A geometric model for the generation of models defined in Complex Systems (original) (raw)
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A computational algorithm for system modelling based on bi-dimensional finite element techniques
Advances in Engineering Software, 2009
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Numerical modeling for some fields related to engineering and obstacle problems.
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A New Computational Algorithm To ConstructMathematical Models
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There are several methodologies to study dynamic complex structural systems and their modelling. Each methodology implies the use of a language, whose theory studies and formatting are essential for the development of the model. The authors have already started these studies with the construction of grammars in ecological models (e.g.Villacampa et al [5]). These studies start from the fact that all the models have signs, syntax rules and the capacity to codify and decodify information. This paper presents an algorithm for the generation of a new language. The computational new language, "ALMOD", is the basis for the development of a useful new tool to build mathematical equations which model complex structural systems according to the methodology used by the authors (e.g. Uso et al[3], Villacampa et al[4]).
Mathematical treatment of environmental models
Large-scale environmental models can successfully be used in different important for the modern society studies as, for example, in the investigation of the influence of the future climatic changes on pollution levels in different countries. Such models are normally described mathematically by non-linear systems of partial differential equations, which are defined on very large spatial domains and have to be solved numerically on very long time intervals. Moreover, very often many different scenarios have also to be developed and used in the investigations. Therefore , both the storage requirements and the computational work are enormous. The great difficulties can be overcome only if the following four tasks are successfully resolved: (a) fast and sufficiently accurate numerical methods are to be selected, (b) reliable and efficient splitting procedures are to be applied, (c) the cache memories of the available computers are to be efficiently exploited and (d) the codes are to be parallelized.
Multi-modeling and multi-scale modeling as tools for solving complex real-world problems
Journal of Serbian Society for Computational Mechanics, 2016
In previous decades a number of computational methods for calculation of very complex physical phenomena with a satisfactory accuracy have been developed. Most of these methods usually model only a single physical phenomenon, while their performance regarding accuracy and efficiency are limited within narrow spatial and temporal domains. However, solving realworld problems often requires simultaneous analysis of several coupled physical phenomena that extend over few spatial and temporal scales. Thus, in the last decade, simultaneous modeling of a number of physical phenomena (multi-modeling) and modeling across few scales (multi-scale modeling) have gained huge importance. In this paper, we give an overview of multi-modeling and multi-scale methods developed during the last decade within the Group for Scientific Computing at the Faculty of Science, University of Kragujevac. In addition, we give a short review of accompanying problems that we had to be solved in order to make the methods applicable in practice, such as parallelization of computations, parameters calibration, etc. In the first part of the paper we present methods for modeling various aspects of muscle behavior and their coupling into complex multi-models. The mechanical behavior of muscles is derived from the behavior of many individual components working together across spatial and temporal scales. Capturing the interplay between these components resulted in efficient multiscale model. The rest of the paper is reserved for the presentation of multi-models for solving real-world problems in the field of water resources management, as well as methods for calibration of complex models' parameters. As the most illustrative example, we present methodology for solving the problem of water leakage under Visegrad dam at Drina River in Republic of Srpska. With the aim to support decision-making process during dam remediation, we have developed specialized multi-model that continuously uses the acquired observations to estimate spatial distribution of the main karst conductors, their characteristics, as well as hydraulic variables of the system.
Mathematical models in science and engineering
Notices of the AMS, 2009
Mathematical modeling aims to de-scribe the different aspects of the real world, their interaction, and their dynamics through mathematics. It constitutes the third pillar of science and engineering, achieving the fulfillment of the two more traditional disciplines, which are theoretical analysis and experimentation. Nowadays, mathematical modeling has a key role also in fields such as the environment and industry, while its potential contribution in many other areas is becoming more and more evident. One of the reasons for this growing ...
Multiphysics Modelling and Simulation in Engineering
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As more and more complex and sophisticated hardware and software tools are available, complex problems described by consistent mathematical models are successfully approached by numerical simulation: modelling and simulation are present at almost each level in education, research, and production. Numerical "experiments" have predictive value, and complement physical experiments. They are unique in providing valuable insights in Gedankenexperiment-class (thought experiment) investigations. This chapter presents numerical simulation results related to a structural optimization problem that arises in systems with gradients and fluxes. Although the discussion concerns the optimal electrical design of photovoltaic systems, it may be extended to a larger class of applications in electrical and mechanical engineering: diffusion and conduction problems. The first concern in simulation is the proper formulation of the physical model of the system under investigation that should lead to consistent mathematical models, or well-posed problems (in Hadamard sense) . When available, analytic solutions -even for simplified mathematical models -may outline useful insights into the physics of the processes, and may also help deciding the numerical approach to the solution to more realistic models for the systems under investigation. Homemade and third party simulation tools are equally useful as long as they are available and provide for accurate solutions. Recent technological progresses brought into attention the Spherical PhotoVoltaic Cells (SPVC), known for their capability of capturing light three-dimensionally not only from direct sunlight but also as diffuse light scattered by the clouds or reflected by the buildings. This chapter reports the structural optimization of several types of spherical photovoltaic cells (SPVC) by applying the constructal principle to the minimization of their electrical series resistance. A numerically assisted step-by-step construction of optimal, minimum series resistance SPVC ensembles, from the smallest cell (called elemental) to the largest assembly that relies on the minimization of the maximum voltage drop subject to volume (material) constraints is presented. In this completely deterministic approach the SPVC ensembles shapes and structures are the outcome of the optimization of a volume to point access problem imposed as a design request. Specific to the constructal theory, the optimal shape (geometry) and structure of both natural and engineered systems are morphed out of their functionality and resources, and of the constraints to which they are subject.