Advanced finite element method

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Presentation transcript:

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

Presentation schedule Finite element method Nodal finite elements Edge finite elements Perfectly matched layers Example of results Contact xseden01@stud.feec.vutbr.cz

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: xseden01@stud.feec.vutbr.cz

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 xseden01@stud.feec.vutbr.cz

Edge finite elements Can handle anisotropic media Can avoid spurious solutions N12 N23 N31 xseden01@stud.feec.vutbr.cz

Perfectly matched layers Reflectionless termination of the structure Possible solutions: Modification of Maxwell’s equations (Berenger) Usage of an anisotropic media (Sacks) Condition: xseden01@stud.feec.vutbr.cz

Example of results Mesh Electric field Magnetic field xseden01@stud.feec.vutbr.cz

Contact xseden01@stud.feec.vutbr.cz Department of Radio Electronics, Brno University of Technology Purkyňova 118, 612 00 Brno, Czech Republic Tel: +420 541 149 117 Fax: +420 541 149 244 xseden01@stud.feec.vutbr.cz

This work was supported by the project CZ. 1. 07/2. 3. 00/09 This work was supported by the project CZ.1.07/2.3.00/09.0092 Communication Systems for Emerging Frequency Bands