Scientific Subroutine Research Articles

Hydraulic Transient Prevention with Dipping Tube Hydropneumatic Tank

The dipping tube hydropneumatic tank is one of the most efficient equipments to prevent water hammer in water distribution and long distance transmission pipe systems. Due to its low costs and easy to maintain features, dipping tube hydropneumatic tank has many irreplaceable advantages, however it is difficult to determine the correct size and gas volume for real world engineering applications. This paper presents a robust method to solve the problems from theory and application. Based on the Method of Characteristics (MOC) equations, this paper derives the equations for modeling dipping tube hydropneumatic tanks in water distribution systems to prevent water hammer. The equations include MOC, differential orifice head loss equation, gas law, air mass, air velocity and etc. The IBMs scientific subroutine package (SSP) is applied to solve the equations by deriving to the form of X=f (X). The method has been integrated into HAMMER. This paper also presents an example to illustrate the methods of determining the tank size, and the comparison results with sealed hydropneumatic tank and surge tank equipment.

Optimizing matrix transposes using a POWER7 cache model and explicit prefetching

We consider the problem of efficiently computing matrix transposes on the POWER7 architecture. We develop a matrix transpose algorithm that uses cache blocking, cache prefetching and data alignment. We model the POWER7 data cache and memory concurrency and use the model to predict the memory throughput of the proposed matrix transpose algorithm. The performance of our matrix transpose algorithm is up to five times higher than that of the dgetmo routine of the Engineering and Scientific Subroutine Library and is 2.5 times higher than that of the code generated by compiler-inserted prefetching. Numerical experiments indicate a good agreement between the predicted and the measured memory throughput.

Program for calculating SU(4) Clebsch–Gordan coefficients

The SU(4) Clebsch–Gordan coefficients of the decomposition { N a } ⊗ { N b } → { N } are calculated for arbitrary irreducible representations { N a } , { N b } and { N } . They are efficiently computed for the group chain SU(4) ⊃ SU(3)×U(1) ⊃ SU(2)×U(1) ⊃ U(1) using the eigenfunction method along with recurrence relations. Program summary Program title: CGSU4 Catalogue identifier: AEBL_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEBL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2847 No. of bytes in distributed program, including test data, etc.: 23 794 Distribution format: tar.gz Programming language: Fortran 95 Computer: Personal computer Operating system: Linux, Windows RAM: 2 MB Classification: 4.2 Subprograms used: ACRM_v1_0; Title: SU(3) [1] Nature of problem: The SU(4) Clebsch–Gordan coefficients according to the group chain SU(4) ⊃ SU(3) × U(1) ⊃ SU(2) × U(1) ⊃ U(1) are calculated for arbitrary couplings. Solution method: The eigenfunctions method in combination with recurrence relations is used to generate tables of the SU(4) ⊃ SU(3) × U(1) isoscalar factors for the decomposition { N a } ⊗ { N b } → { N } γ with the multiplicity label γ. The SU(4) Clebsch–Gordan coefficients are then composed by these isoscalar factors and SU(3) Clebsch–Gordan coefficients according to the Racah factorization lemma. Restrictions: The dimensions of the involved representations are limited by the size of the arrays defined in the program. Additional comments: If many Clebsch–Gordan coefficients are needed for the same decomposition { N a } ⊗ { N b } → { N } γ , the running time is significantly reduced if the table of isoscalar factors is calculated only once. The SU(3) code [1] and the code for eigen, a matrix diagonalization program (IBM scientific subroutine package) are included in the CGSU4 code package. Running time: The running time sensitively depends on the specific Clebsch–Gordan decomposition and the dimensions of the involved representations, varying from parts of a second to a minute.

A parallel approach to STAP implementation for fMRI data

To exploit the capabilities of parallel processing in applying the space-time adaptive processing (STAP) algorithm, previously explored on a small scale for functional magnetic resonance imaging (fMRI) applications, to conventional size fMRI data sets. STAP is a two-dimensional filter that is able to locate fMRI activations in both space and frequency. It is applied here for the construction of brain activation maps in fMRI using Visual Age C, incorporating Engineering and Scientific Subroutine Library (ESSL) functions, compiled in 64-bit, and executed on an IBM SP supercomputer. Computer simulations incorporating actual MRI noise indicate that STAP, incorporated using the method of steepest descent, is feasible on conventional size data sets and exhibits an improvement in detecting activations over the more traditional cross correlation method of fMRI analysis when the response is unknown. STAP is feasible on traditional size fMRI data sets and useful in elucidating spatial and temporal connectivity.

