International Journal of Modeling, Simulation, and Scientific Computing

The discipline of modeling and simulation (M&S) is advancing, maturing, and is being used in more and more challenging areas. Appreciation of its comprehensive and integrative view, i.e., its big picture would be very useful for its continued and systematic growth and successful applications. The article starts with a rationale for the needs to see the big picture of M&S and ways to see the big picture. Since M&S is closely related with reality and its representations i.e., models, reality/model dichotomy is clarified. As the core of the article, detailed perceptions of M&S from different perspectives such as: purpose of use, problem to be solved, connectivity of operations, and types of knowledge processing are clarified. Then, three aspects of ways to increase the trustworthiness of M&S are outlined (i.e., validation and verification (V&V), quality assurance (QA), and failure avoidance (FA). The article ends with a discussion of M&S from the perspective of professionalism. Some recommendations or challenges are still open for implementations for the success of M&S.

As a consequence of the permanently increasing complexity of modeling and simulation (M&S) applications, the demand for controlling and demonstrating the quality of a model and its applications by introducing adequate quality measures, techniques, and tools is obvious. Since efforts toward quality assurance such as model documentation and verification and validation (V&V) are time consuming and costly, a reasonable balance between quality and efficiency should be achieved in all practical applications. In the context of an integrated quality assurance strategy, several quality- and efficiency-related concepts have been developed and combined, including a model documentation guideline, a generalized V&V concept (the V&V Triangle), a graph-based V&V, and a multistage tailoring process. This article describes the proposed concepts and their applications in two selected simulation development projects. While the primary objective of the first project was introduction and application of the documentation guideline and the tailoring concept; the second project focused more on applying the V&V Triangle and the graph-based V&V. Based on the findings achieved by the case studies, some relevant lessons learned are summarized, which serve as expertise for both theoretical concept refinement and practical applications.

This article proposes a methodology for real-time simulation of electric circuits consisting of linear circuit components combined with nonlinear elements, such as diodes and electronic switches, that exhibit discontinuous behavior. The methodology consists of sub-dividing fixed numerical integration time-steps into sub-steps over which the entire circuit behaves linearly, thus permitting the simulation over each sub-step to be performed using analytic formulas. For non-real-time simulation, this has routinely been accomplished using variable-step numerical integration. In the article, we show how real-time integration can be accomplished using a linear analytic formula over each fixed integration step, where the formula coefficients are stored functions of the sub-step parameters. For example, in a single-phase diode rectifier circuit, each fixed integration step h is divided into two sub-steps, the first of duration he_n over which the diode is not conducting and the second of duration h(1 - e_n) over which the diode is conducting, with a simple formula used to calculate the dimensionless sub-step parameter e_n. The output current for the n + 1 frame is then calculated with a linear formula requiring four multiplications and four additions. Three of the five coefficients required for this calculation are rather complex functions of the parameter e_n. However, by restricting e_n to N + 1 equally spaced values between 0 and 1, the 3(N + 1) possible coefficient values can be pre-computed and stored in memory, which results in a sizeable reduction in execution time for each fixed integration step. The article includes a three-phase diode rectifier example that sub-divides each fixed integration step h into three sub-steps of duration hd_n, h(e_n - d_n) and h(1 - e_n).

In this article, a methodology and its application in various fields is dealt with. The theoretical research work has been undertaken at the McLeod Institute of Simulation Sciences Hungarian Center and its results have been implemented in the CASSANDRA (Cognizant Adaptive Simulation System for Applications in Numerous Different Relevant Areas) simulation system. The applications covered a wide range of areas where the tool system and the methodology have been applied with success. Most of these were in the framework of international projects of the European Union.

Some applications of real-time simulation now require frame times that are shorter in duration than can be delivered by traditional methods such as real-time versions of Linux (RT-Linux). RT-Linux can be satisfactory for frames as short as 10μS, but there is now a need, for example in the simulation of power-electronic systems, for frame times as short as 1 μS or even less. Techniques based on the interfacing of digital signal processors (DSPs) to a Windows PC have achieved a 2 μS frame time for a typical power electronics application and less than 1 μS is shown to be possible using field-programmable gate arrays (FPGAs). Combining these high-speed techniques with simulations of the rest of the system necessitates the use of multi-rate techniques. Software tools, interfacing issues, and system architecture for a high-speed, real-time, distributed, multi-rate (HRDM) simulator are discussed.

In this article, we introduce spline collocation methods to solve fractional boundary value problems (BVPs). The existence and uniqueness theorem of collocation solutions is studied, and the error estimate of collocation solutions is discussed. Numerical experiments are presented to demonstrate the theoretical results.

In this article, a new unconditionally stable method based on alternating direction implicit (ADI) method for solving nonlinear unsteady 2D parabolic problems is presented. The order of this method in both time and space is 2. For this development, the Peaceman–Rachford ADI method has been modified suitably to take care of nonlinear forcing term of the equation appropriately. The unconditional stability of the method is shown under discrete L₂ norm on bounded sets. The method of solution consists of a number of strictly diagonally dominant tridiagonal matrices, which make the method computationally efficient. The accuracy of the proposed method is also demonstrated by some numerical examples.

Hardware accelerators (such as the Cell Broadband Engine) have recently received a significant amount of attention from the computational science community because they can provide significant gains in the overall performance of many numerical simulations at a low cost. However, such accelerators usually employ a rather unfamiliar and specialized programming model that often requires advanced knowledge of their hardware design. In this article, we demonstrate an alternate and simpler approach toward managing the main complexities in the programming of the cell processor, called software caching. We apply this technique to a numerical relativity (NR) application: a time-domain, finite-difference Kerr black hole perturbation evolver, and present the performance results. We obtain gains in the overall performance of generic simulations that are close to the theoretical maximum that can be obtained through our parallelization approach.