Fortran Version Research Articles

DUGKS-GPU: An efficient parallel GPU code for 3D turbulent flow simulations using Discrete Unified Gas Kinetic Scheme

This paper presents a parallel implementation of the Discrete Unified Gas Kinetic Scheme (DUGKS) on the GPU system using the CUDA Fortran and CUDA C++ programming languages. Firstly, we conducted an extensive revision of our original CPU-based code, resulting in a threefold decrease in memory usage. This new implementation is also paired with a novel approach to compute cell face flux using trilinear interpolation. It is shown analytically that the interpolation-based approach to flux calculation is more accurate compared to the one used in the original DUGKS. The initial simulation results using this new approach suggest that trilinear interpolation can reduce numerical errors on a coarse mesh. For example, in the case of the decaying Taylor-Green vortex flow at a 1283 mesh resolution, the relative numerical error in the energy dissipation rate at t⁎=2, using the spectral simulation result as the benchmark, is approximately 30% lower than that of the original implementation. The improved GPU DUGKS method is applied to laminar and turbulent flows in periodic and wall-bounded boundary configurations. A performance comparison of the GPU implementation is also presented and compared to the previous CPU implementation. A maximum speedup of 7.64x was achieved on a desktop-level GPU compared to a 32-core CPU. The strong scaling test, conducted on an eight-GPU node, demonstrated the efficient utilization of available multiple GPU resources by the code. Program summaryProgram Title: DUGKS-GPUCPC Library link to program files:https://doi.org/10.17632/yykv5s9g2n.1Developer's repository link:https://github.com/kairzhan/DUGKS-GPUCode Ocean capsule:https://codeocean.com/capsule/3b1e4f74-cdd3-4781-8923-8514d5923dfb/Licensing provisions: GNU General Public License 3Programming language: CUDA C++, CUDA FortranSupplementary material:Nature of problem: DUGKS-GPU is an advanced numerical code designed to accelerate the simulation of turbulent fluid flows through the application of the kinetic method known as the Discrete Unified Gas Kinetic Scheme (DUGKS). This computational tool comprises a CUDA Fortran version, tailored for a single GPU, as well as a CUDA C++ version developed for multi-GPU platforms.Solution method: The code employs a second-order finite-volume discretization of the discrete velocity Boltzmann equation with the BGK collision model. It can be used to simulate small to medium-scale problems on modern multi-GPU platforms with CUDA architecture.

Air showers and hadronic interactions with CORSIKA 8

The CORSIKA 8 project is a collaborative effort aiming to develop a versatile C++ framework for the simulation of extensive air showers, intended to eventually succeed the long-standing FORTRAN version. I present an overview of its current capabilities, focusing on aspects concerning the hadronic and muonic shower components. In particular, I demonstrate the “cascade lineage” feature and its application to quantify the importance of certain phase-space regions in hadronic interactions for muon production. Additionally, I show first results using Pythia 8.3, which as of late is usable as interaction model in cosmic-ray applications and is currently being integrated into CORSIKA 8.

An open-source tool for improving on-farm yield forecasting systems

IntroductionThe increased frequency of extreme climate events, many of them of rapid onset, observed in many world regions, demands the development of a crop forecasting system for hazard preparedness based on both intraseasonal and extended climate prediction. This paper presents a Fortran version of the Crop Productivity Model AquaCrop that assesses climate and soil fertility effects on yield gap, which is crucial in crop forecasting systemsMethodsFirstly, the Fortran version model - AQF outputs were compared to the latest version of AquaCrop v 6.1. The computational performance of both versions was then compared using a 100-year hypothetical experiment. Then, field experiments combining fertility and water stress on productivity were used to assess AQF model simulation. Finally, we demonstrated the applicability of this software in a crop operational forecast system.ResultsResults revealed that the Fortran version showed statistically similar results to the original version (r2 > 0.93 and RMSEn < 11%, except in one experiment) and better computational efficiency. Field data indicated that AQF simulations are in close agreement with observation.ConclusionAQF offers a version of the AquaCrop developed for time-consuming applications, such as crop forecast systems and climate change simulations over large areas and explores mitigation and adaptation actions in the face of adverse effects of future climate change.

