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The aim is to acquaint students with the basic problems of numerical mathematics. Thematic areas are:
• Systems of linear equations. Direct and basic iterative methods.
• Solving nonlinear equations and their systems
• Eigenvalue problem
• Approximation of functions
• Numerical quadrature
• Numerical methods of solving ordinary differential equations with initial and boundary conditions.

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The subject follows the Applied Mathematics and Numerical Methods I, the aim is to master methods of solving partial differential equations. Both elliptical and parabolic tasks will be solved. Less attention will be paid to hyperbolic problems. Problems of effective preconditioning of emerging systems of linear systems will also be addressed.

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Random sample. Idea of statistical inference. Random variables and their distribution. Normal distribution. Central limit theorem. Multiple distribution. Independence. Correlation. Theory of estimation. – point and interval estimate. Hypotheses testing. Test statistic and statistical decision. P-value. Simple linear regression – parameters estimation, hypotheses testing, prediction intervals, regression diagnostic. Simulation independent realizations of random variables.

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Multivariate normal distribution. Principal component analysis. Linear regression. Nonlinear regression. Bayes theorem. Bayesian parameters estimates. Bayesian inference in linear model. Time series and their frequency domain description. Kalman-Bucy filtr.
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Basic principles of object-oriented programming (C ++, D, ADA, Fortran), algorithms design, component programming,
coexistence of different platforms, portability of programs on various hardware platforms, security aspects of programming.

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The aim of the subject is to provide to students detailed knowledge in the field of current trends in materials used in
construction industry and also in materials applied historically in older and culture heritage valuable buildings. The scope of the subject comprises description of building materials and interpretation of their properties and performance in relation to their structure and composition. Within the frame of Materials Engineering course, the students will summarize their knowledge in materials behaviour and dependence of their mechanical-physical parameters on exterior effects and climate conditions changes. The students will also gain knowledge and skills in the field of materials research and actual and latest trends in materials basis for building industry.

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The aim of the course is to solve coupled multiphysics problems, e.g. thermoelasticity, coupled heat and moisture transfer, thermo-hydro-mechanical problem, electordiffusion, etc. First, the balance equations together with constitutive laws will be summarized for selected coupled multiphysics problems. Discretization in space and time (Galerkin-Bubnov method, Galerkin-Petrov method, generalized trapezoidal rule, etc.) will follow. Solution of systems of linear algebraic equations obtained after discretization (the use of symmetry and sparsity, direct methods, iterative methods). Solution of systems of nonlinear algebraic equations (Newton-Raphson method, the arc-length method). Utilization of parallel computers for solution of large problems based on domain decomposition methods.

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The objective of this course is to gain knowledge and skills necessary for advanced design of structures subjected to dynamic loading.
Eigenvalue analysis and forced vibration analysis using finite element method. Properties of materials subjected to dynamic loading. Dynamic analysis of continuum, wave propagation. Soil-structure interaction. Earthquake and technical seismicity. Aeroelasticity of structures, wind loading. Vibration of structures – high-rise buildings, chimneys, masts, towers, transportation structures, machine foundations. Reduction of dynamic effects. Basic principles of nonlinear analysis.

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The course is intended for students who did not have the opportunity to study basic goals, tasks and elementary means of an experimental analysis during the course of the bachelor’s and master’s degree study. Within the course, students will familiarize with basic procedures and principles of the experimental analysis of building and civil engineering structures. The interpretation of the problems will include the overview of testing methods used to determine basic material properties, the description of experiments focused on observation of climate loads, the examples of verification and identification of theoretical models based on experimental results, the experiments realized on physical models for estimation of wind effects in wind tunnels and for investigation of earthquake effect on shake tables, the long term monitoring of building and civil engineering structures. The interpretation will further include the principles of preparation, realization and evaluation of static load tests realized on structural elements or whole structures, the basic methods used for an analysis of measured data obtained during dynamic tests, the principles of preparation, realization and evaluation of dynamic tests including an experimental modal analysis and a dynamic load test, the principles of experiments focused on evaluation and assessment of vibration effects on building structures from the view of the load capacity limit state and on users of building structures from the view of the serviceability limit state, the demonstration of several practical tasks.

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The major goal of the course is to expand knowledge about experimental analysis of building and civil engineering structures obtained during master’s or doctoral degree study. Within the course, students will familiarize with the basic design of the static and dynamic experiments applied on building and civil engineering structures, relative sensors, absolute sensors, strain gauges, principles of strain measurement by means of strain gauges, basics of estimating measurement uncertainty, experiments realized on physical models, basics of the similarity theory, model laws, experimental methods for axial tensile force determination in rods, cables and stays, static and dynamic load tests and long term monitoring realized on building and civil engineering structures illustrated on practical examples (real reasons for realization, arrangement of experiments, ways of processing data, basic conclusions), the demonstration of practical tasks.

