## Интезивни курсеви на DAAD

**2014 DAAD INTENSIVE COURSES 2014**

1.

**Measures of Noncompactness and Applications**, August 18 – August 22, Prishtina, Kosovo

- Lecturer: Malkowsky, University of Gießen, Germany
- Lecturer: Braha, University of Prishtina, Kosovo

**Regular and Rapid Variation and Applications**, September/October, Vrnjacka Banja, Serbia

- Lecturer: Ljubisa D.R. Kocinac, University of Nis, Serbia
- Lecturer: Jelena Manojlovic, University of Nis, Serbia

**Nonsmooth Numeric and Piecewise Linearization**, September 15 – September 20, Novi Sad, Serbia

- Lecturer: A. Griwank, Humboldt University Berlin, Germany
- Lecturers: N. Krejic, University of Novi Sad, Serbia

**Nonsmooth Analysis with Applications**, September 8 – September 12, Cluj, Romania

- Lecturer: Muresan, University of Cluj, Romania
- Lecturer: Vrdoljak, University of Zagreb, Croatia

2012/2013DAAD INTENSIVE COURSE

FIRST IDEAS

1. Day 1: SL2(

Action on the upper half plane, fundamental domain, relation to reduction theory of binary quadratic forms, class numbers of imaginary quadratic fields, modular curve and its interpretation as the moduli space of 1-dim complex tori.

2. Day 2: Arithmetic of quaternion algebras

Structure theorems (over local and global number fields), orders and ideals in local and global case, local-global principle)

3. Day 3: Arithmetic groups and actions on hyperbolic spaces

Arithmetic groups derived from quaternion algebras, action on

4. Day 4 and 5: Applications

Hyperbolic manifolds of small volume, isospectral-non-isometric hyperbolic manifolds, algebraic varieties with fixed cohomological invariants, rational homology spheres, first Betti number. Mumford curves, expanders and Ramanujan graphs.

5. Prerequisites

Arithmetic in number fields, simple algebras.

6. Bibliography

**ARITHMETIC OF QUATERNION ALGEBRAS, DISCRETE GROUPS AND APPLICATIONS IN GEOMETRY**, September 23, 2013 -- September 28, 2013, SaraevoFIRST IDEAS

1. Day 1: SL2(

**Z**)Action on the upper half plane, fundamental domain, relation to reduction theory of binary quadratic forms, class numbers of imaginary quadratic fields, modular curve and its interpretation as the moduli space of 1-dim complex tori.

2. Day 2: Arithmetic of quaternion algebras

Structure theorems (over local and global number fields), orders and ideals in local and global case, local-global principle)

3. Day 3: Arithmetic groups and actions on hyperbolic spaces

Arithmetic groups derived from quaternion algebras, action on

**H**^2 x**H**^2 x**H**^3 x**H**^3. Corresponding hyperbolic (orbi-) manifolds, volumes.4. Day 4 and 5: Applications

Hyperbolic manifolds of small volume, isospectral-non-isometric hyperbolic manifolds, algebraic varieties with fixed cohomological invariants, rational homology spheres, first Betti number. Mumford curves, expanders and Ramanujan graphs.

5. Prerequisites

Arithmetic in number fields, simple algebras.

6. Bibliography

- M-F Vigneras: Arithmetique des algebres de quaternions, Springer LNM 800
- C Maclachlan, A Reid: The arithmetic of hyperbolic manifolds. Springer GTM 219
- A. Lubotzky: Discrete groups, expanding graphs, and invariant measures . Birkhauser PM 125

DAAD INTENSIVE COURSE

Lecturers: Stevan Pilipovic (Novi Sad, Serbia) and Nenad Teofanov (Novi Sad, Serbia), University of Novi Sad,

Topics:

1. Function and generalized function spaces (6 hours)

2. Global pseudo-differential operators- basic calculus and regularity property (six hours)

3. Anti-Wick quantization (6 hours)

4. Wave front sets (6 hours)

5. Exercis will be done separately.

**Micro local Analysis, Wave Fronts and Propagation of Singularities**, September 16, 2013 -- September 22, 2013, Novi SadLecturers: Stevan Pilipovic (Novi Sad, Serbia) and Nenad Teofanov (Novi Sad, Serbia), University of Novi Sad,

