Finite-difference time-___domain method: Difference between revisions

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| 2009 || Oliveira and Sobrinho applied the FDTD method for simulating lightning strokes in a power substation<ref name="oliveira09" />

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| 2012 || Moxley ''et al'' developed a generalized finite-difference time-___domain quantum method for the N-body interacting Hamiltonian.<ref name="Moxley2012" />

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| 2013 || Moxley ''et al'' developed a generalized finite-difference time-___domain scheme for solving nonlinear Schrödinger equations.<ref name="Moxley2013" />

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| 2014 || Moxley ''et al'' developed an implicit generalized finite-difference time-___domain scheme for solving nonlinear Schrödinger equations.<ref name="Moxley2014" />

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| 2021 || Oliveira and Paiva developed the Least Squares Finite-Difference Time-Domain method (LS-FDTD) for using time steps beyond FDTD CFL limit.<ref name="oliveira2021" />

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While the FDTD technique computes electromagnetic fields within a compact spatial region, scattered and/or radiated far fields can be obtained via near-to-far-field transformations.<ref name="umashankar82" />

==== Stability ====

Due to the linearity of the FDTD method, the region of stability of the FDTD method may be determined by [[Von Neumann stability analysis]]. This method assumes that electric and magnetic fields are proportional to a monochromatic complex exponential. After a single time-step, the magnitude amplitude of the stable fields need to remain the same or less. This leads to the [[Courant–Friedrichs–Lewy condition]], which describes the relationship of the FDTD parameters to ensure stability.<ref name="taflove05"/>

=== Strengths of FDTD modeling ===

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# Parallel-processing computer architectures have come to dominate supercomputing. FDTD scales with high efficiency on parallel-processing CPU-based computers, and extremely well on recently developed GPU-based accelerator technology.<ref name="taflove05" />

# Computer visualization capabilities are increasing rapidly. While this trend positively influences all numerical techniques, it is of particular advantage to FDTD methods, which generate time-marched arrays of field quantities suitable for use in color videos to illustrate the field dynamics.<ref name="taflove05" />

# Anisotropy is treated naturally by the FDTD method. Yee cells, having components in each Cartesian direction, can be easily configured with anisotropic characteristics.<ref name="taflove05"/>

Taflove has argued that these factors combine to suggest that FDTD will remain one of the dominant computational electrodynamics techniques (as well as potentially other [[multi-physics|multiphysics]] problems).<ref name="taflove05" />

the dominant computational electrodynamics techniques (as well as potentially other [[multi-physics|multiphysics]] problems).<ref name="taflove05" />

==See also==

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| doi = 10.1002/sapm1950291223

}}</ref>

<ref name="Moxley2012">

{{cite journal

|author1=F. I. Moxley III |author2=T. Byrnes |author3=F. Fujiwara |author4=W. Dai | title = A generalized finite-difference time-___domain quantum method for the N-body interacting Hamiltonian

| journal = Computer Physics Communications

| volume = 183

| issue = 11

| pages = 2434–2440

| year = 2012

| doi=10.1016/j.cpc.2012.06.012

|bibcode = 2012CoPhC.183.2434M }}</ref>

<ref name="Moxley2014">{{cite book

| author=Frederick Moxley

| display-authors=etal

| title=Contemporary Mathematics: Mathematics of Continuous and Discrete Dynamical Systems

| publisher=American Mathematical Society

| year=2014

| isbn=978-0-8218-9862-8

| url=https://www.ams.org/bookstore-getitem?item=CONM-618| author-link=Frederick Moxley

}}

</ref>

<ref name="Moxley2013">

{{cite journal

|author1=F. I. Moxley III |author2=D. T. Chuss |author3=W. Dai | title = A generalized finite-difference time-___domain scheme for solving nonlinear Schrödinger equations

| journal = Computer Physics Communications

| volume = 184

| issue = 8

| pages = 1834–1841

| year = 2013

| doi=10.1016/j.cpc.2013.03.006

|bibcode = 2013CoPhC.184.1834M }}</ref>

<ref name="vonneumann49">

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* [http://ab-initio.mit.edu/meep/ Meep] ([[Massachusetts Institute of Technology|MIT]], 2D/3D/cylindrical parallel FDTD)

* [http://freshmeat.net/projects/radarfdtd/ (Geo-) Radar FDTD]

* [httphttps://sourceforge.net/projects/bigboy bigboy] (unmaintained, no release files. must get source from cvs)

* [httphttps://sourceforge.net/projects/pfdtd/files/ Parallel (MPI&OpenMP) FDTD codes in C++] (developed by Zs. Szabó)

* [https://archive.today/20121217222254/http://cs.tu-berlin.de/~peutetre/sfdtd/ FDTD code in Fortran 90]

* [http://code.google.com/p/emwave2d/ FDTD code in C for 2D EM Wave simulation]