Course Contents

NUMERICAL LINEAL ALGEBRA

Speaker: Alba Muixí
Description: The course reviews methods for solving linear systems of equations, from direct methods based on matrix factorization to iterative approaches. It discusses the solution of overdetermined (and also underdetermined) systems via least-squares criteria, associated with the pseudo-inverse of the matrix and its singular value decomposition. Special attention is paid to difficulties induced by ill-conditioning. It also reviews standard matrix-storage schemes in computational engineering.

PROGRAMMING: GOOD PRACTICE RULES

Speaker: Sergio Zlotnik
Description: Best practices to reduce (at least a bit) the burden of programming: testing, version control, coding style, pair programming... these might smooth out your excursion into computer programs.

FEM BASICS

Speaker: Ignasi de Pouplana
Description: This course aims at giving a brief overview on the Finite Element Method. The first part reviews the Weighted Residual Method (WRM) in the 1D Poisson problem, and the Principle of Virtual Work (PVW) in the 2D solid mechanics problem. The second part is devoted to show the different steps in the solution of a 2D plane stress solid mechanics test example.

Theory (1.5h)

• Introduction to the Finite Element Method
• Weighted Residual Method in the 1D Poisson problem
  • Galerkin technique
  • Discretization of the weak form
  • Shape functions
  • Global assembly and solution of the linear system of equations
  • Principle of Virtual Work in the 2D solid mechanics static problem
  • Equivalence with the WRM
  • Elementary contributions
  • Numerical integration

Practice (2h)

• Step by step solution of a Three-point bending test example (linear elastic plane stress hypothesis)
  • Installation of the necessary software
  • Preparation and resolution of the example

ORAL COMMUNICATION

Speaker: Narges Dialami
Description:This course develops students’ abilities to communicate science effectively in the real world starting with the key elements of clear and persuasive speaking, writing and exhibiting. The objective of the module is to help the students identify the important aspects of the preparation of scientific works, while improving their oral and written communication skills. In this first session the course will focus on oral communication skills.

WRITTEN COMMUNICATION

Speaker: Narges Dialami
Description:This course develops students’ abilities to communicate science effectively in the real world starting with the key elements of clear and persuasive speaking, writing and exhibiting. The objective of the module is to help the students identify the important aspects of the preparation of scientific works, while improving their oral and written communication skills. In this first session the course will focus on written skills.

CONTINUUM MECHANICS

Speaker: Oriol Lloberas
Description: Continuum mechanics is an essential discipline for the understanding of motion, deformation and constitutive behaviour of any continuous medium. It transversally impacts many engineering fields such as solid and fluid mechanics. Within this course the basic knowledge on the description of motion and deformation are outlined together with the concept of stress. Balance principles valid for any continuous media will be enunciated and some basic notions on elastic solids and their governing equations will be introduced. A simple practical case will be explored in which the Navier equations will be employed to fully solve a linear elastic problem.

REDUCED ORDER MODELS

Speaker: Pavel Ryzhakov & Raul Bravo
Description: This course aims at giving an overall idea of model reduction techniques and concentrates on the introduction to one of the most popular aposteriori methods, namely the Proper Orthogonal Decomposition (POD). Concepts of snapshots and dominant patters are introduced. Singular Value Decomposition (SVD) is presented as a method for the identification of dominant patterns, which can be used for projecting the full-dimensional problem onto a reduced-dimensional space in the framework of Galerkin approach. In the second part of the class the “hands-on” ROM tutorial using Python and Jupyter notebooks is carried out showing the application of ROM to sample probelms.

INFORMATION SEARCH AND INFORMATION RESOURCES

Speaker: Ruth Iñigo
Description: During this session we will discuss how to structure your information search strategy and how to find relevant bibliography for both your research plan and your thesis. We will also look at how to access and search for information in the Web of Science, Scopus and Compendex databases, as well as other information resources.

HIGH PERFORMANCE COMPUTING

Speaker: Ricardo Rossi
Description: The goal of this brief course is to provide a general overview about the methods and programming environment which allow exploiting the use of supercomputers or even simply the internal parallelism of CPUs. The course will provide a hint of loop-level parallelization models, of task-based models which allow addressing complex concurrency problems, and of the MPI paradigm. A hint of other parallelization models will also be provided.