Topics:

1. Function and generalized function spaces (6 hours)

2. Global pseudo-differential operators- basic calculus and regularity property (six hours)

3. Anti-Wick quantization (6 hours)

4. Wave front sets (6 hours)

5. Exercis will be done separately.

DAAD Summer School

DAAD International School on Applied Dynamic Programming

Applications until June 20, 2013 at [email protected]

**Applied Dynamic Programming**, Ohrid, 20.08-26.08,2013DAAD International School on Applied Dynamic Programming

Applications until June 20, 2013 at [email protected]

DAAD Summer School

The principal lecturer will be Prof. Marian Muresan. A more detailed information on the content of the course could be found at Marian Mureşan.

The arrival day is Sunday, June 23. The school will start on Monday, June 24. The teaching time will be from 9 am to 1.30 pm, with a pause from 11 am to 11.30 am. The departure day is Saturday, June 29.

Applications at [email protected] until May 30th, 2013.

**Applications of Calculus of Variations and Optimal Control to Space Rendezvous**, Sarajevo June 24-29, 2013.The principal lecturer will be Prof. Marian Muresan. A more detailed information on the content of the course could be found at Marian Mureşan.

The arrival day is Sunday, June 23. The school will start on Monday, June 24. The teaching time will be from 9 am to 1.30 pm, with a pause from 11 am to 11.30 am. The departure day is Saturday, June 29.

Applications at [email protected] until May 30th, 2013.

**DAAD International School on Linear Optimal Control of Dynamic Systems**

- The summer school is held on 23 - 28 September 2013, in Osijek, Croatia

- Venue: Lectures will be at Department of mathematics, J. J. Strossmayer University of Osijek

- Address: Trg Lj. Gaja 6, Osijek, Croatia.

- Accommodation for participants will be organized at Student dormitory, J.J. Strossmayer University Of Osijek,

- Address: Kralja Petra Svačića 1c, HR-31000 Osijek, Croatia

**Lecturers:**

1) Zlatko Drmač, Department of Mathematics, Zagreb, Croatia / Numerical algorithms in Control of Dynamic Systems

2) Daniel Kressner, EPF Lausanne, Switzerland / Tensor Techniques for High-Dimensional Problems in Control

3) Serkan Gugercin, Department of Mathematics, Blacksburg, USA / Approximation and Control of Large-Scale Dynamical Systems

More information:

2011/2012DAAD INTENSIVE COURSE

12-18 August, 2012, Ohrid, Macedonia

1) Hans-Dieter Burkhard, Institute of Computer Science, Faculty of Mathematics and Natural Sciences, Humboldt University of Berlin, Germany

2) Nevena Ackovska, Institute of Intelligent Systems, Faculty of Computer Science and Engineering, University St. Cyril and Methodius, Macedonia

6 lecture days, maximum 4 classes per day including robotic exercises, sun and lake in the afternoons

• Computer engineering aspects of Robotics (N. Ackovska)

• Motion control, kinematics (H.D. Burkhard)

• Sensors, perception (H.D. Burkhard)

• Behavior and control (H.D. Burkhard)

• Image processing, world model (H.D. Burkhard)

• Bio-inspired Robotics, Emotions and Robotics (N. Ackovska)

Accommodation will be provided by the organizers.

Prerequisites for the exercises:

а) Soccerserver package running under windows XP or 7 (can be distributed upon arrival)

b) Java Netbeans 7.1.1 for development

**Robotics and Mathematics**12-18 August, 2012, Ohrid, Macedonia

**Lecturers:**1) Hans-Dieter Burkhard, Institute of Computer Science, Faculty of Mathematics and Natural Sciences, Humboldt University of Berlin, Germany

2) Nevena Ackovska, Institute of Intelligent Systems, Faculty of Computer Science and Engineering, University St. Cyril and Methodius, Macedonia

**Program:**6 lecture days, maximum 4 classes per day including robotic exercises, sun and lake in the afternoons

**Topics:**• Computer engineering aspects of Robotics (N. Ackovska)

• Motion control, kinematics (H.D. Burkhard)

• Sensors, perception (H.D. Burkhard)

• Behavior and control (H.D. Burkhard)

• Image processing, world model (H.D. Burkhard)

• Bio-inspired Robotics, Emotions and Robotics (N. Ackovska)

**Arrival and registration:**12th August at 1PM. Lectures start: 12th August 3PM.**Departure:**18th August AM or PMAccommodation will be provided by the organizers.