WinSAAM: application and explanation of use.

The WinSAAM modeling software is an integrated package of mathematical, simula-tion, and graphical tools for analysis of biokinetic data. WinSAAM is the Windows version of SAAM, the Simulation, Analysis, and Modeling computer program. SAAM, a collection of scientific subroutines, was created in the 1950s by Dr. Mones Berman to meet the mathematical needs of his research program. Over the decades, SAAM has been continually developed and enhanced (Berman and Weiss, 1978; Boston et al., 1981), and today, WinSAAM is an elegant and powerful tool for mathematical and compartmental modeling.

INTEGRAL TRANSFORM ANALYSIS OF MULTIDIM ENSIONAL EIGENVALUE PROBLEMS WITHIN IRREGULAR DOMAINS

The generalized integral transform technique (GITT) is employed in obtaining formal solutions for eigenvalue problems of the Sturm-Liouville type, described by multidimensional partial differential models within irregularly shaped domains. The successive elimination of independent variables in the appropriate order through integral transformations produces the associated algebraic eigenvalue problem, which is then readily solved by algorithms from scientific subroutine libraries. A representative example of the known exact solution is presented, of particular interest to the field of heat and mass diffusion, for validation purposes.

The design, implementation, and evaluation of a symmetric banded linear solver for distributed-memory parallel computers

This article describes the design, implementation, and evaluation of a parallel algorithm for the Cholesky factorization of symmetric banded matrices. The algorithm is part of IBM's parallel engineering and scientific subroutine library version 1.2 and is compatible with ScaLAPACK's banded solver. Analysis, as well as experiments on an IBM SP2 distributed-memory parallel computer, shows that the algorithm efficiently factors banded matrices with wide bandwidth. For example, a 31-mode SP2 factors a large matrix more than 16 times faster than a single node would factor it using the best sequential algorithm, and more than 20 times faster than a single node would using LAPACK's DPBTRF. The algorithm uses novel ideas in the area of distributed dense-matrix computations that include the use of a dynamic schedule for a blocked systolic-like algorithm and the separation of the input and output layouts from the layout the algorithm uses internally. The algorithm alson uses known techniques such as blocking to improve its communication-to-computation ratio and its data-cache behavior.

Integral transformation of elliptic problems within irregular domains

Employs the integral transform method in the hybrid numerical‐analytical solution of fully developed laminar flow within a class of irregularly shaped ducts, with respect to the co‐ordinate system chosen to represent the geometry under consideration. A quite general formulation of a two‐dimensional steady‐state diffusion problem is initially considered, and a formal solution is provided. The original partial differential equation is analytically transformed into an infinite system of ordinary differential equations for the transformed velocity field in the flow direction. On truncation to a sufficiently large finite order, adaptively chosen to meet prescribed accuracy requirements, well‐established numerical schemes for boundary value problems are utilized, readily available in scientific subroutines libraries. Illustrates convergence rates for a few typical duct geometries and critically examines previously reported numerical solutions.

Flame and droplet interaction effects during droplet-stream combustion at zero reynolds number

This work presents a numerical analysis of the quasi-steady combustion of an infinite stream of droplets in the limit of infinite Damköhler number and stagnant ambient conditions. The small and large length-scale phenomena associated with the process are addressed by splitting the physical domain into near- and far-field subdomains. Within the inner subdomain, validated expressions are used during the grid generation procedure, allowing the development of appropriate finite-difference expressions and control of the distribution of points. Analytical transformations are developed and applied to the outer subdomain coordinate system in order to match the inner and outer grids along the domain interface and to properly address the outflow boundary conditions using a regularly spaced grid. A system of transformed governing equations is obtained and discretized into a coupled system of algebraic equations, which are solved by standard scientific subroutines, incorporating automatic control of error. The developed transformations are inverted and the solutions within the physical domain are obtained. Interdroplet interaction effects are presented in terms of droplet mass vaporization rate, droplet lifetime, and flame-sheet shape and position for different droplet spacings and fuels. The results indicate interaction effects present over a broad range of interdroplet spacings and are compared with theoretical and experimental ones available in the literature.