Introducing bellhopcxx/bellhopcuda: Modern, parallel BELLHOP(3D)

BELLHOP and BELLHOP3D are popular ray/beam based underwater acoustics simulation programs, written in Fortran by Dr. Michael B. Porter starting in 1983. We introduce bellhopcxx/bellhopcuda, a translation of these programs into a modern, multithreaded C + +/CUDA codebase. This open-source codebase can be built and run on a multicore CPU or an NVIDIA GPU and can also be built as a library for integration into other software without requiring output data to be written to files. The new version is typically somewhat faster than the Fortran version even in single-threaded mode, and in multithreaded mode usually scales roughly with the number of logical CPU cores minus some overhead. In runs with large numbers of rays, depending on the hardware, the CUDA version can bring several times additional performance gain over the multithreaded CPU version, sometimes reaching over 100x the performance of BELLHOP or BELLHOP3D. The results of the new version closely match those of the original version in most cases, but there are occasionally mismatches, partly due to edge case issues inherent in the BELLHOP physics model. We have improved the handling of these cases and made other improvements to the Fortran version, bringing these changes to the new version.

Contact-based molecular dynamics of structured and disordered proteins in a coarse-grained model: Fixed contacts, switchable contacts and those described by pseudo-improper-dihedral angles

We present a coarse-grained Cα-based protein model that can be used to simulate structured, intrinsically disordered and partially disordered proteins. We use a Go-like potential for the structured parts and two different variants of a transferable potential for the disordered parts. The first variant uses dynamic structure-based (DSB) contacts that form and disappear quasi-adiabatically during the simulation. By using specific structural criteria we distinguish sidechain-sidechain, sidechain-backbone and backbone-backbone contacts. The second variant is a non-radial multi-body pseudo-improper-dihedral (PID) potential that does not include time-dependent terms but requires more computational resources. Our model can simulate in reasonable time thousands of residues on millisecond time scales. Program summaryProgram Title: cgCPC Library link to program files:https://doi.org/10.17632/dp7gwrs94n.1Code Ocean capsule:https://codeocean.com/capsule/9528010Licensing provisions: MITProgramming language: C++ (new version), Fortran (old version)Nature of problem: Simulations of one or more protein chains, structured, intrinsically disordered or partially disordered. Calculating their equilibrium and kinetic properties in processes including but not limited to: folding, aggregation, conformational changes, formation of complexes, aggregation, response to deformation. All those processes need long simulation times or many trajectories to properly sample the system.Solution method: The simulations use a molecular dynamics implicit-solvent coarse-grained model where each pseudoatom represents one amino acid residue. Residues are harmonically connected to form a chain. The system evolves according to Langevin dynamics. The backbone stiffness potential involves bond angle and dihedral angle terms (or a chirality term in the structured case). Residues interact via modified Lennard-Jones or Debye-Hueckel potentials.The potential is different for structured and disordered parts of a protein. A Go model contact map is used for the structured parts, where an interaction between two residues is attractive if effective spheres associated with their heavy atoms overlap in the native structure [1,2,3,4]. Non-attractive contacts use only the repulsive part of the Lennard-Jones potential. The potential for the disordered parts has two versions: in the quasi-adiabatic Dynamic Structure-Based (DSB) variant, the contacts are formed dynamically based on the structure of the chain and are quasi-adiabatically turned on and off [5,6]. In the slower, but more accurate Pseudo-Improper-Dihedral (PID) variant the Lennard-Jones term is multiplied by a pseudo-improper-dihedral term that gives similar geometric restrictions with a time-independent Hamiltonian [7].Proteins can be pulled by their termini to mimic stretching by an Atomic Force Microscope [8,9]. Multiple protein chains can be put in a simulation box with periodic boundary conditions or with walls that may be repulsive or attractive for the residues. The walls may move to mimic pulling or shearing deformations. The program accepts PDB files or protein sequences with optional user-defined contact maps. It saves the results in an output file (summary), a PDB file (structure) and a map file (contact map in a given snapshot).Additional comments including restrictions and unusual features: The program supports openMP (effective up to 8 cores, use 4 cores for optimal speed-up). The C++ version is hosted on Github, the Fortran version is distributed as a .tar archive.