**The participants at the course Robotics and Mathematics are supposed to have their own laptops.**Prerequisites for the exercises:

а) Soccerserver package running under windows XP or 7 (can be distributed upon arrival)

b) Java Netbeans 7.1.1 for development

DAAD INTENSIVE COURSE

(Vrnjacka Banja, Hotel Breza, Serbia, August 28 – September 3, 2012)

1) Robert Elsasser, Paderborn, Germany (10 x 45)

2) Dragan Stevanovic, Nis, Serbia (10 x 45)

1. Standard matrices associated to graphs: A, L, NL and Q, and their selected spectral properties

2. Expander graphs, interconnection networks

3. Graph clustering and partitioning

4. PageRank and HITS, spectral retrieval

5. Load balancing algorithms

6. Spreading in networks: rumor spreading, information dissemination, epidemic threshold

7. Semidefinite connection: max-cut and Goemans-Williamson algorithm, Shannon capacity and Lovasz' Theta function

8. Markov chains and random walks

In graph theory, the spectra of matrices associated with a graph are widely used to characterize its properties and to extract structural information. There are several graph matrix representations such as the adjacency matrix, combinatorial Laplacian, normalized Laplacian and signless Laplacian. Spectral graph theory has also many applications in other scientific fields such as chemistry, theoretical physics, and quantum mechanics, but we will focus here to applications in computer science. One of the oldest applications of graph spectra in Computer Science is related to expander graphs. It is known that graphs having a large eigenvalue gap possess very good expansion and connectivity properties. This property is used in the design of interconnection networks with good algorithmic properties. Another application of graph spectra is in the area of graph partitioning. This problem naturally arises in e.g. numerical simulations, VLSI design, or data mining. On one hand, the eigenvalues of the corresponding graph are used to derive lower and upper bounds on the quality of partitioning algorithms. On the other hand, the eigenvector corresponding to the second eigenvalue of Laplacian matrix can be used to partition the graph into two (equal) parts such that the number of edges separating the two parts is small.

Eigenvalues of graphs are also used to capture the convergence of certain (diffusion based) load balancing algorithms, whose schemes can be described by iterative methods based on certain matrices associated with the underlying network topology. The eigenvalues of these matrices are closely related to the Laplacian eigenvalues of the corresponding graph, and then we are able to apply known techniques from linear algebra to bound the running time of these load balancing algorithms. A somewhat related process to diffusion load balancing is the PageRank algorithm of Google. Of particular importance are, again, linear algebraic methods. Spectral retrieval is a popular approach to rank Web pages among large collections of documents. The basic scheme assumes that the documents as well as the queries are represented by high dimensional vectors. Then, these are projected to a low dimensional eigenspace, which is computed from the document vectors. The rank of the documents is obtained by their similarity to the query in the eigenspace.

In the last years, a relationship between graph spectra and certain information dissemination algorithms has been discovered. It has been shown that the second eigenvalue is well suited to capture the expected running time of so called rumor spreading algorithms in graphs with large eigenvalue gap. Furthermore, there is a close connection between the cover time of random walks and rumor spreading.

The spectrum of a graph can also be used to describe the spread of certain epidemic models in networks. Whenever the question is, how fast the disease reaches all persons, the problem reduces to randomized rumor spreading. However, in most of these studies, spreaders are only active in a certain time window, and the question of interest is, whether on certain networks modeling personal contacts an epidemic outbreak occurs.

