An <i>N</i>-dimensional Fortran interpolation programme (NterGeo.v2020a) for geophysics sciences – application to a back-trajectory programme (Backplumes.v2020r1) using CHIMERE or WRF outputs

An interpolation programme coded in Fortran for irregular N-dimensional cases is presented and freely available. The need for interpolation procedures over irregular meshes or matrixes with interdependent input data dimensions is frequent in geophysical models. Also, these models often embed look-up tables of physics or chemistry modules. Fortran is a fast and powerful language and is highly portable. It is easy to interface models written in Fortran with each other. Our programme does not need any libraries; it is written in standard Fortran and tested with two usual compilers. The programme is fast and competitive compared to current Python libraries. A normalization option parameter is provided when considering different types of units on each dimension. Some tests and examples are provided and available in the code package. Moreover, a geophysical application embedding this interpolation programme is provided and discussed; it consists in determining back trajectories using chemistry-transport or mesoscale meteorological model outputs, respectively, from the widely used CHIMERE and Weather Research and Forecasting (WRF) models.

Modern Fortran Explained

Fortran marches on, remaining one of the principal programming languages used in high-performance scientific, numerical, and engineering computing. A series of significant revisions to the standard versions of the language have progressively enhanced its capabilities, and the latest standard—Fortran 2018—includes many additions and improvements. This second edition of Modern Fortran Explained expands on the first. Given the release of updated versions of Fortran compilers, the separate descriptions of Fortran 2003 and Fortran 2008 have been incorporated into the main text, which thereby becomes a unified description of the full Fortran 2008 version of the language. This is much cleaner, many deficiencies and irregularities in the earlier language versions having been resolved. It includes object orientation and parallel processing with coarrays. Four completely new chapters describe the additional features of Fortran 2018, with its enhancements to coarrays for parallel programming, interoperability with C, IEEE arithmetic, and various other improvements. Written by leading experts in the field, two of whom have actively contributed to Fortran 2018, this is a complete and authoritative description of Fortran in its latest form. It is intended for new and existing users of the language, and for all those involved in scientific and numerical computing. It is suitable as a textbook for teaching and, with its index, as a handy reference for practitioners.

Fortran 90: A simple programming language

Before diving into the art of solving economic problems on a computer, we want to give a short introduction into the syntax and semantics of Fortran 90. As describing all features of the Fortran language would probably fill some hundred pages, we concentrate on the basic features that will be needed to follow the rest of this textbook. Nevertheless, there are various Fortran tutorials on the Internet that can be used as complementary literature. Fortran is pretty old; it is actually considered the first known higher programming language. Going back to a proposal made by John W. Backus, an IBM programmer, in 1953, the term Fortran is derived from The IBM Formula Translation System. Before the release of the first Fortran compiler in April 1957, people used to use assembly languages. The introduction of a higher programming language compiler tremendously reduced the number of code lines needed to write a program. Therefore, the first release of the Fortran programming language grew pretty fast in popularity. From 1957 on, several versions followed the initial Fortran version, namely FORTRAN II and FORTRAN III in 1958, and FORTRAN IV in 1961. In 1966, the American Standards Association (now known as the ANSI) approved a standardized American Standard Fortran. The programming language defined on this standard was called FORTRAN 66. Approving an updated standard in 1977, the ANSI paved the way for a new version of Fortran known as FORTRAN 77. This version became popular in computational economics during the late 80s and early 90s. More than 13 years later, the Fortran 90 standard was released by both the International Organization for Standardization (ISO) and ANSI consecutively. With Fortran 90, the fixed format standard was exchanged by a free format standard and, in addition, many new features like modules, recursive procedures, derived data types, and dynamic memory allocation made the language much more flexible. From Fortran 90 on, there has only been one major revision, in 2003, which introduced object oriented programming features into the Fortran language. However, as object-oriented programming will not be needed and Fortran 90 is by far the more popular language, we will focus on the 1990 version in this book.

Three Dimensional Finite Element Program for Determination of Cure Level in Thick Rubber Part

The vulcanization or curing process begins in a heated mould to convert viscous uncured rubber materials into functional elastic ones. As the mechanical properties and service performances of the final products are greatly affected by the state of cure or cure level of rubbers, thus it is very crucial to use suitable time, pressure and temperature for the curing process to ensure that the desired quality of the final products are obtained. A computer program “RACE-CURE” written in standard FORTRAN code has been developed by our research team for the analysis of curing process of large rubber parts. The program is developed based on the incremental finite element formulation for three dimensional nonlinear transient heat transfer analysis coupled with cure kinetics. The RACE-CURE is tested for a test problem of curing of a large rubber block and results are compared to another two programs: ANSYS Polyflow v.14 and CFEM, a MATLAB© FEM program with capability to add curing kinetics, independently developed at our research group.

Reformulation RELAP5-3D in FORTRAN 95 and Results

RELAP5-3D is a nuclear power plant code used worldwide for safety analysis, design, and operator training. In keeping with ongoing developments in the computing industry, we have re-architected the code in the FORTRAN 95 language [2], the current, fully-available, ANSI standard FORTRAN language. These changes include a complete reworking of the database and conversion of the source code to take advantage of new constructs. The improvements and impacts to the code are manifold. It is a completely machine-independent code that produces machine independent fluid property and plot files and expands to the exact size needed to accommodate the user’s input. Runtime is generally better for larger input models, many prior user-reported problems have been resolved, and the program is better tested. Other impacts of code reformulation are improved code readability, reduced maintenance and development time, increased adaptability to new computing platforms, and increased code longevity. Comparison between the pre- and post-conversion code are made on the basis of programming metrics and code performance.

Speeding up N-body Calculations on Machines without Hardware Square Root

The most time consuming part of an N-body simulation is computing the components of the accelerations of the particles. On most machines the slowest part of computing the acceleration is in evaluating r-3/2, which is especially true on machines that do the square root in software. This note shows how to cut the time for this part of the calculation by a factor of 3 or more using standard Fortran.

A hybrid fast Hankel transform algorithm for electromagnetic modeling

A hybrid fast Hankel transform algorithm has been developed that uses several complementary features of two existing algorithms: Anderson’s digital filtering or fast Hankel transform (FHT) algorithm and Chave’s quadrature and continued fraction algorithm. A hybrid FHT subprogram (called HYBFHT) written in standard Fortran-77 provides a simple user interface to call either subalgorithm. The hybrid approach is an attempt to combine the best features of the two subalgorithms in order to minimize the user’s coding requirements and to provide fast execution and good accuracy for a large class of electromagnetic problems involving various related Hankel transform sets with multiple arguments. Special cases of Hankel transforms of double‐order and double‐argument are discussed, where use of HYBFHT is shown to be advantageous for oscillatory kernel functions.