On the solution of non‐linear drying problems in capillary porous media through integral transformation of Luikov equations

AbstractThe generalized integral transform technique is employed to provide hybrid numerical–analytical solutions to the non‐linear Luikov equations, that govern drying within capillary porous media. The coupled equations for moisture and temperature distributions are integral transformed to eliminate the spatial co‐ordinates, yielding an ordinary differential system for the time variation of the transformed potentials, which is readily solved through scientific subroutine libraries with automatic error control schemes. The analytical inversion formula is then recalled to provide explicit expressions for the original potentials at any desired position. The convergence behaviour of the proposed eigenfunction expansions is illustrated, and a parametric study is performed, for the drying of a slab subjected to non‐linear radiative boundary conditions.

LARGE-EDDY SIMULATIONS OF TURBULENCE ON THE CM-2

This paper reports the development and performance of a computer program for large-eddy simulations (LES) of turbulence on a massively parallel computer, the Connection Machine-2 (CM-2). The computer program solves the time-dependent Navier-Stokes equations for large scales of turbulence using a second-order time and space accurate, semi-implicit, finite-difference scheme. The effects of small scales of turbulence are represented by a subgrid closure model. The computer program is written in CM Fortran but uses some of the Connection Machine Scientific Subroutine Library (CMSSL) routines for line inversions and discrete Fourier transforms. Calculations are performed for fully developed channel flow and results are compared with previously published numerical and experimental data. In comparison with a similar calculation on a single-processor Cray-2, a speedup factor of 2.1 has been achieved with a 32 K CM-2. It is observed that the CM-2 provides a promising environment for turbulence simulations. Details...

Vector finite‐element analysis using IBM 3090–600e VF

AbstractA finite‐element computer program consists of four basic modules, namely, computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses. Vector algorithms consisting of direct vector Fortran code and the Engineering and Scientific Subroutine Library (ESSL) routines are presented for these modules. Numerical investigations were conducted using the IBM 3090–600E VF computer.For element stiffness matrix calculation, using a vector length equal to the number of elements produced speed‐up in the range of 3·2 to 3·7 over the corresponding scalar code. The vectorized global element stiffness matrix assembly was accomplished with the help of an INDEX array and the ESSL routine DAXPYI that resulted in the speed‐up of 2·6 to 4·3. The ESSL routines DPBF and DPBS gave speed‐up of 7·7 to 53·6 over a scalar Gaussian solver. The scalar‐to‐vector speed‐up for the stress calculation ranges from 2·2 to 5·33. The speed‐up of the totally vectorized program over the scalar program is from 7·4 to 51·9.As would be expected, the equation solution takes up the most computational effort in a finite‐element analysis. For the models we analysed the equation solution consumed 93 per cent to almost 100 per cent of the total CPU time in the scalar computations. Vectorizing the equation solver only reduces the percentage of its share to the range of 63 per cent to 88 per cent. In a totally vectorized program, the share of the equation solver effort is 85 per cent to 97 per cent. For the models analysed, the additional speed‐up accomplished by vectorizing the whole program over the one with a vectorized equation solver only was from 10 per cent to 40 per cent.

Implementation and use of high-performance parallel skyline matrix subroutines on the IBM vector facility

Skyline matrix storage format is widely used by computer programs which do finite element analysis. The popularity of skyline format stems from its simplicity, compactness, and efficiency. Even with these advantages, skyline matrix factorization and solution often consumes large amounts of processing time in finite element analysis programs. To reduce the sometimes overwhelming processing requirements of finite element analysis programs, high-performance skyline matrix subroutines were developed specifically for the IBM ES/3090™ and ES/9000™ processors. Both symmetric and unsymmetric skyline matrices are supported. These subroutines, which became available in Release 4 of IBM's Engineering and Scientific Subroutine Library (ESSL), achieve high performance through vector and parallel processing. Serial vector performance of these routines is over two times that of conventional methods, and parallel processing amplifies the vector performance with a high degree of efficiency. General strategies for achieving similar levels of performance are presented; these strategies are applicable in certain ways to other algorithms and other computers. Also presented are benchmark results for the symmetric skyline routine alone and in combination with three finite element analysis programs.

