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Numerical Methods in Engineering

Master's Degree in Numerical Methods in Engineering

Nowadays, the industrial sector requires precise and reliable numerical simulations of product and process design: the Master's Degree in Numerical Methods in Engineering meets the needs of simulating, forecasting and optimising any problem in the field of engineering through computational mechanics. Given the transversality and universality of this discipline, and in order to facilitate the internationalisation of its graduates, these studies are taught in English.

The Master's Degree in Numerical Methods in Engineering provides multidisciplinary training in computational mechanics in view of the growing demand for accurate and reliable numerical simulations. It aims to produce specialists in the theory and applications of calculation methods for product and process design, in the widest possible sense. Graduates will immediately be able to apply the knowledge acquired in industry. Their solid scientific training will also enable them to pursue a doctoral degree.

Academic year starts in Fall semester (Q1): September
Spring semester (Q2): February
Duration 2 years
Study load 120 ECTS (including the Master's Final Thesis)
Minimum academic progress The minimum academic progress for first year students is 15 ECTS.
Delivery On-campus
Enrolment
  • Part-time
    At least 15 ECTS (and up to 60 ETCS) enrolled on the first year, and up to 72 ECTS the rest of the years
  • Full-time
    At least 15 ECTS and up to 40 ECTS
Language English
Places 25
Official degree Master's Degree in Numerical Methods in Engineering by Universitat Politècnica de Catalunya (recorded in the Spanish Ministry of Education's degree register)
Fees

More information about fees and payment options

More information about grants and loans

Academic coordinator Riccardo Rossi

Specific admission requirements

In order to gain admission to the Master's Degree in Numerical Methods in Engineering applicants must have studied one of the following studies:

  • Bachelor's Degree (5-year degree) in Engineering in the following fields: mechanical, electrical, materials, civil, aeronautical, systems, mining, naval, telecommunications, physics, forest or agricultural
  • Bachelor's Degree (5-year degree) in Mathematical, Physical, Chemical, Biological or Geological Sciences
  • Diploma (3-year degree) in Engineering in the following fields: mechanical, electrical, materials, civil, aeronautical, systems, mining, naval, telecommunications, physics, forest or agricultural
  • Diploma (3-year degree) in Mathematical, Physical, Chemical, Biological or Geological Sciences
  • Other studies:

    If the diploma or degree is different from the ones listed above, the Academic Committee in charge of the master's degree will assess the applicant's curriculum in order to grant them access and establish the necessary bridging courses.

Students pending obtaining the degree that gives access to the master's degree

Students who are currently pursuing their undergraduate studies and have registered all the credits to complete their studies may apply for access to the master's degree as long as they fulfil, during the registration period of the master's degree, the requirements above-established.

Undergraduate students who have failed to complete their degree because they are awaiting the defence of their final year project will be conditionally admitted. They will be admitted definitively if they have obtained the title of degree:

  • By October 31st, students applying for admission in the 1st semester.
  • By February 28th, students applying for admission in the 2nd semester.

Admission criteria

The following factors or parameters are considered for admission to the Master's Degree in Numerical Methods in Engineering:

Students interested in enrolling in this master's degree must certify their B2.2 proficiency level in English. The Consell Interunivesitari de Catalunya establishes the official certificates for meeting the B2 requirement on gaining admission to all UPC master's degrees.

You can check the results of the evaluation and selection of the applications for the current academic year here.

Pre-enrolment and enrolment

Check here the general admission requirements for UPC masters and information on pre-enrolment: calendar, how to apply for admission, how to reserve a place if the resolution is favourable, etc.

Objectives

The Master's Degree in Numerical Methods in Engineering provides a multidisciplinary and in-depth training in the most popular calculation methods —called numerical—, such as finite elements and other similar numerical techniques. With a theoretical and applied teaching, the aim is to train specialists with the ability to immediately incorporate the acquired knowledge into the industry and with sufficient basic training to successfully face a doctoral degree.

Career opportunities

The course addresses real educational needs in Europe and worldwide. Computational mechanics is set to become even more multidisciplinary than in the past, and it is expected that in the coming decade the demand for accurate and reliable numerical simulation of engineering systems will undergo explosive growth and have a major impact on our everyday lives. Graduates of this master's degree will be experts in numerical methods in engineering. They will be professionals able to put into practice the acquired knowledge directly to industry and they will also have the necessary scientific background to undertake a doctoral degree successfully.

Basic competencies

  • CB6 Possessing and understanding knowledge that provides the basis or opportunity to be original in the development and/or application of ideas, often in a research context.
  • CB7 For students to know how to apply the knowledge acquired and their ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of study.
  • CB8 For students to be able to integrate knowledge and face the complexity of formulating judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments.
  • CB9 For students to know how to communicate their conclusions (and the knowledge and ultimate reasons that support them) to specialized and non-specialized audiences in a clear and unambiguous way.
  • CB10 For students to possess the learning skills that allow them to continue studying in a way that will be largely self-directed or autonomous.

