263-5001-00L  Introduction to Finite Elements and Sparse Linear System Solving

SemesterAutumn Semester 2016
LecturersP. Arbenz
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
263-5001-00 VIntroduction to Finite Elements and Sparse Linear System Solving2 hrs
Fri08-10CAB G 56 »
P. Arbenz
263-5001-00 UIntroduction to Finite Elements and Sparse Linear System Solving1 hrs
Fri10-11CAB G 56 »
P. Arbenz

Catalogue data

AbstractThe finite element (FE) method is the method of choice for (approximately) solving partial differential equations on complicated domains. In the first third of the lecture, we give an introduction to the method. The rest of the lecture will be devoted to methods for solving the large sparse linear systems of equation that a typical for the FE method. We will consider direct and iterative methods.
ObjectiveStudents will know the most important direct and iterative solvers for sparse linear systems. They will be able to determine which solver to choose in particular situations.
ContentI. THE FINITE ELEMENT METHOD

(1) Introduction, model problems.

(2) 1D problems. Piecewise polynomials in 1D.

(3) 2D problems. Triangulations. Piecewise polynomials in 2D.

(4) Variational formulations. Galerkin finite element method.

(5) Implementation aspects.


II. DIRECT SOLUTION METHODS

(6) LU and Cholesky decomposition.

(7) Sparse matrices.

(8) Fill-reducing orderings.


III. ITERATIVE SOLUTION METHODS

(9) Stationary iterative methods, preconditioning.

(10) Preconditioned conjugate gradient method (PCG).

(11) Incomplete factorization preconditioning.

(12) Multigrid preconditioning.

(13) Nonsymmetric problems (GMRES, BiCGstab).

(14) Indefinite problems (SYMMLQ, MINRES).
Literature[1] M. G. Larson, F. Bengzon: The Finite Element Method: Theory, Implementation, and Applications. Springer, Heidelberg, 2013.

[2] H. Elman, D. Sylvester, A. Wathen: Finite elements and fast iterative solvers. OUP, Oxford, 2005.

[3] Y. Saad: Iterative methods for sparse linear systems (2nd ed.). SIAM, Philadelphia, 2003.

[4] T. Davis: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia, 2006.

[5] H.R. Schwarz: Die Methode der finiten Elemente (3rd ed.). Teubner, Stuttgart, 1991.
Prerequisites / NoticePrerequisites: Linear Algebra, Analysis, Computational Science.
The exercises are made with Matlab.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersP. Arbenz
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 30 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
Main linkInformation
Only public learning materials are listed.

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Biomedical Engineering MasterRecommended Elective CoursesWInformation
Certificate of Advanced Studies in Computer ScienceFocus Courses and ElectivesWInformation
Computer Science MasterFocus Elective Courses Computational ScienceWInformation
MAS in Medical PhysicsElectivesWInformation
Computational Science and Engineering BachelorElectivesWInformation
Computational Science and Engineering MasterElectivesWInformation