. La primera contribució és una nova metodologia per a calcular cotes de l'error en una quantitat d'interès del problema. Les cotes proposades són més precises i proporcionen una millor estima de l'error que les cotes calculades amb tècniques prèvies. La segona contribució és una una nova tècnica que proporciona aproximacions de l'error en una quantitat d'interès utilitzant càlculs eficients. La novetat principal d'aquesta proposta és aproximar la solució del problema adjunt associat a la quantitat d'interès utilitzant l'anàlisi modal. El resultat és un estimador de l'error indicat particularment per a problemes transitoris, ja que el cost de calcular l'estimador a cada pas de temps és molt baix. La tercera contribució és una tècnica que permet construir de manera adaptada tant la discretizació temporal com espacial amb l'objectiu de millorar l'eficiència de la simulació. Aquesta tècnica es basa en la informació proporcionada per l'estima de l'error amb anàlisi modal. Les aproximacions calculades utilitzant les discretitzacions adaptades són més precises que les obtingudes amb un simple refinament uniforme de la malla de càlcul. És a dir, les discretitzacions adaptades proporcionen un error en la quantitat d'interès menor que les discretizacions no adaptades per al mateix nombre d'elements espai-temps. Finalment, la quarta contribució és un nou tipus de quantitats d'interès especialment indicades per a estimar l'error en problemes transitoris. Aquest nou tipus de quantitats són funcions escalars dependents del temps que proporcionen una informació més completa sobre l'error en problemes transitoris que les quantitats d'interès estàndard. L'error en aquestes noves quantitats és estimat eficientment utilitzant la descripció modal de la solució del problema adjunt. Les contribucions d'aquest treball es troben recopilades en cinc articles que s'inclouen adjunts en el document de la tesi