Identifying Data 2019/20
Subject (*) Boundary element methods Code 614855230
Study programme
Mestrado Universitario en Matemática Industrial (2013)
Descriptors Cycle Period Year Type Credits
Official Master's Degree 2nd four-month period
 First Optional 3
Language
Spanish
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Gonzalez Taboada, Maria
 E-mail
maria.gonzalez.taboada@udc.es
Lecturers
Gonzalez Taboada, Maria
 E-mail
maria.gonzalez.taboada@udc.es
Web http://http://www.m2i.es
General description Neste curso preséntase unha introdución ao método dos elementos de contorno. Usando como modelo un problema de potencial, estudianse o método directo e os métodos indirectos baseados nas formulacións de capa simple e capa dobre para resolver problemas interiores e exteriores en dúas e tres dimensións. Tamén descríbese a aplicación do método a problemas de dispersión (scattering) e de radiación acústica.

Study programme competencies
Code Study programme competences
A4 Ser capaz de seleccionar un conjunto de técnicas numéricas, lenguajes y herramientas informáticas, adecuadas para resolver un modelo matemático.
A8 Saber adaptar, modificar e implementar herramientas de software de simulación numérica.
B3 Ser capaz de integrar conocimientos para enfrentarse a la formulación de juicios a partir de información que, aun siendo incompleta o limitada, incluya reflexiones sobre las responsabilidades sociales y éticas vinculadas a la aplicación de sus conocimientos.
B5 Poseer las habilidades de aprendizaje que les permitan continuar estudiando de un modo que habrá de ser en gran medida autodirigido o autónomo, y poder emprender con éxito estudios de doctorado.

Learning aims
Learning outcomes Study programme competences
To know the advantages and limitations of the boundary element method AC4
 BC2
BR1
To know the steps to solve a boundary value problem using the boundary element method BC2
BR1
To know the fundamental solutions, the integral representation formula and the boundary integral equations related to the problems considered in this subject AC4
 BC2
BR1
Be able to construct Matlab programs that solve an elliptic problem using the boundary element method. AC8
 BC2
BR1
To know and be able to apply the direct and indirect methods AC4
 BC2
BR1
Given a boundary integral equation, be able to discretize it using the boundary element method and to derive the associated linear system AC8
 BC2
BR1

Contents
Topic Sub-topic
Introduction to the boundary element method. Potential problems. - Interior and exterior problems for the Laplace equation.
- Fundamental solution for the Laplace operator.
- Representation formulae of an harmonic function.
- Integral equations on the boundary.
- Direct and indirect methods. Analysis of the variational formulations.
- Discretization. A priori error estimates.
- Some practical considerations on the numerical solution of the discrete problem.
Boundary element methods in acoustics. - The wave equation and the Helmholtz equation.
- Acoustic scattering and radiation problems in harmonic regime.
- Fundamental solutions of the Helmholtz operator.
- Green's representation formulae. Single and double layer potentials.
- Boundary integral equations.
- Direct and indirect methods.
- Discretization of the equations.
- Implementation.
Introduction to the coupling of boundary elements and finite elements

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Guest lecture / keynote speech A4 B5 B3 14 35 49
Laboratory practice A8 B5 B3 7 7 14
Supervised projects A4 A8 B5 B3 1 9 10
 
Personalized attention 2 0 2
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies Description
Guest lecture / keynote speech The theoretical contents will be presented through lectures.
Laboratory practice The implementation in Matlab of the boundary element method to solve the problems considered in the subject will be shown.
Supervised projects At the end of the course, a project will be proposed to each student.

Personalized attention
Methodologies
Supervised projects
Description
Students can ask to the teacher any questions that arise during the performance of the project that has been proposed to them.

Assessment
Methodologies Competencies Description Qualification
Supervised projects A4 A8 B5 B3 The evaluation of the knowledge acquired in this subject will take into account the completion of the exercises presented in the lectures (50% of the final grade) and the supervised work that will be proposed at the end of the subject (50% remaining). 100
 
Assessment comments

Sources of information
Basic S.A. Sauter y C. Schwab (2011). Boundary Element Methods. Springer
G. Chen y J. Zhou (1992). Boundary Element Methods. Academic Press
K.-C. Ang (2007). Introducing the boundary element method with MATLAB. Int. J. Math. Education in Sci. and Technology

Complementary C.A. Brebbia y J. Dominguez (1992). Boundary Elements. An introductory course.. McGraw-Hill
W. Hackbusch (1995). Integral Equations. Birkhauser
R. Kress (2014). Linear integral equations. Springer
G. Beer (2001). Programming the Boundary Element Method. John Wiley & Sons
R. Adams (1979). Sobolev spaces. Academic Press
W. McLean (2000). Strongly elliptic systems and boundary integral equations. Cambridge University Press


Recommendations
Subjects that it is recommended to have taken before
Numerical methods and programming/614855201
Numerical methods for partial differential equations/614855204

Subjects that are recommended to be taken simultaneously
Acoustics/614855209

Subjects that continue the syllabus

Other comments

It is recommended that students take the subject up to date and use the tutorial hours to resolve their doubts.


(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.