| Code |
18143
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
MECÂNICA COMPUTACIONAL
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Entry requirements |
N.A.
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Learning outcomes |
It is intended to provide a common base of knowledge in the field of computational mechanics. The basic knowledge about numerical methods learned in the bachelor degree is developed in order to incorporate a more in-depth level of knowledge in the domain of Fourier series and wavelet transform, and the various discretization methods. In this regard, special attention is given to solving the inherent
systems of equations and to the convergence and stability of the solutions.
A second objective aims at the development of skills and competences on convergence acceleration techniques in numerical methodologies to solve advanced problems of computational mechanics. This approach uses an approach to the bases followed by interconnection with the commercial codes used by mechanical engineers in high-performance computing and quantum computers
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Syllabus |
1. Introduction. Programming and data structures with application to computational mechanics. Fourier series and FFT with time series data analysis. Energy spectrum in hot wire signals and vibrations. Wavelet transform.
2. Computational mechanics complements. Consistency, stability and convergence. Fourier analysis in the grid (von Neumann). Finite volumes (wave equation) and finite elements (chord with two fixed ends). Errors. Iterative methods. SOR, Gradient Conjugate, GMRES.
3. Acceleration of numerical convergence in computational mechanics. Geometric and algebraic multigrid methods. Preconditioning.
4. Hybrid techniques to accelerate productivity in computational mechanics. HPC and CUDA in commercial program implementations. Tensor Processing Unit (TPU) technologies and quantum computing applied to computational mechanics.
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Main Bibliography |
[1] Numerical Methods Using MATLAB; G. Lindfield & J. Penny; Academic Press; 2019
[2] Fourier and Wavelet Analysis; G. Bachman et al; Springer, 1999.
[3] Numerical Methods for Conservation Laws, R. Levecque, Lectures in Mathematics, Birkhauser, 1992.
[4] Briggs, W. L., et al. A Multigrid Tutorial. SIAM, 2000
[5] Numerical Solution of Partial Differential Equations by the Finite Element Method; C. Johnson, Dover Books, 2009.
[6] Introduction to High Performance Computing for Scientists and Engineers; G. Hager, G. Wellein; Chapman & Hall, 2010.
[7] CUDA for Engineers: An Introduction to High-Performance Parallel Computing; D. Storti & M. Yurtoglu; Addison-Wesley; 2015.
[8] A TensorFlow simulation framework for scientific computing of fluid flows on tensor processing units, Qing Wang et al; Computer Physics Communications, Volume 274, 2022
[9] FEqa: Finite element computations on quantum annealers; Raisuddin et al; Computer Methods in Applied Mechanics and Engineering; Volume 395; 2022.
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Teaching Methodologies and Assessment Criteria |
The evaluation consists of different differentiating elements duly linked to the syllabus of the curricular unit:
- Frequency Test, TF (11 Vs) on the theoretical-practical subject of the classes.
-Practical Laboratory Assignments, TP (5Vs) originating from the development of several computer codes in the classroom referring to the syllabus of the curricular unit.
- Mini-project work, PM (4Vs) which comprises the development of a more substantial code to solve a problem that is included in the UC program, to be developed by the student individually and outside the classroom.
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Language |
Portuguese. Tutorial support is available in English.
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