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The aim is to explain basic properties of anisotropic and heterogeneous materials, philosophy of their solution and ways of homogenization. Micro-, meso-, macro-, view of composite materials. Hill's theory of composites. Variation formulation, Hashin-Shtrikman's variation principle, consequences for the methods of homogenization of composites. Tension, Eshelby tractions, Mori-Tanaka method, self-consistent, penalty method. Applications, cylindrical shells, deskframe structures, selected building structures (tunnels, underground constructions, etc.).

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The objective of the course is to deliver an introduction to numerical methods for solving partial differential equations, with particular focus on finite element method. It is suitable for students without previous knowledge in the field. It consists of the two main parts:
- overview and derivation of fundamental equations for theory of elasticity and heat transfer, introduction to method of weighted residuals, strong and weak solution, choice of approximation and weight functions.
- application of finite element and finite difference method to solution of selected problems from engineering practice (1D elasticity, beams, grids on elastic foundation, plates on elastic foundation, 1D and 2D stationary and transient heat transfer).
The students will not only understand theoretical aspects of the methods, but will use and further develop prototype implementations in Matlab to understand the algorithmic aspects of the methods. During the seminars, the students will individually or in a small teams solve selected problems, interpret and discuss results.

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The objective of the course is to extend basic knowledge of numerical methods for solving PDEs and particularly finite element method towards their advanced applications in engineering. The course will focus on problems of geometrically and materially nonlinear static (theoretical framework, linearization, algorithmic aspects, solution methods – direct and indirect control, plasticity and damage based models). Introduction to Isogeometric analysis, eXtended finite element method, mesh generation and efficient methods for solution sparse linear systems.
The students will not only understand theoretical aspects of the methods, but will use and further develop prototype implementations in Matlab to understand the algorithmic aspects of the methods. During the seminars, the students will individually or in a small teams solve selected problems, interpret and discuss results.

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The aim is to clarify the approaches and methods of optimization of building structures and their associated computational models. Types of optimization of building structures, variation formulations, selected optimization methods, using modern numerical methods - FEM, BEM, SPH, semianalytical methods, models of rod and plate structures. Nonlinear optimization, plastic analysis, buckling. Eigenparameters, transformation field analysis. Application, modeling of steel bridges, contact problems (piping, slopes, tunnel lining).

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The course focuses at systematic description of nonlinear mechanical behavior of homogeneous and heterogeneous materials: Formulation of constitutive equations of fundamental material models (elastoplastic, viscoelastic, progressive damage). Mathematical models of heterogeneous materials (fundamentals of mesomechanics). Fundamentals of linear fracture mechanics (stress intensity factor, energetic criterion of local crack stability, other criteria). Fundamentals of nonlinear fracture mechanics (crack with localized plastic zone, cohesive crack model, size effect). Fundamentals of the theory of fatigue processes.

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This course covers the fundamentals of tensor algebra and calculus and demonstrates the power of tensor notation applied to formulation and solution of engineering problems. Selected examples cover solid and fluid mechanics, as well as heat and mass transport problems. The first part of the course is devoted to the definition of tensors, understood as linear mappings, to algebraic operations with tensors, to tensor fields and their differentiation, and to transformations between volume and surface integrals based on the Green and Gauss theorems. In the second part, it is shown how these mathematical tools enable an elegant description and analysis of various physical problems, with focus on applications in civil and structural engineering.
The classes combine lectures and seminars, with emphasis on problems assigned as homework, which form the basis of presentations and discussions in class. The objective is not only to transfer specific knowledge, but also to develop the students‘ aptitude for independent thinking and critical analysis. At the same time, mastering of tensorial notation by the students will greatly facilitate their future reading of modern scientific literature in many fields of research.

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The covered material splits into three blocks: (i) Important relations and theorems necessary in the area of the theory of reliability and mathematical statistics, (ii) Analytical and simulation methods to analyze reliability of structures, (iii) Advanced methods or reliability analysis exploiting the Bayesian inference in conjunction with MCMC simulation.
List of lectures:
1. Basic relations, definitions and notation, 2. Selected probability distributions and important inequalities, 3. Transformation of probability density function (one and more variables), 4. Reliability of simple structures, 5. Evolution of reliability in time, 6. Reliability and solution methods, 7. Renewable systems, 8. Reflection of the theory in EC standards, 9. Analytical methods to address reliability, 10. Simulation methods, 11. Monte Carlo type simulation, 12. MCMC sampling (Markov chain-Monte Carlo, Bayesian statistical method).

