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In the present work, a compact, fast, and yet accurate algorithm is developed to calculate the numerical values of the Ambartsumian-Chandrasekhar's H -function for isotropic scattering and its moments on the basis of the double exponential (DE) formula of Takahashi and Mori (RIMS, Kyoto Univ., 9:721, 1974). The main improvement made in the new method is an elimination of the iterative procedure for automatic adjustment of the step-size of integrations carried out with the DE-formula. Instead, a set of optimal values for the upper limit of integration T max and the number of division points N T to specify the step-size of the quadrature is predetermined for calculations of the H -function with a 15-digit accuracy, and also another for the evaluations of the moments with an accuracy of 14-digits or better. FORTRAN90 subroutines HFISCA for the H -function and HFMOMENT for the moments of arbitrary degrees are subsequently constructed (their source codes and a driver together with a sample set of output are shown in Appendix of this paper). Tables of sample calculations of the H -function and its moments of degree −1 through 6 carried out by these programs are also presented. The routines HFISCA and HFMOMENT should prove useful not only in astrophysical applications but also in other disciplines of science such as the electron transports in condensed matter and remote-sensing data analyses. A request for a copy of the Fortran 90 source code of the program can be made by writing to kawabata@rs.kagu.tus.ac.jp. [ABSTRACT FROM AUTHOR]

Fortran is still widely used in scientific computing, and a very large corpus of legacy as well as new code is written in FORTRAN 77. In general this code is not type safe, so that incorrect programs can compile without errors. In this paper, we present a formal approach to ensure type safety of legacy Fortran code through automated program transformation. The objective of this work is to reduce programming errors by guaranteeing type safety. We present the first rigorous analysis of the type safety of FORTRAN 77 and the novel program transformation and type checking algorithms required to convert FORTRAN 77 subroutines and functions into pure, side-effect free subroutines and functions in Fortran 90. We have implemented these algorithms in a source-to-source compiler which type checks and automatically transforms the legacy code. We show that the resulting code is type safe and that the pure, side-effect free and referentially transparent subroutines can readily be offloaded to accelerators. [ABSTRACT FROM AUTHOR]

Computer simulations of experimentally comparable system sizes in soft matter often require considerable elapsed times. The use of many cores can reduce the needed time, ideally proportionally to the number of processors. In this paper a parallel computational method using coarray Fortran is implemented and tested for large systems of purely block copolymer melts, as well as block copolymer nanocomposites. A satisfactory strong scaling is shown up to 512 cores while a weak scaling with a drop in performance is achieved up to 4096 cores. The scaling of the parallel cell dynamic simulations scheme displays no drawbacks over MPI and provides an example of the simplicity of the coarray approach. The code has been tested on several architectures and compilers. The hybrid block copolymer/nanoparticle algorithm can achieve previously unavailable system sizes. [ABSTRACT FROM AUTHOR]

Abstract: Several numerical landscape evolution models (LEMs) have been developed to date, and many are available as open source codes. Most are written in efficient programming languages such as Fortran or C, but often require additional code efforts to plug in to more user-friendly data analysis and/or visualization tools to ease interpretation and scientific insight. In this paper, we present an effort to port a common core of accepted physical principles governing landscape evolution directly into a high-level language and data analysis environment such as Matlab. SIGNUM (acronym for Simple Integrated Geomorphological Numerical Model) is an independent and self-contained Matlab, TIN-based landscape evolution model, built to simulate topography development at various space and time scales. SIGNUM is presently capable of simulating hillslope processes such as linear and nonlinear diffusion, fluvial incision into bedrock, spatially varying surface uplift which can be used to simulate changes in base level, thrust and faulting, as well as effects of climate changes. Although based on accepted and well-known processes and algorithms in its present version, it is built with a modular structure, which allows to easily modify and upgrade the simulated physical processes to suite virtually any user needs. The code is conceived as an open-source project, and is thus an ideal tool for both research and didactic purposes, thanks to the high-level nature of the Matlab environment and its popularity among the scientific community. In this paper the simulation code is presented together with some simple examples of surface evolution, and guidelines for development of new modules and algorithms are proposed. [Copyright &y& Elsevier]

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables). [ABSTRACT FROM AUTHOR]

