Development of the Finite Difference Time Domain Method on a Lebedev Grid for Anisotropic Materials

The finite-difference time-domain (FDTD) method is derived on a Lebedev grid, instead of the standard Yee grid, to better represent the constitutive relations in anisotropic materials. The Lebedev grid extends the Yee grid by approximating Maxwell's equations with tensor constitutive relations using only central differences. A dispersion relation with stability criteria is derived and it is proven that the Lebedev grid has a consistent calculus. An integral derivation of the update equations illustrates how to appropriately excite the grid. This approach is also used to derive the update equations at planar material interfaces and domain edge PEC. Lebedev grid results are compared with analytical and Yee grid solutions using an equal memory comparison. Numerical results show that the Lebedev grid suffers greater dispersion error but better represents material interfaces. Focus is given to generalizing the concepts that make the Yee grid robust for isotropic materials.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Grantor dc:publisher.institution

Graduate Studies

Year dc:date.issued

2012

Author dc:creator

• Nauta, Marcel

Advisors dc:contributor.advisor

• Potter, Mike
• Okoniewski, Michal

• Engineering--Electricity and Magnetism
• Computer Science
• Engineering--Electronics and Electrical

Statement dc:rights

• University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.

Language dc:language.iso

eng

DOI

http://dx.doi.org/10.11575/PRISM/25689

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:11023/355