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In this course, which is taught exclusively in English, attention is paid to the structure of a scientific or technical paper, to grammatical and stylistic aspects and to the creative scientific writing process from manuscript preparation up to its publication (including the selection of an appropriate journal and the manuscript submission and review process). Other topics covered in the course include effective search for and processing of information sources in a network environment, exploitation of library, open-access and other resources and tools, citation rules and publication ethics. Students get acquainted with citation managers, manuals of style, typesetting rules and tools for the preparation of a technical manuscript in LaTeX. Basic information on bibliometric tools and evaluation of scientific output is also provided.

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The objective of this course is to gain knowledge and skills necessary for design of concrete and masonry structures when automated production is used. This course consists of lectures focused on digital fabrication technology, structural aspects of production equipment, automata control systems, definition of building materials which are used by automata, structural analysis methods suitable for digital fabrication construction processes.

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The use of probabilistic approaches and modern computational methods at one time represents an effective tool for concrete structures analyses. By using stochastic methods, an optimized design of concrete structures can be achieved with respect to particular conditions, uncertainties and random variables. Non-linear analyses of concrete structures serve for simulating the real behaviour of structures subject to various load. The objective of this course is to gain practical knowledge necessary for the evaluation of experimental data of advanced materials, development of material models and numerical simulations of concrete structures by using modern computational methods and approaches.

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The objective of the course is to introduce the students into the state of the art in the area of concrete nuclear containments. The course will cover selected topics from the following areas: Historical development of nuclear containments. Containment vs. confinement. Types of containments, alternative solutions. Overview of valid standards and safety requirements. Loads and load cases for structural design. Principles of structural design and design of prestress. Structural and material design of internal sealing liner. Numerical modeling of containments and their components. Construction of containments.

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Deterioration processes in concrete structures (chemical, physical and mechanical deterioration) including diagnostic
methods and design and performing of rehabilitation measures. Deterioration of concrete structures documented by bestrespectively
worse-practice examples. Deterioration of masonry structures at examples of housing and transport
infrastructure.

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Issues related to early age concrete – hydration, development of microstructure, stress-strain diagrams. Numerical modeling of early age concrete. Advanced methods for analysis and their application to formwork removal with respect to displacement control. Design of anchor zones for prestressed concrete at very early ages.

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Performance of concrete subjected to high (strain) velocity loading, such as blast, impact (objects, vehicles, etc.) or
penetration (projectiles). Blast wave propagation in (confined) space and in material in particular with respect to the
heterogeneity of material. Interaction of various extreme loadings, e.g. blast and fire. Principles of numerical modeling of
fast dynamic phenomena.

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Fibre reinforced concrete as a structural material has become popular in the construction industry. Its nonlinear behaviour and material properties encourage to use nonlinear computational methods for the design of fibre reinforced concrete structures. The computational accuracy of obtained results leans on the development and the calibration of material models. The objective of this course is to gain knowledge of short-term and long-term behaviour of fibre reinforced concrete composites, general rules, regulations and recommendations for the design of fibre reinforced concrete structures, as well as the utilization of modern computational approaches for the predication of both crack occurrence and crack propagation.

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The objective of this course is to gain knowledge and skills necessary for work with uncertainty or insufficient information, which can be used for numerical description of behavior of materials and structural systems. This course consists of lectures focused on difference between classical and fuzzy sets, definition of fuzzy sets, basic operations on fuzzy sets, fuzzy arithmetic, difference between classical and fuzzy logic, fuzzy logic modeling and methodology of fuzzy logic modeling.

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Lectures
- Structural fire design.
- Physical and chemical processes in concrete and steel at high temperatures.
- Models of transport processes in concrete (heat transfer, coupled heat and mass transfer).
- Numerical methods (finite difference method, finite element method, time discretization methods).
- Coupled thermo-mechanical problem, damage mechanics, moving boundary problem (Stefan problem).
- Modelling of structures at high temperatures, analysis of structures after fire.
Seminars
- Studying the worked examples, solution of selected problems related to the topic of the lectures and the seminar paper.
Consultations
- Consultations of the examples and the seminar paper.

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The subject is focused on assessment of existing sconcrete and masonry structures in terms of contemporary approaches and standards. The main topics of the subject are:
- theory of existing structures assessment
- material properties determination based on investigation and testing
- differencies in design of a new structure and assessment of existing one
- methods and approaches to assessment of existing structures
- investigation methods, results and its application in assessment of masonry, RC and presstressed concrete structures
- design principles of remedial actions for superstructures

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Advanced design of reinforced concrete structures - comparison of analysis models and methods. Non-linear behaviour,
concrete structures in high temperatures mode. Plastic behaviour, formation of yield hinges, plastic strain in the ultimate
limit state, rotation capacity. Limit of load capacity, strain control of elements.