The aim of proposed summer school is to introduce students to the theoretical properties of different graph spectra and to explain in detail the abovementioned applications, thereby creating a comprehensive foundation for students’ introduction to research in this important field of graph theory.

**Graph Spectra and Applications**(Vrnjacka Banja, Hotel Breza, Serbia, August 28 – September 3, 2012)

**Lecturers:**1) Robert Elsasser, Paderborn, Germany (10 x 45)

2) Dragan Stevanovic, Nis, Serbia (10 x 45)

**Topics:**1. Standard matrices associated to graphs: A, L, NL and Q, and their selected spectral properties

2. Expander graphs, interconnection networks

3. Graph clustering and partitioning

4. PageRank and HITS, spectral retrieval

5. Load balancing algorithms

6. Spreading in networks: rumor spreading, information dissemination, epidemic threshold

7. Semidefinite connection: max-cut and Goemans-Williamson algorithm, Shannon capacity and Lovasz' Theta function

8. Markov chains and random walks

**School overview:**In graph theory, the spectra of matrices associated with a graph are widely used to characterize its properties and to extract structural information. There are several graph matrix representations such as the adjacency matrix, combinatorial Laplacian, normalized Laplacian and signless Laplacian. Spectral graph theory has also many applications in other scientific fields such as chemistry, theoretical physics, and quantum mechanics, but we will focus here to applications in computer science. One of the oldest applications of graph spectra in Computer Science is related to expander graphs. It is known that graphs having a large eigenvalue gap possess very good expansion and connectivity properties. This property is used in the design of interconnection networks with good algorithmic properties. Another application of graph spectra is in the area of graph partitioning. This problem naturally arises in e.g. numerical simulations, VLSI design, or data mining. On one hand, the eigenvalues of the corresponding graph are used to derive lower and upper bounds on the quality of partitioning algorithms. On the other hand, the eigenvector corresponding to the second eigenvalue of Laplacian matrix can be used to partition the graph into two (equal) parts such that the number of edges separating the two parts is small.

Eigenvalues of graphs are also used to capture the convergence of certain (diffusion based) load balancing algorithms, whose schemes can be described by iterative methods based on certain matrices associated with the underlying network topology. The eigenvalues of these matrices are closely related to the Laplacian eigenvalues of the corresponding graph, and then we are able to apply known techniques from linear algebra to bound the running time of these load balancing algorithms. A somewhat related process to diffusion load balancing is the PageRank algorithm of Google. Of particular importance are, again, linear algebraic methods. Spectral retrieval is a popular approach to rank Web pages among large collections of documents. The basic scheme assumes that the documents as well as the queries are represented by high dimensional vectors. Then, these are projected to a low dimensional eigenspace, which is computed from the document vectors. The rank of the documents is obtained by their similarity to the query in the eigenspace.

In the last years, a relationship between graph spectra and certain information dissemination algorithms has been discovered. It has been shown that the second eigenvalue is well suited to capture the expected running time of so called rumor spreading algorithms in graphs with large eigenvalue gap. Furthermore, there is a close connection between the cover time of random walks and rumor spreading.

The spectrum of a graph can also be used to describe the spread of certain epidemic models in networks. Whenever the question is, how fast the disease reaches all persons, the problem reduces to randomized rumor spreading. However, in most of these studies, spreaders are only active in a certain time window, and the question of interest is, whether on certain networks modeling personal contacts an epidemic outbreak occurs.

The aim of proposed summer school is to introduce students to the theoretical properties of different graph spectra and to explain in detail the abovementioned applications, thereby creating a comprehensive foundation for students’ introduction to research in this important field of graph theory.

**Participants (20):**Students, Master degree students, Ph. D. Students, young researches interested in the field**Location:**Hotel Breza, Vrnjacka Banja; Participants can use covered semi-olympic swimming pool, sauna, table tennis hall.**Financial conditions:**DAAD covers all local and travel expenses for all participantsDAAD INTENSIVE COURSE

1. The course will take place on the Black sea cost in the city of Pomorie which is between Bourgas and Nessebar (about 20 km north from Bourgas). There is regular bus connection between Bourgas and Pomorie. From Sofia to Bourgas there are trains and about every hour buses – 5-6 hours trip, ~30 Euro round trip. Please do not worry about Sofia-Pomorie travel;

2. The course will take place in the period June 15-21, 2012:

3. The course will be in the same hotel and can be considered as a satellite event of the 13-th International Conference on Algebraic and Combinatorial Theory of Coding. About 80 prominent scientists from Germany, Russia, etc. in the field of Coding, Cryptography, Data Protection, etc. will be there – this is a conference with decades lasting history;

4. Lecturers and course material (it is expected that except attending the course lectures the students can attend more than 60 talks) :

Duration: 10 h

Description: Shannon's famous channel coding theorem asserts that information can be reliably transmitted over noisy communication channels at any rate below channel capacity. Algebraic coding theory employs concepts from abstract algebra for the actual construction of error-correcting codes for reliable communication. The course provides an introduction at the Ph.D. level to the most important classes of algebraic codes and their decoding.

Major Topics:

1) Basic terminology

2) Bounds for codes

3) Linear codes

4) MacWilliams identities

5) Cyclic codes

6) CRC codes

7) Polynomial codes

8) Decoding of cyclic codes

9) List decoding of Reed-Solomon codes.

Duration: 10 h

Description: It is known that linear codes over finite fields are equivalent to arcs with certain parameters in the projective geometries. In this course we consider some important problems about objects in finite geometry and their relevance to optimization problems in coding theory.

Major Topics:

1) Arcs and blocking sets in PG(t,q)

2) Ovals and hyperovals

3) Maximal arcs. The maximal arc conjecture.

4) Caps

5) The Griesmer bound

6) Minihypers and characterization theorems

7) The main conjecture for MDS codes

8) Extensions and divisibility of linear codes

**Data Protection**1. The course will take place on the Black sea cost in the city of Pomorie which is between Bourgas and Nessebar (about 20 km north from Bourgas). There is regular bus connection between Bourgas and Pomorie. From Sofia to Bourgas there are trains and about every hour buses – 5-6 hours trip, ~30 Euro round trip. Please do not worry about Sofia-Pomorie travel;

2. The course will take place in the period June 15-21, 2012:

3. The course will be in the same hotel and can be considered as a satellite event of the 13-th International Conference on Algebraic and Combinatorial Theory of Coding. About 80 prominent scientists from Germany, Russia, etc. in the field of Coding, Cryptography, Data Protection, etc. will be there – this is a conference with decades lasting history;

4. Lecturers and course material (it is expected that except attending the course lectures the students can attend more than 60 talks) :

**Course Title:****Coding Theory---An Advanced Introduction**Duration: 10 h

Description: Shannon's famous channel coding theorem asserts that information can be reliably transmitted over noisy communication channels at any rate below channel capacity. Algebraic coding theory employs concepts from abstract algebra for the actual construction of error-correcting codes for reliable communication. The course provides an introduction at the Ph.D. level to the most important classes of algebraic codes and their decoding.

Major Topics:

1) Basic terminology

2) Bounds for codes

3) Linear codes

4) MacWilliams identities

5) Cyclic codes

6) CRC codes

7) Polynomial codes

8) Decoding of cyclic codes

9) List decoding of Reed-Solomon codes.

**Lecturer:**Prof. Thomas Honold – Munich Technical University**Course Title: Linear Codes and Finite Geometries**Duration: 10 h

Description: It is known that linear codes over finite fields are equivalent to arcs with certain parameters in the projective geometries. In this course we consider some important problems about objects in finite geometry and their relevance to optimization problems in coding theory.

Major Topics:

1) Arcs and blocking sets in PG(t,q)

2) Ovals and hyperovals

3) Maximal arcs. The maximal arc conjecture.

4) Caps

5) The Griesmer bound

6) Minihypers and characterization theorems

7) The main conjecture for MDS codes

8) Extensions and divisibility of linear codes

**Lecturer:**Prof. Ivan Landjev – Institute of Math and Informatics, SofiaDAAD INTENSIVE COURSE

Novi Sad, Serbia, May 28 - June 2, 2012.