Data parallel programming languages, such as High Performance Fortran, are widely regarded as a promising means for writing portable programs for distributed-memory machines. In this paper, we present a new algorithm for computing the communication sets in array section movements with block-cyclic (cyclic (k) in HPF) distribution. Our framework can handle multi-level alignments, multi-dimensional arrays, array intrinsic functions, affine indices and axis exchanges in the array subscript. Instead of employing the linear diophantine equation solver, a new algorithm which does not rely on the linear diophantine equation solver to calculate communication sets is proposed. We use formal proof and experimental results to show that it is more efficient than previous solutions to the same problem. Another important contribution of this paper is that we prove that the compiler is able to compute efficiently the communication sets of block-cyclic distribution as long as the block sizes of the arrays are set to be identical or the lowest common multiple (LCM) of block sizes is not a huge integer. We demonstrate it by thorough complexity analyses and extensive experimental results. [Copyright &y& Elsevier]

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform refinement-based discretizations of elliptic equations, they tend to be less effective for algebraic systems, which arise from discretizations on locally refined meshes, losing their optimal behavior in both storage and computational complexity. Our primary focus here is on Bramble, Pasciak, and Xu (BPX)-style additive and multiplicative multilevel preconditioners, and on various stabilizations of the additive and multiplicative hierarchical basis (HB) method, and their use in the local mesh refinement setting. In parts I and II of this trilogy, it was shown that both BPX and wavelet stabilizations of HB have uniformly bounded condition numbers on several classes of locally refined two- and three-dimensional meshes based on fairly standard (and easily implementable) red and red-green mesh refinement algorithms. In this third part of the trilogy, we describe in detail the implementation of these types of algorithms, including detailed discussions of the data structures and traversal algorithms we employ for obtaining optimal storage and computational complexity in our implementations. We show how each of the algorithms can be implemented using standard data types, available in languages such as C and FORTRAN, so that the resulting algorithms have optimal (linear) storage requirements, and so that the resulting multilevel method or preconditioner can be applied with optimal (linear) computational costs. We have successfully used these data structure ideas for both MATLAB and C implementations using the FEtk, an open source finite element software package. We finish the paper with a sequence of numerical experiments illustrating the effectiveness of a number of BPX and stabilized HB variants for several examples requiring local refinement. [ABSTRACT FROM AUTHOR]

Abstract  Expression Templates (ET) are a powerful tool for development of user-friendly numerical libraries. By this concept and by operator overloading in C, numerical algorithms can be implemented in a mathematical notation without decreasing the performance in comparison to optimized C or FORTRAN codes. In this paper, we present new Expression Template techniques. First, we explain the concept of “Easy Expression Templates”, which are easier to implement than classical ET. Then, we explain “Fast Expression Templates”. This concept leads to an optimal performance even on special architectures like vector machines. Furthermore, concepts for storing expressions and code optimizing are presented. In order to verify the usability of these programming techniques in real applications, we discuss a template library which calculates local stiffness matrices arising from Finite Element discretizations. [ABSTRACT FROM AUTHOR]

The magnetic gradient tensor provides a powerful tool for detecting magnetic bodies because of its ability to emphasize detailed features of the magnetic anomalies. To interpret field measurements obtained by magnetic gradiometry, the forward calculation of magnetic gradient fields is always necessary. In this paper, we present a contraction integral equation method to simulate the gradient fields produced by 3-D magnetic bodies of arbitrary shapes and high susceptibilities. The method employs rectangular prisms to approximate the source region with the assumption that the magnetization in each element is homogeneous. The gradient fields are first solved in the Fourier domain and then transformed into the spatial domain by 2-D Gauss-FFT. This calculation is performed iteratively until the required accuracy is reached. The convergence of the iterative procedure is ensured by a contraction operator. To facilitate application, we introduce a FORTRAN program to implement the algorithm. This program is intended for users who show interests in 3D magnetic modeling at high susceptibility. The performance of the program, including its computational accuracy, efficiency and convergence behavior, is tested by several models. Numerical results show that the code is computationally accurate and efficient, and performs well at a wide range of magnetic susceptibilities from 0 SI to 1000 SI. This work, therefore, provides a significant tool for 3D forward modeling of magnetic gradient fields at high susceptibility. [ABSTRACT FROM AUTHOR]

