| Study programme competencies |
| Code | Study programme competences / results |
| A4 | Ser capaz de seleccionar un conjunto de técnicas numéricas, lenguajes y herramientas informáticas, adecuadas para resolver un modelo matemático. |
| A5 | Ser capaz de validar e interpretar los resultados obtenidos, comparando con visualizaciones, medidas experimentales y/o requisitos funcionales del correspondiente sistema físico/de ingeniería. |
| A8 | Saber adaptar, modificar e implementar herramientas de software de simulación numérica. |
| A9 | Conocer, saber seleccionar y saber manejar las herramientas de software profesional (tanto comercial como libre) más adecuadas para la simulación de procesos en el sector industrial y empresarial. |
| B1 | Saber aplicar los conocimientos adquiridos y su capacidad de resolución de problemas en entornos nuevos o poco conocidos dentro de contextos más amplios, incluyendo la capacidad de integrarse en equipos multidisciplinares de I+D+i en el entorno empresarial. |
| B4 | Saber comunicar las conclusiones, junto con los conocimientos y razones últimas que las sustentan, a públicos especializados y no especializados de un modo claro y sin ambigüedades. |
| 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 / results | ||
| To know the steps to solve a boundary value problem using the boundary element method | AC4 |
BJ1 BC3 |
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| To know the advantages and limitations of the boundary element method | AC4 |
BJ1 |
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| To know the fundamental solutions, the integral representation formula and the boundary integral equations related to the problems considered in this subject | AC4 |
BJ1 BC3 |
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| To know and be able to apply the direct and indirect methods | AC4 |
BJ1 BC3 |
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| Given a boundary integral equation, be able to discretize it using the boundary element method and to derive the associated linear system | BJ1 BC3 |
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| Be able to construct Matlab programs that solve an elliptic problem using the boundary element method. | AC4 AC5 AC8 AC9 |
BJ1 BC3 BR1 |
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| Contents |
| Topic | Sub-topic |
| The boundary element method for potential problems | - Interior and exterior problems for the Laplace equation - Fundamental solution of the Laplacian - Representation formula of a harmonic function - Derivation of the boundary integral equations - Direct and indirect methods. Analysis of the variational formulations - Discretization. A priori error estimates - Practical considerations of the numerical solution of the discrete problem |
| The boundary element method 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 formula. Single and double layer potentials - Boundary integral equations - Direct and indirect methods - Discretization - Implementation |
| Planning | ||||
| Methodologies / tests | Competencies / Results | Teaching hours (in-person & virtual) | Student’s personal work hours | Total hours |
| Guest lecture / keynote speech | 14 | 35 | 49 | |
| Laboratory practice | 7 | 7 | 14 | |
| Supervised projects | 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 |
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| Assessment | |||
| Methodologies | Competencies / Results | Description | Qualification |
| Supervised projects | The understanding of the methods presented during the course and the ability to use them will be assessed. | 100 | |
| Assessment comments | |||
| Sources of information |
| Basic |
G. Chen y J. Zhou (1992). Boundary Element Methods. Academic Press
R. Kress (2014). Linear integral equations. Springer
G. Beer (2001). Programming the Boundary Element Method. An introduction for engineers. John Wiley & Sons |
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| Complementary |
(). .
C.A. Brebbia y J. Dominguez (1992). Boundary Elements. An introductory course.. McGraw-Hill
W. Hackbusch (1995). Integral Equations. Birkhauser
J. Saranen y G. Vainikko (2002). Periodic integral and pseudodifferential equations with numerical approximations. Springer
W. McLean (2000). Strongly elliptic systems and boundary integral equations. Cambridge University Press |
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| Recommendations | ||
| Subjects that it is recommended to have taken before | ||
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| Subjects that are recommended to be taken simultaneously | |
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| Subjects that continue the syllabus |
| Other comments | |