Faculty of Science, Novi Sad, Department of Mathematics and Informatics

Andreas Fischer, Technical University of Dresden, Germany

Ana Friedlander, State University of Campinas, Brasil

Nataša Krejić, University of Novi Sad, Serbia

José Mario Martínez, State University of Campinas, Brasil

Program: 6 lectures of 45 minutes per day, coffee break and lunch break

Themes:

Data Classification and Optimization (A. Fischer)

Inexact Restoration (A. Friedlander)

Optimization Models in Algorithmic Trading (N. Krejić)

Applied Optimization and Software (J.M. Martínez)

Arrival and registration on May 27th at 6pm or May 28th at 9am. Lectures start on May 28th at 10 AM. Departure on June 2nd PM or June 3rd AM.

Accommodation will be provided by tech. organizers. Lectures will be held at the Department of Mathematics and Informatics, Trg Dositeja Obradovica 4.

**Intensive course on "Numerical Optimization and Applications"**Novi Sad, Serbia, May 28 - June 2, 2012.

Faculty of Science, Novi Sad, Department of Mathematics and Informatics

**Lecturers:**Andreas Fischer, Technical University of Dresden, Germany

Ana Friedlander, State University of Campinas, Brasil

Nataša Krejić, University of Novi Sad, Serbia

José Mario Martínez, State University of Campinas, Brasil

Program: 6 lectures of 45 minutes per day, coffee break and lunch break

Themes:

Data Classification and Optimization (A. Fischer)

Inexact Restoration (A. Friedlander)

Optimization Models in Algorithmic Trading (N. Krejić)

Applied Optimization and Software (J.M. Martínez)

Arrival and registration on May 27th at 6pm or May 28th at 9am. Lectures start on May 28th at 10 AM. Departure on June 2nd PM or June 3rd AM.

Accommodation will be provided by tech. organizers. Lectures will be held at the Department of Mathematics and Informatics, Trg Dositeja Obradovica 4.

**Summability theory and statistical convergence**

Lecturer: Prof. Malkowsky (University of Giessen)

Lecturer: Prof. Heinrich Voss, Institute of Numerical Simulation Hamburg University of Technology, Germany

**Lectures on Industrial Mathematics**

SOFIA, September 25 - October 1, 2011

- Lecturer: Prof. Oleg Iliev, ITWM, Kaiserslautern, Germany

Lecture 1.

Lecture 1.

Multiscale problems: Multiscale problems in industry. Homogenization approach. Numerical upscaling methods (multiscale FEM, multiscale FV, variational multiscale method, heterogeneous multiscale method).

**Lecture 2.**

Heat transfer in insulation materials: Examples and specific of different insulation materials - glass wool, mineral wool, foams. Types of heat transfer. Efficient approach for computing effective heat conductivity of highly conductive materials.

**Lecture 3.**

Meso scale and macro scale modeling and simulation of processes in Li-ion batteries: Isothermal and non-isothermal models. FV and FEM discretizations. Newton method for coupled system of nonlinear PDEs. Battery Electrochemistry Simulation Tool (BEST) for solving industrial problems.

**Lecture 4.**

Modeling and simulation of filtration (separation) processes (Part 1): Introduction: Navier-Stokes equations, Darcy law, Navier-Stokes-Brinkman equations; FV discretizations in space; Fractional time step discretizations, Solution methods.

**Lecture 5.**

Modeling and simulation of filtration (separation) processes (Part 2): Macro scale and micro scale modeling of filtration processes. Available analytical solutions. Coupling macro-scale and micro scale models. Subgrid approach.

**Lecture 6.**

Modeling and simulation of fractionation (separation) processes: Microscale (nano-particle level) and macro scale (device) level models for asymmetric flow field flow fractionation. Monte Carlo and Multilevel Monte Carlo methods for solving stochastic differential equations. Examples of simulation based improvements of existing devices.

- Lecturer: Prof. Svetozar Margenov, IICT – BAS, Sofia, Bulgaria

Lecture 1.

Lecture 1.

