The finite-difference frequency-domain (FDFD) is a numerical solution for problems usually in electromagnetism. The method is, of course, based on finite-difference approximations of the derivative operators in the differential equation being solved. While FDFD is a generic term describing all frequency-domain finite-difference methods, the title seems to mostly describe the method as applied to scattering problems. The method shares many similarities to the finite-difference time-domain method so much of the literature on FDTD can be directly applied. The method works by transforming Maxwell's equations (or other partial differential equation) into matrix form [A] [x] = [b] . The matrix [A] is the wave equation operator, the column vector [x] contains the field components, and the column vector [b] describes the source.
FDFD is arguably the simplest numerical method to implement to solve Maxwell's equations. The method does little to minimize the size of the matrices it produces so it tends to be less efficient than techniques like the finite element method. It resolves the field throughout a volume so it is an excellent technique for modeling devices with high volumetric complexity or visualizing the fields. For 2D simulations, it is capable of modeling finite sized devices or complicated waveguide discontinuity problems.
Tips for Implementing the Method
1. Use a Yee grid as this implicitly satisfies the zero divergence conditions to avoid spurious solutions.
2. Much of the literature on finite-difference time-domain (FDTD) applies to FDFD, particularly topics on how to represent materials and devices on a Yee grid.
See Chapter 3 in... [http://purl.fcla.edu/fcla/etd/CFE0001159]
Finite-difference time-domain method
* [http://ab-initio.mit.edu/wiki/index.php/MPB_Introduction MPB Introduction: Comparison of FDTD and FDFD]
Wikimedia Foundation. 2010.
Look at other dictionaries:
Finite-difference time-domain method — Finite difference time domain (FDTD) is a popular computational electrodynamics modeling technique. It is considered easy to understand and easy to implement in software. Since it is a time domain method, solutions can cover a wide frequency… … Wikipedia
Finite difference — A finite difference is a mathematical expression of the form f(x + b) − f(x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences… … Wikipedia
Finite impulse response — A finite impulse response (FIR) filter is a type of a digital filter. The impulse response, the filter s response to a Kronecker delta input, is finite because it settles to zero in a finite number of sample intervals. This is in contrast to… … Wikipedia
Computational electromagnetics — Computational electromagnetics, computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment. It typically involves using computationally… … Wikipedia
List of mathematics articles (F) — NOTOC F F₄ F algebra F coalgebra F distribution F divergence Fσ set F space F test F theory F. and M. Riesz theorem F1 Score Faà di Bruno s formula Face (geometry) Face configuration Face diagonal Facet (mathematics) Facetting… … Wikipedia
Метод конечных разностей во временной области — (англ. Finite Difference Time Domain, FDTD) один из наиболее популярных методов численной электродинамики, основанный на дискретизации уравнений Максвелла, записанных в дифференциальной форме. Содержание 1 Описание 2 Алгоритм Йи … Википедия
Maxwell's equations — For thermodynamic relations, see Maxwell relations. Electromagnetism … Wikipedia
Spectral method — Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain Dynamical Systems, often involving the use of the Fast Fourier Transform. Where applicable, spectral methods have… … Wikipedia
Charles E. Smith (engineer) — Dr. Charles E. Smith was professor and Chair in the Department of Electrical Engineering at the University of Mississippi. His focus research areas included: application of electromagnetic theory to microwave circuits, application of numerical… … Wikipedia
Multigrid method — Multigrid (MG) methods in numerical analysis are a group of algorithms for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multiresolution methods, very useful in (but not… … Wikipedia