Finite-difference frequency-domain method

Frequency-domain analysis | Numerical differential equations

The finite-difference frequency-domain (FDFD) method is a numerical solution method for problems usually in electromagnetism and sometimes in acoustics, 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 (FDTD) 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) for sources and fields at a constant frequency into matrix form . The matrix A is derived from the wave equation operator, the column vector x contains the field components, and the column vector b describes the source. The method is capable of incorporating anisotropic materials, but off-diagonal components of the tensor require special treatment. Strictly speaking, there are at least two categories of "frequency-domain" problems in electromagnetism. One is to find the response to a current density J with a constant frequency ω, i.e. of the form , or a similar time-harmonic source. This frequency-domain response problem leads to an system of linear equations as described above. An early description of a frequency-domain response FDTD method to solve scattering problems was published by Christ and Hartnagel (1987). Another is to find the normal modes of a structure (e.g. a waveguide) in the absence of sources: in this case the frequency ω is itself a variable, and one obtains an eigenproblem (usually, the eigenvalue λ is ω2). An early description of an FDTD method to solve electromagnetic eigenproblems was published by Albani and Bernardi (1974). (Wikipedia).

Horn Antenna Simulation using Finite Difference Time Domain (FDTD) Method 📡

Here we show the radiation from various horn antenna types using the finite difference time domain algorithm. First we starts with a basic horn antenna and compare it with free space propagation. Then, horn antenna is compared to a waveguide without any horns. Finally the impact of horn an

From playlist Electromagnetic Animations

Finite Difference Method

Finite Difference Method for finding roots of functions including an example and visual representation. Also includes discussions of Forward, Backward, and Central Finite Difference as well as overview of higher order versions of Finite Difference. Chapters 0:00 Intro 0:04 Secant Method R

From playlist Root Finding

Lecture 15 (CEM) -- Finite-Difference Time-Domain

This lecture introduces the finite-difference time-domain method. It includes the basic method, derivation of the update equations, and some implementation issues such as Fourier transforms and calculation of transmittance and reflectance. This lecture is NOT intended to leave the studen

From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering

Method of Finite Differences

From playlist ℕumber Theory

Parametric vs Nonparametric Spectrum Estimation

http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Introduces parametric (model-based) and nonparametric (Fourier-based) approaches to estimation of the power spectrum.

From playlist Estimation and Detection Theory

Lecture 23 (CEM) -- Slice Absorption Method

This lecture introduces the student to the slice absorption method, which is essentially a block tridiagonal solver for the finite-difference frequency-domain method. It is able to solve larger problems than the conventional finite-difference frequency-domain method. Prerequisite Lecture

From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering

Lecture 12 (CEM) -- Formulation of Finite-Difference Frequency-Domain

This lecture steps the student through the formulation of the finite-difference frequency-domain model. Many concepts from previous lectures come together in this formulation. Prerequisite Lectures: 2, 3, 6, 7, 8, and 9

From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering

Lecture 1 (CEM) -- Introduction to CEM

This lecture introduces the course and steps the student through an overview of most of the major techniques in computational electromagnetics.

From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering

ME565 Lecture 20: Numerical Solutions to PDEs Using FFT

ME565 Lecture 20 Engineering Mathematics at the University of Washington Numerical Solutions to PDEs Using FFT Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L20.pdf Matlab code: * http://faculty.washington.edu/sbrunton/me565/matlab/HeatConvolution.m * http://faculty.wash

From playlist Engineering Mathematics (UW ME564 and ME565)

Lecture 16 (CEM) -- Beam Propagation Method

This lecture steps the student through the formulation and implementation of a basic finite-difference beam propagation method. A brief overview of wide-angle and bi-directional BPM is given, but not discussed in detail. Prerequisite Lectures: 10

From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering

Lec 14 | MIT RES.6-008 Digital Signal Processing, 1975

Lecture 14: Design of IIR digital filters, part 1 Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES6-008S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-008 Digital Signal Processing, 1975

Frequency Domain Interpretation of Sampling

http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Analysis of the effect of sampling a continuous-time signal in the frequency domain through use of the Fourier transform.

From playlist Sampling and Reconstruction of Signals

Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations

Generalized Finite Difference Method for Simultaneous Nonlinear Systems by approximating the Jacobian using the limit of partial derivatives with the forward finite difference. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:13 Prerequisites 0:3

From playlist Solving Systems of Nonlinear Equations

Modeling Acoustics with Differential Equations

To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technology-conference/ Speaker: Yi-Lin Chiu Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, and m

From playlist Wolfram Technology Conference 2018

ME565 Lecture 26: Solving PDEs in Matlab using FFT

ME565 Lecture 26 Engineering Mathematics at the University of Washington Solving PDEs in Matlab using FFT Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L26.pdf Course Website: http://faculty.washington.edu/sbrunton/me565/ http://faculty.washington.edu/sbrunton/

From playlist Engineering Mathematics (UW ME564 and ME565)

Sascha Husa (5) - Introduction to theory and numerics of partial differential equations

PROGRAM: NUMERICAL RELATIVITY DATES: Monday 10 Jun, 2013 - Friday 05 Jul, 2013 VENUE: ICTS-TIFR, IISc Campus, Bangalore DETAL Numerical relativity deals with solving Einstein's field equations using supercomputers. Numerical relativity is an essential tool for the accurate modeling of a wi

From playlist Numerical Relativity

The Fourier Transform and Derivatives

This video describes how the Fourier Transform can be used to accurately and efficiently compute derivatives, with implications for the numerical solution of differential equations. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow

From playlist Fourier

Samuli Siltanen: Reconstruction methods for ill-posed inverse problems - Part 2

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Partial Differential Equations

Finite-difference frequency-domain method

Related pages