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structures, and engineering systems, as well as to develop digital twins of manufacturing processes and its individual components, what is commonly referred as simulation-based engineering science. Professors from the Center for Design, Manufacturing and Materials will provide

overviews of their laboratories and research projects. This course will help students to select a specialization and a future research adviser. The information about the Center for Design, Manufacturing and Materials and its laboratories can be found at: https://https://crei.skoltech.ru/cdmm As a final project students should select a research topic, write a short text about a possible project and discuss it.

*Course description***:** The course is intended to provide the understanding and working knowledge of numerical methods required for modeling and simulation of complex phenomena. It focuses on fundamentals of the methods such as accuracy, stability, convergence, and consistency rather than learning how to use canned computer codes. The course involves first-hand experience with programming and solving real problems on computers. Solid knowledge of calculus, linear algebra, complex variables is essential, and basic understanding of the theory of ordinary and partial differential equations of physics and engineering as well as basic programming skills are required. The following topics will be covered: solving nonlinear equations, matrix equations, eigenvalue problems, interpolation, numerical differentiation and integration, numerical solution of ordinary and partial differential equations, optimization problems, and data analysis.

*Course description***:** The course presents modern numerical methods used in solving problems of fluid and solid mechanics. It covers finite-volume and finite-difference methods for conservation laws. Essential theoretical properties of the methods as well as their practical implementations in open source environments, such as OpenFOAM, will be introduced.

*Course description***:** The course introduces essential mathematical modeling techniques emphasizing analytical methods and their use in solving various problems of applied science and engineering. The topics include: asymptotic and perturbation methods for ordinary and partial differential equations, singular perturbations, homogenization, analysis of models of heat transfer, fluid and solid mechanics, electromagnetism, chemical kinetics, chemical reactors, convection in porous media, one-dimensional two-phase flow, linear and nonlinear stability, alloy solidification, interfacial instabilities and pattern formation.

*Course description***: **Classification, principles and techniques of digital modelling of point sets are presented for points, curves, surfaces and solids. Specifically these include methods of modelling of point clouds, depth fields, parametric curves and surfaces, implicit surfaces and solids. Solid modelling includes such representations as Constructive Solid Geometry (CSG), Boundary Representation (BRep) with polygonal meshes and parametric surfaces, sweeping, spatial occupancy enumeration, and Function Representation (FRep).

*Course description***:** Continuum mechanics is a section of mechanics and theoretical physics, or rather the continuation of theoretical mechanics that deals with analysis of deformable bodies. However, mathematics in continuum mechanics represents the main constructive tool. Continuum mechanics allows to demonstrate the power of logic and mathematical thinking. Based on a few fundamental postulates and principles, using the mathematical apparatus can reveal non-trivial, and even striking results. Foundation of continuum mechanics consists of: 1) material continuum model in the form of a deformable (with mechanical stresses and other macroparameters) continuous medium, described via several piecewise continuous differentiable functions. Building such a model is carried out by averaging the parameters of real materials that have a discrete atomic and molecular structure; 2) differential, integral, tensor calculus and the theory of dimensions with the fundamental idea of invariance under transformation of coordinate systems and systems dimension; 3) The laws of conservation of mass, momentum, angular momentum and energy, the laws of thermodynamics, expressed in terms of macroscopic parameters of the material continuum; 4) mechanical (rheological), thermal and electrical experiments that allow us to find connections between macroparameters of different substances at different mechanical, thermal, electromagnetic and physical-chemical processes. These representations constitute, in particular, the mathematical theory of thermoelectro-magneto-mechanical field. This course uses tensor representations in the Cartesian coordinate system of the observer. But it will one shown in detail how to to write the continuum mechanics equations in the arbitrary curvilinear coordinate system. This way the common link is not lost and the exposition becomes easier and clearer.

*Course description***:** This course is developed to give students a broad background and hands on experience in manufacturing of advanced composite materials. Both materials and manufacturing methods are discussed. A brief introduction to advanced composite materials and processes is presented. The course is focused on the innovative non-autoclave technologies of thermosetting resin based/fiber reinforced advanced composites. Manufacturing is covered in terms of the major steps required to fabricate laminated composite parts. These will be described and discussed in details and worked out experimentally through conducting a set of lab projects. The following technologies and methods will be covered: Vacuum Infusion, Press Molding, Pultrusion, Filament Winding, and Mechanical Testing. Typical problems of materials, tooling, cure, and technological defects will be discussed. The physics, chemistry, and mechanics to develop the fundamental and constitutive laws describing the processing steps of the polymer composite fabrication processes will be discussed.

*Course description***:** The course is designed to give an overview of the fluid mechanics, gas dynamics, thermodynamics, and electromagnetic phenomena in fluids and gasses. The following topics are discussed:

- Kinematics of continuous media
- Basic concepts and equations of fluid dynamics and thermodynamics
- Models of fluid and gas media
- Contact discontinuities in fluids, gases, and plasma
- Flow of ideal, incompressible fluid
- Incompressible viscous flow. Boundary layer theory. Turbulence
- Compressible fluid flow. Gasdynamic
- Electromagnetic phenomena in fluids Students will have to complete daily homework, theoretical, computer, and design projects, mid-term and final exams.

the Bachelor program or the course «Structural analysis and design» included in the Skoltech program.

*Course description***:** Participants will learn fundamentals of these areas through active participation in teamwork. The course will provide practical knowledge on applications of composite materials in aerospace and mechanical engineering. The course includes practical experience of composite manufacturing and mechanical tests. During the last part of the course the participants will be presented a ‘challenge’ project in design and structural analysis, which they may attack experimentally, analytically or by means of finite-element package Abaqus. Participants are expected to demonstrate their collective knowledge while at the same time solving individually a real problem.