1. Advanced finite element method
ITSS 2010, Metz
Advanced finite element method
Vladimír Šeděnka
PhD student since September 2009
Supervisor: Zbyněk Raida
Brno University of Technology

2. Presentation schedule
Finite element method
Nodal finite elements
Edge finite elements
Perfectly matched layers
Example of results
Contact

3. Residual minimization Solving linear system of equations
Finite element method
Numerical technique for solving partial differential equations (PDEs)
Converts PDE into system of linear equations
Structure, PDE
Discretization
Approximation
Residual minimization
Solving linear system of equations
Frequency domain:
Time domain:

4. Nodal finite elements Basic elements
Do not guarantee continuity of tangential components of the field across element interfaces
N3(3) = 1 3 2 1
N1(1) = 1
N2(2) = 1 3 2 1 3 2 1 N1 N2 N3

5. Edge finite elements Can handle anisotropic media
Can avoid spurious solutions
N12
N23
N31

6. Perfectly matched layers
Reflectionless termination of the structure
Possible solutions:
Modification of Maxwell’s equations (Berenger)
Usage of an anisotropic media (Sacks)
Condition:

7. Example of results Mesh Electric field Magnetic field

8. Contact xseden01@stud.feec.vutbr.cz
Department of Radio Electronics, Brno University of Technology
Purkyňova 118, Brno, Czech Republic
Tel:
Fax:

9. This work was supported by the project CZ. 1. 07/2. 3. 00/09
This work was supported by the project CZ.1.07/2.3.00/ Communication Systems for Emerging Frequency Bands