The evaluation of magnetic and electric fields is repeated for the desired duration, and this will give the desired solution for the electromagnetic problem.įDTD Absorbing Boundary Conditions in Open Boundary Electromagnetic ProblemsĪs mentioned above, FDTD simulations are driven by update equations.Similarly, the electric fields are also evaluated and the results become past field values. The magnetic fields transform from future fields to past fields after evaluation. The magnetic fields are evaluated one time step into the future.The update equations express the electric and magnetic fields of future (unknown values) in terms of past fields (known values). The resulting finite difference equations are solved to obtain update equations.Space staggering and time staggering are used to discretize space and time so that the electric and magnetic fields are staggered in both space and time. The electric and magnetic fields of each grid are defined. The partial derivatives in the equations representing electromagnetic problems are replaced by central difference equations or finite difference equations.The FDTD algorithm can be summarized as follows: For each grid, both electric and magnetic fields are defined using mathematical equations and are solved grid-by-grid to reach the final desired solution. The electromagnetic solution region is discretized in such a way that the size of the grids present in it are shorter than the electromagnetic wavelength and the geometrical details. In the FDTD method, the solution region of electromagnetic field problems is discretized with cells or grids. FDTD absorbing boundary conditions are introduced to solve open boundary electromagnetic problems so that a solution obtained can be presented as the accurate approximation of the real solution that considers unlimited space surrounding it. In the case of electromagnetic field problems that are unbounded in space, boundary conditions are required to bring the infinite space to a finite computational domain. The equations of each grid connect with the terms from the neighboring grids, and the whole 3D Cartesian grid is modeled like that until it reaches the physical boundary of the solution region. Maxwell’s equations and wave equations representing electromagnetic problems are modified to simple simultaneous equations associated with each grid present in the solution region. The FDTD method uses grid-based differential time-domain modeling, and this helps to cover a wide frequency range in one simulation run. The FDTD method is easy to understand and its algorithm is far less complex to implement compared to other numerical methods such as the finite element method (FEM) or method of moments (MoM) solvers. The finite-difference time-domain (FDTD) method is the most popular computational numerical method used to solve time-dependent electromagnetic field problems.
#Fdtd solution free
The radiation of an antenna in free space is an example of an open boundary problem In open boundary problems, absorbing boundary conditions (otherwise called radiation boundary conditions) are introduced.įDTD absorbing boundary conditions are helpful in replacing the infinite space that surrounds the solution region with the finite computational domain. FDTD uses grid-based differential time-domain modeling, and this helps to cover a wide frequency range in one simulation run.
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