Finite Element Simulation of Moisture Content Changes of Peeled Banana (Musa x paradisiaca L.) during Drying

This paper presents finite element simulation of drying of peeled banana. A two-dimensional finite element model was developed for simulation of moisture content changes during drying of peeled banana. The finite element simulation model was programmed in Compaq Visual FORTRAN version 6.5. Classical models for moisture diffusivity, sorption isotherm and volumetric shrinkage of peeled banana were experimentally determined and used in the finite element simulation. The finite element model prediction was compared with the experimental data. The agreement between the simulated moisture content changes and the experimental data was in reasonable agreement with a discrepancy in root mean square error being in the range of 2.2-14.6%. Moisture content change profiles inside peeled banana during drying were predicted and these profiles give a good picture of the moisture movement inside peeled banana during drying. Keywords: Drying, Peeled banana, Finite element, Moisture diffusion

Multisphere Representation of Convex Polyhedral Particles for DEM Simulation

The representation of particles of complex shapes is one of the key challenges of numerical simulations based on the discrete element method (DEM). A novel algorithm has been developed by the authors to accurately represent 2D arbitrary particles for DEM modelling. In this paper, the algorithm is extended from 2D to 3D to model convex polyhedral particles based on multisphere methods, which includes three steps: the placement of spheres at the corners, along the edges, and on the facets in sequence. To give a good representation of a polyhedral particle, the spheres are placed tangent to the particle surface in each step. All spheres placed in the three steps are clumped together into a clump in DEM. In addition, the mass properties of the clump are determined based on the corresponding polyhedral particle to obtain accurate simulation results. Finally, an example is used to validate the robust and automatic performance of the algorithm in generating a sphere clump model for an assembly of polyhedral particles. A current FORTRAN version of the algorithm is available by contacting the authors.

GPU-RRTMG_SW: Accelerating a Shortwave Radiative Transfer Scheme on GPU

As high performance computing technology continues to develop rapidly, graphics processing units (GPUs) are more widely used for daily computing tasks. However, some applications, such as weather forecasting, require large-scale computation. Thus, due to the computationally intensive characteristics of the rapid radiative transfer model for general circulation models (RRTMG) in the Earth system model, this study uses GPU-related technology to accelerate computation of the model. First, two kinds of algorithms using GPU technology to accelerate the RRTMG shortwave radiation scheme (RRTMG_SW) are proposed. Then, an optimization method for data transmission between host and device is proposed. Finally, after using CUDA Fortran and CUDA C to implement these algorithms, two GPU versions of RRTMG_SW, namely CF-RRTMG_SW (CUDA Fortran version) and CC-RRTMG_SW (CUDA C version), were developed. The experimental results demonstrate that the proposed acceleration algorithms are effective. Without I/O transfer, running CC-RRTMG_SW on a NVIDIA GeForce Titan V GPU achieved a 38.88× speedup when compared to a single Intel Xeon E5-2680 CPU core.

Study of excitation energies and transmission potential of the reduced quadruple B (E2) for the 70Zn isotope by applying the nuclear shell model

In this paper, the excited energy levels and reduced electric quadrupole transition probabilities (BE2 ↓) in both pure and mixed configuration s of 70Zn nucleus have been calculated by applying the nuclear shell model. In the present study, the surface delta and modified surface delta interactions within the model space (1p3/2,0f5/2, 1p1/2 and 0g9/2) have been used for two protons outside the closed nuclear core represented by the 68Ni nucleus. The equations are programmed for the above two interactions and the reduced electric quadrupole transition probabilities (BE2 ↓) equations using the Fortran version 95. Through the used Fortran version 95 program code, the elements of the matrix have been calculated for two particles which are necessary to calculate the eigenvalues, the eigenvectors and then the final energies of the nucleus that has been used in the current study. Through the calculations, theoretical results that have well agreement with the available practical values have been obtained. The total angular momentum and parity of some uncertain and unspecified energy levels have been confirmed and determined by the total angular momentum and the practical parity. Also, new values have been identified for both the excited energy levels and the reduced electric quadrupole transition probabilities (BE2 ↓), these values are considered as a suggestion that increases theoretical knowledge of each of the energy levels and the expected transition probabilities during this study.