In order to achieve higher load balancing, it is necessary to solve irregular block redistribution problems, which are different from regular block-cyclic redistribution. High Performance Fortran version 2 (HPF-2) provides irregular distribution functionalities, such as GEN_BLOCK and INDIRECT. This paper is devoted to develop an efficient algorithm that attempts to obtain near optimal scheduling while satisfying the conditions of minimal message size of total steps and the minimal number of steps for irregular array redistribution. The algorithm intends to decrease the computation costs by dividing the whole block into sub-blocks and solving the sub-problems accordingly, and then merging them together to get final results. Simulation results show that our algorithm has comparable performance with a relocation algorithm developed previously (H. Yook and M. Park. Proceedings of the IASTED International Conference Parallel and Distributed Computing and Systems, Nov. 3–6, MIT, Boston, USA, 1999). [ABSTRACT FROM AUTHOR]

In this paper, we propose a new automatic data alignment model called segmented alignment. The conventional data alignment model, such as that used in High-Performance Fortran (HPF), aligns arrays with the whole index domain. The principle of our proposed segmented alignment is to allow alignment relations within delimited index domains. We first provide motivating examples to illustrate how code fragments of HPF with EOSHIFT or CSHIFT operations, or produced by synthesis operations can benefit from our enhanced alignment scheme. Second, we show that this new model can be implemented in HPF-like languages by adding WHEN and IN constructs to them. In addition, we show that the new proposed schemes for WHEN and IN constructs can be emulated using standard HPF syntax. Finally, we address issues related to automatic data alignment for the new proposed model, and present an algorithm to automatically align programs using our segmented alignment scheme. Since the optimal algorithm to do this is NP-hard, a practical heuristic is also given. Our experiments were performed on a DEC Alpha Farm with HPF environments. Our experiments confirm our theory that our proposed alignment scheme can significantly enhance not only the performance of HPF code fragments with EOSHIFT or CSHIFT operations, but also that of codes produced by synthesis operations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a semicoarsening multigrid algorithm for solving the finite difference discretization of symmetric and nonsymmetric, two and three-dimensional elliptic partial differential equations with highly discontinuous and anisotropic coefficients. The discrete equations are assumed to be defined on a logically rectangular grid, obtained possibly through grid generation for a problem defined on an irregular domain. The basic algorithm is described along with some modifications which are designed to improve its efficiency and robustness for certain types of problem cases. FORTRAN codes that implement the two- and three-dimensional semicoarsening multigrid algorithms are described briefly, and numerical results are presented. [ABSTRACT FROM AUTHOR]

The proliferation of large software systems written in high level programming languages insures the utility of analysis programs which examine interprocedural communications. Often these analysis programs need to reduce the dynamic relations between procedures to a static data representation. This paper presents one such representation, a directed, acyclic graph named the call graph of a program. We delineate the programs representable by an acyclic call graph and present an algorithm for constructing it using the property that its nodes may be linearly ordered. We prove the correctness of the algorithm and discuss the results obtained from an implementation of the algorithm in the PFORT Verifier [1]. [ABSTRACT FROM AUTHOR]

In view of the strong constraint zones of the concrete structure on the pile foundation, there are some differences between the calculation results of the isotropic equivalent pile foundation by the volume replacement ratio method and the actual engineering. In this paper, referring to the relevant algorithm of rock mass with anchor, the anchor and rock mass are, respectively, compared to pile and surrounding soil foundation. Eshelby equivalent inclusion theory is introduced into the equivalent mechanical model of soil foundation with pile, and a new equivalent pile foundation algorithm considering anisotropic elastic constant is compiled by Fortran. Three kinds of calculation methods are used to calculate the stress field of the concrete structure of the large pump station on the pile foundation during the construction period, and the stress in the strong constraint zones of the concrete structure are mainly analyzed. It is found that the calculation accuracy of Algorithm 3 is the highest, and the calculation results of Algorithm 2 can be modified by the coefficients to achieve the calculation accuracy of Algorithm 3 and the calculation efficiency is actually improved. Finally, the accuracy of the proposed method is verified by the engineering measured data. [ABSTRACT FROM AUTHOR]