A programming language for engineering computations

C-Map was initially developed for computer-aided instruction in structural analysis and design; however, its present capability extends far beyond, to cover a broad spectrum of numerical methods for engineering computations ranging from elementary calculus to nonlinear constrained optimization problems. The flexibility and power of C-Map derive from the technique of recursive nesting of functions which releases the power of previously isolated, yet robust, algorithms. Such capability far surpasses that of the most comprehensive collection of FORTRAN scientific subroutine package. C-Map comprises four integrated components: (i) a full-screen text editor with multiple stacked windows for simultaneous editing of programs and output files; (ii) a simplified C-like programming language with the basic control structures do-while, while, for, if/else, recursive functions, math library, built-in functions for advanced engineering computations including matrix operations for structural analysis; (iii) an interactive expression evaluator; and (iii) a simple authoring system with automatic cross-referencing of key-words. The program's versatility helps to meet the different needs of users at different stage of learning. A beginner may use only the built-in functions for math and matrix operations to get immediate, useful results; and the advanced users may write their own functions for more complex problems. This paper discusses the features of C-Map and its applications in teaching structural engineering.

Conjugate-gradient subroutines for the IBM 3090 Vector Facility

This paper describes a set of optimized subroutines for use in solving sparse, symmetric, positive definite linear systems of equations using iterative algorithms. The set has been included in the Engineering and Scientific Subroutine Library (ESSL) for the IBM 3090 Vector Facility (VF). The subroutines are based on the conjugate-gradient method, preconditioned by the diagonal or by an incomplete factorization. They make use of storage representations of sparse matrices that are optimal for vector implementation. The ESSL vector subroutines are up to six times faster than a scalar implementation of the same algorithm.

Engineering and Scientific Subroutine Library Release 3 for IBM ES/3090 vector multiprocessors [Technical note

This technical note should be read in conjunction with the paper by McComb and Schmidt 1 which describes the Engineering and Scientific Subroutine Library through Release 2. In this technical note, which is an addendum to that paper, we briefly describe some of the new features in Release 3 and indicate some of the techniques used to optimize vector and parallel performance.

Engineering and Scientific Subroutine Library for the IBM 3090 Vector Facility

The Engineering and Scientific Subroutine Library (ESSL) provides FORTRAN, Assembler, and APL2 application programmers with a high-performance set of mathematical subroutines which take advantage of the performance gains offered by the IBM 3090 Vector Facility. This paper describes the contents of ESSL and presents some of the techniques that were used to develop high-performance vector subroutines. Other key design considerations such as accuracy, ease of use, and error handling are also discussed. This information should be useful to anyone developing programs for the IBM 3090 Vector Facility.

Vectorized mixed radix discrete Fourier transform algorithms

A number of previous attempts at the vectorization of the fast Fourier transform (FFT) algorithm have fallen somewhat short of achieving the full potential speed of vector processors. The algorithm formulation and implementation described here not only achieves full vector utilization but successfully copes with the problems of hierarchical storage. In the present paper, these techniques are described and extended to the general mixed radix algorithms, prime factor algorithm (PFA), the multidimensional discrete Fourier transform (DFT), the rectangular transform convolution algorithms, and the Winograd fast Fourier transform algorithm. Some of the methods were used in the Engineering Scientific Subroutine Library for the IBM 3090 Vector Facility. Using this approach, very good and consistent performance was obtained over a very wide range of transform lengths.

FORTRAN—Scientific Subroutine Library (By Peerless Engineering Service)

FORTRAN—Scientific Subroutine Library (By Peerless Engineering Service)

Fourier transform and convolution subroutines for the IBM 3090 Vector Facility

A set of highly optimized subroutines for digital signal processing has been included in the Engineering and Scientific Subroutine Library (ESSL) for the IBM 3090 Vector Facility. These include FORTRAN-callable subroutines for Fourier transforms, convolution, and correlation. The subroutines are carefully designed and tuned for optimal vector and cache performance. Speedups of up to 9½ times over scalar performance on the 3090 have been obtained.