Efficient Simulation Code Research Articles

Development of new generation software tools for simulation of electron beam formation in novel high power gyrotrons

Computer aided design (CAD) based on numerical experiments performed by using adequate physical models and efficient simulation codes is an indispensable tool for development, investigation, and optimization of gyrotrons used as radiation sources for electron cyclotron resonance heating (ECRH) of fusion plasmas. In this paper, we review briefly the state-of-the-art in the field of modelling and simulation of intense, relativistic, helical electron beams formed in the electron-optical systems (EOS) of powerful gyrotrons. We discuss both the limitations of the known computer codes and the requirements for increasing their capabilities for solution of various design problems that are being envisaged in the development of the next generation gyrotrons for ECRH. Moreover, we present the concept followed by us in an attempt to unite the advantages of the modern programming techniques with self-consistent, first-principles 3D physical models in the creation of a new highly efficient and versatile software package for simulation of powerful gyrotrons.

On the extension of the complex-step derivative technique to pseudospectral algorithms

The complex-step derivative (CSD) technique is a convenient and highly accurate strategy to perform a linearized “perturbation” analysis to determine a “directional derivative” via a minor modification of an existing nonlinear simulation code. The technique has previously been applied to nonlinear simulation codes (such as finite-element codes) which employ real arithmetic only. The present note examines the suitability of this technique for extension to efficient pseudospectral simulation codes which nominally use the fast Fourier transform (FFT) to convert back and forth between the physical and transformed representations of the system. It is found that, if used carefully, this extension retains the remarkable accuracy of the CSD approach. However, to perform this extension without sacrificing this accuracy, particular care must be exercised; specifically, the state (real) and perturbation (imaginary) components of the complexified system must be transformed separately and arranged in such a manner that they are kept distinct during the process of differentiation in the transformed space in order to avoid the linear combination of the large and small quantities in the analysis. It is shown that this is relatively straightforward to implement even in complicated nonlinear simulation codes, thus positioning the CSD approach as an attractive and relatively simple alternative to hand coding a perturbation (a.k.a. “tangent linear”) code for determining the directional derivative even when pseudospectral algorithms are employed.

N-body simulations using customized potential-density pair basis sets

Potential–density pair basis sets can be used for highly efficient N-body simulation codes, but they suffer from a lack of versatility, i.e. a basis set has to be constructed for each different class of stellar system. We present numerical techniques for generating a biorthonormal potential–density pair basis set that has a general specified pair as its lowest-order member. We go on to demonstrate how the set can be used to construct N-body equilibria, which we then evolve using an N-body code that calculates forces using the basis set.

Full-vectorial mode analysis of rib waveguides by iterative Lanczos reduction

A highly efficient computer simulation code is developed to perform full-vectorial mode analysis of rib or channel waveguides. On a workstation, the mode profile and index can be calculated in 410 s if a 192*192 grid is used. The code is based on the iterative Lanczos reduction technique. Although the matrix representation of the transverse Helmholtz operator is slightly asymmetric in the vectorial mode analysis, the Lanczos reduction procedure can still converge to the eigenmode. Results for several rib waveguides are presented. They are compared to the results of the vectorial finite-element method and semivectorial analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Drastic Reduction of Computing Time in Dynamic Simulation for Hydrogen Isotope Distillation Columns

An efficient dynamic simulation code for hydrogen isotope distillation columns is developed. Because of the great dimensionality and stiffness of the basic ordinary differential equations to be integrated, the long computing time required is often the major stumbling block in computer simulation work for column dynamics. Publicly available integration algorithms are reviewed and some are tested. The Ballard-Brosilow algorithm is chosen as the most attractive one in terms of both stability and simplicity. The algorithm requires only solution of linear tridiagonal equations and scalar bubble point calculations at every time step. Replacing the improved Euler algorithm in the previous code by the Ballard-Brosilow algorithm and determining an adjustment method for the time step size, the resultant computer code presents a remarkable success: A typical numerical example simulating column dynamics from a steady state to another indicates that the calculational results can be obtained with engineering accuracy in about two orders of magnitude shorter computing time.

Continuous system simulation languages

Continuous system simulation languages are very high level programming languages which facilitate modelling and simulation of systems characterized by ordinary and partial differential equations. This paper discusses design principles and implementation techniques for continuous system simulation languages. Following a brief introduction to very high level languages, design principles for continuous system simulation languages are presented. These principles are illustrated by examples from the Continuous System Modelling Program (CSMP) and the Partial Differential Equation Language (PDEL). A typical program in each language is included. Batch and interactive implementation techniques for continuous system simulation languages are discussed. The classical batch implementation technique is to provide a preprocessor which translates the simulation language into an algorithmic language such as FORTRAN or PL/1. The PL/1 preprocessor is described as a useful language for the implementation of very high level language translators. The final section of the paper presents an interactive implementation technique which interfaces a batch program processor to interactive graphics display and updating routines. In this manner, efficient simulation code is interfaced to flexible interaction routines. In addition, the batch processor is preserved intact, thus requiring only one implementation of the language for both batch and interactive applications.