Graduate courses on different aspects of numerical analysis
Boundary element methods
(Spanish). By Ricardo Celorrio & Francisco-Javier
Sayas. This is the revised version of the class notes
for the 9th Spanish-French Autumn School on Numerical
Simulation in Physics and Engineering, held in Laredo in
September 2000. It's a 107 page long course on
numerical analysis of Boundary Elements.
Domain decomposition
methods (Spanish). By Salim Meddahi &
Francisco-Javier Sayas. These are the classnotes of a
course taught by Salim Meddahi at the University of Zaragoza
in 1995.
Introduction to the
Boundary Element Method. A case study: Helmholtz
equation. Classnotes of a summer course taught by me
at the University of Concepción (Chile) in January 2006.
A gentle
introduction to the Finite Element Method.
Classnotes from one of my graduate courses on FEM at the
University of Zaragoza updated for a similar course at
UD. Mathematically very light and with an emphasis on
algorithms.
Mathematical Models in Mechanics
(Spanish). A basic course on PDEs, written with
students of computational mechanics in mind.
Advanced Finite Elements
(Spanish). Insisting again on algorithms, but now
learning about mixed, non-conforming, etc, etc.
First Steps in the Boundary
Element Method. Most recently used to give
students a taste of BEM after a healthy portion of FEM.
From
Raviart-Thomas to HDG: a personal voyage.
Adapted from a course prepared for Cádiz Numérica 2013,
Cádiz, Spain.
Retarded
Potentials and Time Domain Boundary Integral Equations: a
road-map. The notes that led to the number 1
best seller!
Convolution
Quadrature for Wave Simulations. By Matthew Hassell
& Francisco-Javier Sayas. These are notes that
were prepared for a course which I taught at the XVI
Jacques-Louis Lions Spanish-French School on Numerical
Simulation in Physics and Engineering in Pamplona,
Spain. It is again focused more on algorithms.
Materials
The Jordan form
(Spanish). Matrix aspects of the construction of the
Jordan form, existence and some related combinatorial
problems. (Elementary/Medium)
Reorganization of
information in matrices (Spanish). From rank one
matrices to the singular value decomposition (Elementary)
Minimum energy solutions to
ill-conditioned systems. Sometimes systems can
be really badly conditioned. What to do. (Elementary)
Static and dynamic recursive
least-squares. A statistical-free introduction
to Kalman filters. Uses only elementary concepts of
matrix analysis and numerical methods.
(Elementary/Medium)
Krylov spaces, GMRES, singular
values and equations of the second kind. Some
results on the theory of GMRES on Hilbert spaces, focused on
equations of the second kind. (Advanced)