Fast and accurate evaluation of geomagnetic field elements at arbitrary points in space

SUMMARY An algorithm and software are developed for fast and accurate evaluation of the elements of the geomagnetic field represented in high-degree (>720) solid spherical harmonics at many scattered points in the space above the surface of the Earth. The algorithm is based on representation of the geomagnetic field elements in solid ellipsoidal harmonics and application of tensor product needlets. Open source FORTRAN and MATLAB realizations of this algorithm that rely on data from the Enhanced Magnetic Models 2015, 2017 (EMM2015, EMM2017) have been developed and extensively tested. The capabilities of the software are demonstrated on the example of the north, east and down components of the geomagnetic field as well as the derived horizontal intensity, total intensity, inclination and declination. For the range from −417 m under the Earth reference ellipsoid up to 1000 km above it the FORTRAN and MATLAB versions of the software run 465 and 189 times faster than the respective FORTRAN and MATLAB versions of the software using the standard spherical harmonic series method, while the accuracy is less than 1 nT and the memory (RAM) usage is 9 GB.

Simulative analysis of turbulent flow through a circular conduit with uniform wall temperature and constant heat flux boundary conditions

PurposeThis study aims to investigate numerically a two-dimensional fully developed mean turbulent fluid flow, and heat transfer in a circular duct is numerically investigated using FORTRAN 95 code that applies the finite difference method to solve the thermal problem for the two thermal boundary conditions, constant surface temperature, constant heat and steady, axisymmetric flow. Several important results have been drawn and discussed from thermal analysis. Finally, the numerical results of the model developed in the document have been validated in good accuracy by comparing them with some correlation results available in the specialized literature.Design/methodology/approachThe methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas' algorithm, a program in FORTRAN version 95 was developed to numerically solve the discretized form of the system of equations describing the problem.FindingsThe profiles of the solutions are provided from which the authors infer that the numerical and literature correlation agreed very well. Another result that they obtained from this study is the number of Nusselt in the thermal entrance region to which a parametric study based on Reynolds and Peclet numbers, and the longitudinal coordinate, was carried out and discussed well for the impact of the scientific contribution.Originality/valueThe novelty of the work is the application of the finite difference method programed on the FORTRAN code, as a sequential numerical method of an ODEs system, to determine the number of Nusselt in both uniform wall temperature and wall heat flux uniform.

Numerical Simulation of Heat Transfer of Turbulent Flow inside a Circular Conduit at Constant Wall Temperature Boundary Condition

A numerical study was conducted by using the finite difference technique to investigate the mechanism of the fully developed turbulent flow and heat transfer in a circular tube in company of large Reynolds number with constant heat flux and at constant wall temperature condition. The methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form in order to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas’ algorithm, a program in FORTRAN version 95 was developed in order to numerically solve the discretized form of the system of equations describing the problem. Finally, thanks to this elaborate program, we were able to play on some parameters involved such as the Reynolds number, the number of Peclet, and the longitudinal coordinate to obtain important results of the treated thermal model which are discussed and well detailed of this work. Comparison between the literature correlation data and the calculated simulation indicates that it is a good match of the results.

CORSIKA 8 – Towards a modern framework for the simulation of extensive air showers

Current and future challenges in astroparticle physics require novel simulation tools to achieve higher precision and more flexibility. For three decades the FORTRAN version of CORSIKA served the community in an excellent way. However, the effort to maintain and further develop this complex package is getting increasingly difficult. To overcome existing limitations, and designed as a very open platform for all particle cascade simulations in astroparticle physics, we are developing CORSIKA 8 based on modern C++ and Python concepts. Here, we give a brief status report of the project.

Veros v0.1 – a fast and versatile ocean simulator in pure Python

Abstract. A general circulation ocean model is translated from Fortran to Python. Its code structure is optimized to exploit available Python utilities, remove simulation bottlenecks, and comply with modern best practices. Furthermore, support for Bohrium is added, a framework that provides a just-in-time compiler for array operations and that supports parallel execution on both CPU and GPU targets. For applications containing more than a million grid elements, such as a typical 1∘×1∘ horizontal resolution global ocean model, Veros is approximately half as fast as the MPI-parallelized Fortran base code on 24 CPUs and as fast as the Fortran reference when running on a high-end GPU. By replacing the original conjugate gradient stream function solver with a solver from the pyAMG Python package, this particular subroutine outperforms the corresponding Fortran version by up to 1 order of magnitude. The study is concluded with a simple application in which the North Atlantic wave response to a Southern Ocean wind perturbation is investigated. It is found that even in a realistic setting the phase speeds of boundary waves matched the expectations based on theory and idealized models.

Nam June Paik's Etude 1 and the Indeterminate origins of Digital Media Art

This essay describes the discovery and significance of Etude 1 (1967), a previously unknown work by media artist Nam June Paik. Composed at Bell Labs and written in an early version of the computer-programming language FORTRAN, Etude 1 stands as one of the earliest works of digital art—though whether Etude 1 was intended to be a film, the “computer opera” that Paik mentions elsewhere in his writings, or some other kind of art work altogether. By exploring Etude 1's uncertain status, as well as more conceptual indeterminacies concerning the relationship between image and code, music and media, and the analog and the digital, this essay demonstrates how such indefinite artifacts allow for a rethinking of cinema's digital past, film's place in computational media, and the nature of the archive.

LHC collider phenomenology of minimal universal extra dimensions

We discuss the collider phenomenology of the model of Minimal Universal Extra Dimensions (MUED) at the Large hadron Collider (LHC). We derive analytical results for all relevant strong pair-production processes of two level 1 Kaluza–Klein partners and use them to validate and correct the existing MUED implementation in the fortran version of the Pythia event generator. We also develop a new implementation of the model in the C++ version of Pythia. We use our implementations in conjunction with the Checkmate package to derive the LHC bounds on MUED from a large number of published experimental analyses from Run 1 at the LHC. Program summaryProgram title:Pythia6 MUED and Pythia8 MUEDProgram Files doi:http://dx.doi.org/10.17632/fkvcgdw9j6.1Licensing provisions: CC0 1.0Programming language: Fortran and C++Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 122–127Does the new version supersede the previous version?: YesReasons for new version: The Minimal Universal Extra Dimension (MUED) model was implemented in the Pythia6 event generator from version 6.4.18 onwards. The new version now allows for different masses for various level 1 KK excitations, modified and corrected subroutines to handle the kinematics and squared matrix elements. A new production process has been added. Additionally the model is now made available in the Pythia8 event generator.Summary of revisions: The Minimal Universal Extra Dimension (MUED) model implementation in the Pythia6 event generator now allows for different masses for various level 1 KK excitations. These may appear both in the final states and in the propagators of t∕u channel contributions. Routines handling the kinematics and squared matrix elements are suitably modified to incorporate correct kinematics and ensure proper interferences of diagrams. For some processes, corrections in the expressions for the existing squared matrix elements have been made. A new subprocess qq̄→g1∗g1∗ has been added. A couple of production modes (which originally had some subprocesses lumped together) are now split to handle different masses of doublet and singlet KK excitations.Nature of problem: The ongoing run of the Large Hadron Collider (LHC) at CERN continues to look for new physics Beyond the Standard Model (BSM). For many years, the only complete models which were seriously investigated by the LHC collaborations, were different versions of low energy supersymmetry: mSUGRA, gauge-mediated SUSY, anomaly-mediated SUSY, etc. The MUED model provides an interesting and motivated alternative to supersymmetry, with unique and challenging collider phenomenology. In order to study the MUED model, it was implemented in the fortran version Pythia6 general purpose event generator from version 6.4.18 onwards. The MUED model is not available in the C++ version of Pythia8.Solution method: The new implementation validates and fixes the backward compatibility and some issues in the current Pythia6 version. The model has now been implemented in the Pythia8 event generator.

A new Fortran 90 program to compute regular and irregular associated Legendre functions (new version announcement)