General competencies

  • CG1 Knowledge of numerical methods and solution mechanisms. Complete and consolidate the basic student training in solving problems using numerical and computational methods, reinforcing their knowledge of the basics, as well as of the specific applications.
  • CG2 Knowledge of the theories and applications of numerical methods. Ability to acquire advanced knowledge and understanding of the theories and applications of numerical methods in solving engineering problems.
  • CG3 Experience in solving problems using numerical methods. Ability to acquire experience and criteria in the application of numerical methods through the use of calculation programs, pre and post graphic processors, programming languages and scientific calculation libraries.
  • CG4 Consolidation of the application criteria of numerical methods. Complete and consolidate the knowledge, criteria and critical spirit to propose conventional solutions and as well as to analyze the results in characteristic numerical modeling problems.
  • CG5 Knowledge of social networks in the field of numerical methods. Knowing and acquiring a critical awareness about the avant-garde of the Spanish, European and international community of numerical methods in engineering.
  • CG6 Numerical modeling of real problems. In depth ability to solve real engineering problems through numerical modeling by identifying the underlying mathematical model, the most appropriate calculation method and the critical interpretation of the results.
  • CG7 Independence to question. Acquire the ability to autonomously use their knowledge and understanding of computational engineering to design solutions to new or unfamiliar problems, incorporating theoretical and practical knowledge and know-how, if necessary, from other disciplines of engineering and basic sciences, and designing new original resolution methods appropriate to the set of final objectives.
  • CG8 Knowledge of the scope of numerical methods. Understand the applicability and limitations of numerical modeling and existing calculation technologies.
  • CG9 Independence to research. Acquire experience and autonomy in the search, analysis, compilation and synthesis of cutting-edge scientific and technical information.

Cross-disciplinary competencies

  • CT1 CAPACITY FOR ENTREPRENEURSHIP & INNOVATION. Knowing and understanding the mechanisms on which scientific research is based, as well as the mechanisms and instruments for transferring results between the different socio-economic agents involved in R+D+I processes, acquiring thus the ability to lead a work team made up of various professional profiles and disciplines.
  • CT2 SUSTAINABILITY & SOCIAL COMMITMENT. Being able to integrate knowledge and face the complexity of formulating judgments based on information that, being incomplete or limited, includes reflections on the social and ethical responsibilities linked to the application of their knowledge and choices.
  • CT3 THIRD LANGUAGE. Having English as a third language, at an appropriate level in oral and written form, so as to being able to work and communicate effectively in international and intercultural environments.
  • CT4 EFFECTIVE ORAL AND WRITTEN COMMUNICATION. Improving communication skills: oral presentations, preparation of professional and scientific reports in a clear and concise way to communicate their conclusions, the knowledge and ultimate reasons that support it, to specialized and non-specialized audiences in a clear and unambiguous way.
  • CT5 TEAM WORK. Being able to work as a member of an interdisciplinary team, not only as a member, but also to perform management tasks in order to contribute to developing projects with pragmatism and a sense of responsibility, assuming commitments considering the resources and time available. Obtaining a good knowledge of the community of numerical methods in engineering at a national and international level.
  • CT6 SOLVENT USE OF INFORMATION RESOURCES. Managing the acquisition, structuring, analysis and visualization of data and bibliographic and computer information of a scientific and technical nature and critically assess the results of this management.
  • CT7 SELF-EMPLOYED LEARNING. Detecting gaps in one's own knowledge and overcome them through critical reflection and the choice of the best action to expand this knowledge and motivate oneself to continue training throughout their professional life.

Specific competencies

  • CE1 Knowledge of practical numerical modeling. Ability to acquire knowledge in advanced numerical modeling applied to different areas of engineering such as: Civil and environmental engineering, Mechanical and aerospace engineering, Nano-engineering and bioengineering, Naval and marine engineering, etc.
  • CE2 Knowledge of the state of the art in numerical algorithms. Ability to catch up on the latest numerical technologies to solve engineering and applied science problems.
  • CE3 Knowledge of modeling materials. Ability to acquire knowledge related to modern physical models in material science (advanced constitutive models) in solid and fluid mechanics.
  • CE4 Knowledge of validation and verification criteria. Management capacity of numerical simulation quality control techniques (validation and verification).
  • CE5 Experience in numerical simulations. Acquisition of fluency in modern numerical simulation tools and their application to multidisciplinary engineering and applied science problems.
  • CE6 Interpretation of numerical models. Understanding the applicability and limitations of different computer calculation techniques.
  • CE7 Experience in programming calculation methods. Ability to acquire training in the development and use of existing calculation programs, as well as pre and post processors, knowledge of programming languages and standard calculation libraries.
2021-2022 Academic year
For more information on course groups, coordinators and codes check the printer version of the curriculum.

COURSES

ECTS

First year
Fall semester
250950 - Numerical methods for PDEs 5
250951 - Finite element 5
250952 - Continuum mechanics 5
250954 - Advanced fluid mechanics 5
250960 - Communication skills 1 5
250961 - Computational mechanics tools 5
Spring semester
250956 - Computational solid mechanics 5
250958 - Computational structural mechanics & dynamics 5
250957 - Finite elements in fluids 5
250963 - Coupled problems 5
250970 - Domain descomposition & large scale scientific computing 5
250955 - Programming for engineers & scientists 5
Second year
Fall semester
Mandatory
250964 - Entrepreneurship 5
250965 - Advanced discretization method 5
250967 - Communication skills 2 5
Elective
250971 - Reduced order modelling 5
Spring semester
Elective
250439 - Numerical models in civil and structural engineering 5
250439 - Machine learning and models for decision making 5
Fall &/or spring semesters
Mandatory
250968 - Master's Thesis 30
Elective
External internship 15
ATTENTION: During the second year, students must choose either to enrol 15 ECTS of external internship, or 15 ECTS of elective courses.

Students enrolled at UPC for the Master's Degree in Numerical Methods in Engineering can access the following information:

The Master's Thesis is an original exercise to be done individually and presented and defended before a university panel consisting in a project in the sphere of the specific civil engineering technologies synthesising and integrating the competences acquired on the course.

List of master's theses currently scheduled for public presentation:

This program has been awarded the following quality labels: