## IASA NTUU “KPI” Projects with the State Agency for Science, Innovations and Informatization for 2011

According to the results of the competition for the Government program of introduction of grid- technologies, conducted by State Agency for Science, Innovations and Informatization (SASII) in April in 2011, the following project of IASA NTUU «KPI» was proclaimed as the one of the winners:

### Project DP/310-2011 «An interdisciplinary complex of optimal mathematical design in grid environment with the automatic composition and solving of equations of corresponding mathematical models»

**Compliance to the Program objectives**:*Objective 4.* Development and introduction of grid technologies in science, industry, financial, social and humanitarian spheres:*Task 4.1*. Development of specialized grid software and grid complexes for the use during scientific and scientifically-applied researches.

**Project Purpose**:

To develop the software complex (grid application to be used in a grid infrastructure), accessible by the user via the Internet that gives possibility for the user to compose and tune the route of mathematical experiment, i.e. to choose necessary procedures and computations to be executed on grid resources, including the automatic forming of equations of mathematical model of task. Thus the list of types of calculations, that is offered, covers considerable part of possible needs at the process of solving scientifically-applied research tasks, for example, these of remote design of different (by physical nature) objects (processes) with possibility of building of macromodels of these objects, and also reflection of objects with mathematical description on the basis of method of finite elements as equivalent substitution circuits of variable accuracy and size.

The interdisciplinary complex of optimal mathematical design that is developed for the complex scientifically-applied researches in grid environment, implements original innovative numeric methods. Among them are: method of diagonal modification for the solving of the bad conditioned linearization problems, method of search of decision curve for the reliable solving of nonlinear problems, implicit method of variable order and step for the solving of hard differential nonlinear equations, method of optimization of variable order with the possibilities that exceed existing solutions, method of maximization to the yield coefficient and others. The complex of these newest methods has got the diploma of the first degree at the competition of scientific and technical innovations in industry of computer aided design, conducted by Intel among the scientists of CIS countries in 2005. The adopted newest algorithms are partly described in the monographs of "**Algorithmic Analysis of Electronic Circuits**" (authors: Petrenko A.I., Sigorsky V.P.), translated into English and published in the USA in 1975 by a publishing house Western Periodical Co., San - Francisco, 618 p., and " **ALLTED - Computer-Aided System for Electronic Circuit Design**" (authors: Petrenko A., Ladogubets V., Tchkalov V., Pudlowski Z)., published in 1997 by a publishing house UICEE (UNESCO), Australia, Melbourne, 204 p.

The project executors have a long-term experience of fruitful work in industry of development of numerical algorithms, interactive applications, creation of separate blocks and whole complexes of the automated design of the different purpose. NTUU «KPI» was among the main contributors of works on the program “PRAM” that was executed in obedience to the corresponding Government programs of the USSR. Then an industry standard was created for Ministry of Defence industries in the field of automated schematics design, and also corresponding standards for the ministries of general engineering.

The interdisciplinary complex of optimal mathematical design that is developed contains the following:

1. The automatic composition of mathematical model of the object (process) after its structure and component properties description as algebraic - differential or differential equations with the sizes of that can reach 10000 and that composing the mathematical models of complex objects and processes of different physical nature.

2. Reduction to the dimension of the formed mathematical model of the object (process) by transformation of structure of object (triangle - star) and receipt of macromodel of the object.

3. A static analysis of the object (process) based on its model with the use of methods of Newton- Raphson, continuation of decision with a variable parameter, the search of curve of decision and others.

4. Application of method of diagonal modification to the decision of the systems of linear equations, that prevents the necessity of equations reorder for the cases of zero pilot elements of matrix and allows to handle the badly conditioned tasks.

5. Frequency analysis of the object (process) based on its model by the solving of the linear systems of equations with complex coefficients and automatic determination of corresponding parameters (bandwidth, resonant frequencies and values and others like that).

6. Analysis of the dynamic modes of the object (process) in a time domain based on its model with the use of implicit methods of variable order (1-6) and variable step, and also automatic determination of corresponding design parameters (time of delay, time of front raising, amplitude of impulse).

7. Sensitive analysis of parameters of the object (process) based on its model in a time or frequency domains according to the change of parameters of internal components.

8. Parametric optimization of the object (process) description bases on its model in a time or frequency domains with the use of the newest method of variable order(1-4), that absorbs the gradient methods of 1th order and quasi-Newtonian methods of variable metrics of the 2nd order.

9. Statistical analysis of the object (process) parameters based on its model in a time or frequency domains with the use of Monte Carlo method with possibility of optimization of the yield coefficient.

10. Web-based user interface allows composition of the necessary workflows of mathematical experiments and contains the tools to visualize the results of calculations in a graphic form.

11. Demo with the examples of solving of the scientifically-applied tasks from energy, electronics, mechanics, ecology and other domains.

12. Educational system of workflows composition of mathematical experiments.

Today there are no acknowledged grid applications for support of mathematical experiment during the scientifically-applied researches. The interdisciplinary complex of optimal mathematical design in grid- environment that is developed is possible to be opposed with the GridModelica system (www.ida.liu.se/labs/pelab/modelica/GridModelica.html) that substantially concedes to the new complex by its capabilities and parameters.

2011 plans: the conduction of research of structure of network interdisciplinary complex of optimal mathematical design in grid environment, architecture of software interface of complex and technical requirements for implementation of functional components, and also development of mechanisms of integration of components of the complex in case of remote composition of workflow of mathematical experiment for the analysis of the static states of the object ( process) on the example of analysis of the static state of the object (process) in grid environment.

**Expected results**:

As a result of implementation of project the interdisciplinary complex of optimal mathematical design, built into the resources of national grid, will be created in 2011-2012, that will provide support of the collective design or research for complex objects and processes of different physical nature by the distributed team of developers on the free resources of grid infrastructures with the bandwidth of communication of data cluster-cluster not less than 10 Gbps; and accessible from any workstation of national grid infrastructure equipped by an ordinary web browser.

For the scientific support of implementation of this work it is planned to prepare for publishing the collective monograph of «Electronic circuit design in grid environment» (in 2012); publication of the 6 scientific articles (annually); participating in 3 conferences (annually) and the exhibition «Science for production» (in 2012) and other measures.

Domestic scientists of different departments at the end of 2012 can get possibility to conduct the scientifically-applied research-and-developments on the base of interdisciplinary complex of the optimal mathematical design built into the resources of national grid infrastructure, without the need of spending money on acquisition and adjusting the facilities of computer design. Except that, the personal interest of scientifically-engineering European community in the testing of this new Ukrainian innovative development is possible, as there is no complete foreign analog of the complex.

**In 2011 the following results were achieved:**

1. The architecture of the interdisciplinary complex of the optimal mathematical modeling GridALLTED was proposed. It is based on grid services (utilizing SOAP, WSDL and UDDI) allowing to leverage of the modern grid technologies for the server side implementation (resource discovery, intermediate data storage, long-term calculations etc.).

2. The possibility of development of the automated method of schematic macro-models composition for the components described by the systems of ordinary linear and non-linear differential equations was proved.

This allows implementation of the standard design procedure of modeling the components of different physical nature.

3. The method of composition of the schematic macro-models for the components described by systems of partial differential equations was improved. It differs from existing one by taking into consideration:

- digits limit for number representation in the real-world computer architecture;

- very big difference in C, G, L matrices elements (up to 30 order).

This allows the achievement of the adequate schematic macro-models of the non-electrical objects.

4. Operability, precision and efficiency of the methods proposed were proved with the results of the modeling of the various typical objects in grid environment.