This is a revised and updated version of a modern Fortran 90 code to compute the regular Plm(x) and irregular Qlm(x) associated Legendre functions for all x∈(−1,+1) (on the cut) and |x|>1 and integer degree (l) and order (m). The necessity to revise the code comes as a consequence of some comments of Prof. James Bremer of the UC//Davis Mathematics Department, who discovered that there were errors in the code for large integer degree and order for the normalized regular Legendre functions on the cut. New version program summaryProgram Title: Associated Legendre FunctionsProgram Files doi:http://dx.doi.org/10.17632/29j2mvwgwt.1Licensing provisions: GPLv2Programming language: Fortran 90Does the new version supersede the previous version?: YesJournal reference of previous version: Comput. Phys. Commun. 181 (2010) 2091Reason for new version: The necessity to revise the code comes as a consequence of some comments of Prof. James Bremer of the UC//Davis Mathematics Department, who discovered that there were errors in the code for large integer degree and order for the normalized regular Legendre functions on the cut. This occurred because renormalization of the un-normalized functions involved the manipulation of factorials of large integer value. The problem was solved by a direct computation of the normalized functions from a revised recursion formula. This completely avoids the manipulation of the factorials that were present in the first version. In re-examining the code we also noticed that there were cases for large degree, order and argument that led to overflows causing the results to display infinities or NaN when printed out, without crashing. There does not appear to be any good approach, other than resorting to extended precision arithmetic, to cure this pathology. Since it was not our original intention to provide such a code, all we can do is to point out that this can happen and that the user should take care not to blindly accept the results of the computation for large degree and order. We have not found a general approach to predict in advance when this will occur in this three dimensional parameter space.Summary of revisions: None of the basic algorithms has been changed. We have eliminated the computation of factorials for large integer values and now calculate the normalized regular Legendre functions on the cut (-1,+1) directly from the recursion relation for those functions rather than computing the unnormalized functions and then normalizing after the computation. This required some modifications of the original Fortran subroutines as well as the addition of a new module.Nature of problem: Compute the regular and irregular associated Legendre functions for integer values of the degree and order and for all real arguments. The computation of the interaction of two electrons, 1∕|r1−r2|, in prolate spheroidal coordinates is used as one example where these functions are required for all values of the argument and we are able to easily compare the series expansion in associated Legendre functions and the exact value.Solution method: The code evaluates the regular and irregular associated Legendre functions using forward recursion when |x|<1 starting the recursion with the analytically known values of the first two members of the sequence. For values of the argument |x|<1, the upward recursion over the degree for the regular functions is numerically stable. For the irregular functions, backward recursion must be applied and a suitable method of starting the recursion is required. The program has two options; a modified version of Miller’s algorithm and the use of the wronskian relation between the regular and irregular functions, which was the method considered in [1]. Both approaches require the computation of a continued fraction to begin the recursion. The wronskian method (which can also be described as a modified Miller’s method) is a convenient method of computations when both the regular and irregular functions are needed.

Comparison of HSPF and PRMS Model Simulated Flows Using Different Temporal and Spatial Scales in the Black Hills, South Dakota

AbstractThe hydrological simulation program Fortran (HSPF) [Hydrological Simulation Program Fortran version 12.2 (Computer software). USEPA, Washington, DC] and the precipitation runoff modeling sy...

OpenMP GNU and Intel Fortran programs for solving the time-dependent Gross–Pitaevskii equation

We present Open Multi-Processing (OpenMP) version of Fortran 90 programs for solving the Gross-Pitaevskii (GP) equation for a Bose-Einstein condensate in one, two, and three spatial dimensions, optimized for use with GNU and Intel compilers. We use the split-step Crank-Nicolson algorithm for imaginary- and real-time propagation, which enables efficient calculation of stationary and non-stationary solutions, respectively. The present OpenMP programs are designed for computers with multi-core processors and optimized for compiling with both commercially-licensed Intel Fortran and popular free open-source GNU Fortran compiler. The programs are easy to use and are elaborated with helpful comments for the users. All input parameters are listed at the beginning of each program. Different output files provide physical quantities such as energy, chemical potential, root-mean-square sizes, densities, etc. We also present speedup test results for new versions of the programs.

Optimization of sequential code for simulation of solar radiative transfer in a vertically heterogeneous environment

This article belongs to the series of works aimed at improving computing capacity of radiation codes implementing the Monte Carlo statistical method. A short description is given of the main blocks of basic (FORTRAN version) and optimized (C version) codes designed for calculation of sky radiance in a vertically heterogeneous medium. We present the results of tests which were aimed at evaluating the performance of each of the codes under different conditions in numerical experiments. In the cases examined, the performance indicators of the optimized C code were higher as compared with the basic one. It is shown that differences in execution time of the codes are reduced by increasing the optical density of the atmosphere, and using more productive computers. The developed C code can serve as a basis for creating a high-performance radiation code.