Large-scale scientific computing in FEM simulations: Introduction to sparse matrix computations. Target PDE problems. Conforming and nonconforming FEM discretization. Conjugate Gradient (CG) and Preconditioned Conjugate Gradient (PCG) iterative solution methods.

**Lecture 2.**

Optimal multilevel preconditioning methods and algorithms: Algebraic two-level methods. Hierarchical two-level splitting: conforming and non-conforming FEM. Local estimates of the constant in the strengthened Cauchy-Bunyakowski-Schwarz (CBS) inequality. Algebraic MultiLevel Iteration (AMLI) methods for strongly discontinuous and anisotropic problems.

**Lecture 3.**

Robust methods and algorithms for coupled problems: Lame system of elasticity. On the robustness of AMLI methods for conforming FE systems. Locking-free AMLI methods for Crouzeix-Raviart FE discretization of pure displacement problems. Optimal order AMLI preconditioning of time dependent Navier-Stokes problems: Crouzeix-Raviart FE discretization of the velocity field; mixed FE system: weighted graph-Laplacian.

**Lecture 4.**

Micro FEM (μFEM) analysis of bio and geo-composites: Crouzeix-Raviart FE discretization of 3D pure displacement elasticity problems. Composite FR preconditioner: linear and nonlinear multilevel algorithms. Towards μFEM analysis of bone microstructure. Numerical upscaling of coal-polyurethane geo-composites.

**Lecture 5.**

Toolbox for efficient parallel implementation of FEM models. Argon National Labs GBB diagram. Computer architecture of supercomputer IBM Blue Gene/P. Scalability toolbox for unstructured meshes: parallel mesh generation; parallel FEM implementation; parallel mesh partitioning (ParMETIS, SCOTCH); parallel algebraic multigrid solver for unstructured grids (BoomerAMG).

**Lecture 6.**

FEM simulation of hepatic tumor ablation on supercomputer IBM Blue Gene/P: Mathematical model of radio-frequency hepatic tumor ablation: bio-heat time-dependent equation; electrical flow model. FEM simulation: voxel approach; unstructured grid discretization. Numerical tests. Parallel scalability issues.

**Applications of Calculus of Variations and Optimal Control. The Smooth and Nonsmooth Cases**

Place: Hotel Drim, - Struga, Macedonia

Time: July 11, 2011 (arrival day) - July 18, 2011 (departure day)

- Lecturer: Marian Muresan, prof. dr., Babes-Bolyai University, Cluj-Napoca, Romania

**Lecture 1.**

The smooth case. The mathematical statement of the calculus of variations problem. Examples. Necessary conditions. The linear case. The general case: Euler, du Bois Reymond, with canonical equations, Weierstrass, Legendre, Hamiltonian, Erdmann, transversality, Gˆateaux, Jacobi. The Mathematica software product. Applications.

**Lecture 2.**

Necessary conditions of Lagrangian depending on higher order derivatives. Constrained variational problems. Isoperimetric problems. Sided variations. Obstacle problems. Applications.

**Lecture 3.**

Brachistochrone problems with initial zero speed and no friction. Brachistochrone from a point to a curve or between two planar curves. Kinematics of a particle. Brachistochrone with initial nonzero speed and with or without friction. The Lavrentiev phenomenon. Sufficient conditions in the calculus of variations. Applications.

**Lecture 4.**

The nonsmooth case. The trolley problem in optimal control. The necessity of nondifferentiable functions. Elements of measurability, topology, mathematical, and functional analysis. Ekeland variational principle and Borwein–Preiss smooth variational principle. Hausdorff-Pompeiu metric and Kuratowski convergence. Multifunctions. Elementary properties of multifunctions. Projection theorems. Measurability concepts of multifunctions. Measurable selections. Applications.

**Lecture 5.**

Lower semicontinuous multifunctions. Continuous selections. Upper semicontinuous multifunctions. Functions of two variables and measurability. Applications. Maximum principle of Pontryagin. The adjoint arc method.

**Lecture 6.**

Applications of the maximum principle of Pontryagin. Taking off and soft landing of a space craft.

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