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Factors influencing creep and shrinkage of concrete. Main features and effects of creep and shrinkage of concrete. Increase of deflections and redistribution of internal forces. Structures changing structural system and second order effects. Time development of the humidity and temperature distributions in concrete members. Environmental conditions and analysis of temperature and humidity transfer. Non-uniformity and time development of humidity distributions. Strain softening. Stress analysis. Creep and shrinkage prediction models. Calculation of strain from a known stress history. Direct integration and methods of time-discretization. Analysis of stress variation with known strain history; relaxation. Creep and shrinkage analysis of structures. Structural analysis of statically determinate and indeterminate structures, homogeneous and non-homogeneous, changing structural system. Methods of structural analysis. Redistribution of internal forces. Stress variation in concrete structures subjected to support settlements. Stress distribution in box girders. Creep analysis of high-rise buildings. Creep buckling. Excessive deflections of prestressed concrete bridges. Findings from experimental investigations. Measurements of stress and deflection developments. Comparison of experimental results with theoretical predictions. Statistical variability of material creep parameters and environmental factors. Uncertainty of creep predictions. Variability of stresses and deformations. Conclusions and practical recommendations.

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The objective of this course is to gain knowledge and skills necessary for design and safety assessment of concrete structures in nuclear facilities. This course focuses on effect of radiation on mechanical properties of concrete and its components, possibilities of numerical modeling of effect of radiation on concrete and concrete structures, corium-concrete interaction and possibilities of hermetic insulation provided by concrete structures and concrete structural components.

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Reliability of steel structures. Global and local stability. Stability of plate structures. Thin walled cold formed structures. Interaction with sheeting structures. Composite steel and concrete structures.Fire design.

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Individual assignment of sophisticated research references dealing with steel structures in English language. Elaborating of his/her own opinion on the contribution of the studied out references for integration into an introductory chapters of his/her PhD thesis.

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Monitoring of structures and subsoil applied as a tool for verification of assumptions made at design stage, selection of input data for calculations and for serviceability approval. Relationship of instrumentation by sensors and reliability to describe subsoil response and development of behaviour of monitored structure in real scale. Data gathering for back analyses and modelling of subsoil and structure deformation development. Practical training of line-wise monitoring of 3D displacement in instrumented borehole in front of the Faculty of Civil Engineering. Examples if instrumentation and data gathering for different types of displacement sensors, mechanical stress and temperature.
Description, execution and evaluation of results of selected field tests. Examples of applications of field tests and applications for calculations and modelling. Design of field tests and field instrumentation for selected types of structures and site conditions.

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- Inaccuracy of the input data and main sources of errors in the numerical modelling of underground structures
- Principles of modelling New Austrian Tunnelling Method (sprayed concrete primary lining, sequence of the excavation – ß method, influence of supporting elements (rock bolts etc.)
- Modelling of the earth shields (EPBS) in soils (including the influence of pre-face pressures).
- parametric studies and back analyses

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Construction, reconstruction and repair of roads, subgrade and its bearing capacity, soil treatment, test of soils, aggregate, general and special requirements, bituminous binder, types, modified bitumen, materials and construction ob base layer, asphalt mixtures for construction and repait of roads, concrete pavement, repair technology of concrete pavement, asset management and maintenance, diagnosis of roads, recycling of roads materials.

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The subject will introduce to students basic principles of landscape engineering and landscape conservation. Complex understanding of the topic, interrelations and synergies will be emphasized, rather than particular tasks of individual disciplines. There will be defined specific target area for individual student, or group of students (according to their specialization), where strong interaction between human activities and landscape occurred or is expected. The goal of the work (project) then will be understanding to relations, processes, effects and conditioning within given locality, possible effects on the landscape by planned or realized activity and possibly brief proposal of compensation or prevention measures or modification of original project. Students should ideally work within the team, search for interdisciplinary solutions, analyses, to apply multicriterial approach.

Knowledge of English and optional language is required for all programs.

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The course is aimed at making doctoral degree students familiar with the basic genres of the academic style and prepare them for real-life communication situations, such as e.g. the presentation of their own research and development achievements, writing grant applications, common correspondence, writing abstracts, etc. The course should also assist in the preparation for the examination in English, which is a compulsory part of doctoral degree study. The course is not compulsory, it is not completed by granting a credit or passing an examination.

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The course in Czech for foreigners is aimed at the university students’ needs for mastering written and spoken language with the basic inventory of linguistic structures needed for making oneself understood in common situations of everyday practical life; advanced students develop the ability of independent work with a simple technical text. The course is not compulsory, it is not completed by granting a credit or passing an examination.

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The doctoral degree student who wants to pass an examination in French can choose from the elective courses offered by the Department of Languages. The course is not compulsory.

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The doctoral degree student who wants to pass an examination in German can choose from the elective courses offered by the Department of Languages. The course is not compulsory.

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The doctoral degree student who wants to pass an examination in Russian can choose from the elective courses offered by the Department of Languages. The course is not compulsory.

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The doctoral degree student who wants to pass an examination in Spanish can choose from the elective courses offered by the Department of Languages. The course is not compulsory.