Dielectric volume averaging (DVA) causes the meshing algorithm to consider the volume around each cell edge and set material properties based on the average of those findings. This affects the mesh of a part's surface where it meets other materials and not the internal, homogeneous area of the part.


2D FDTD cell vs cell edge vs cell edge volume.
Figure 1: White = 2D FDTD cell. Orange = cell edge. Blue = volume represented by a cell edge.

In FDTD, CAD geometry is discretized into cell edges. It is easy to think of discretization in terms of cells, but that is misleading because it adds a layer of abstraction to the actual FDTD update equations. Each cell edge has an electric field associated with it and it is the cell's edges, not the cell, that carry the electromagnetic information during timestepping. As such, each cell edge represents the volume around it—roughly one third the size of the cell—as shown in Figure 1.

Ey cell edge surrounded by four Yee cells.
Figure 2: Ey cell edge surrounded by four different materials.

This leads to well-documented accuracy degeneration at dielectric material interfaces ([1], [2], [3], [4], [5]). Figure 2 illustrates an Ey cell edge surrounded by four different dielectric materials. The uncertainty of the cell edge's value is emphasized by the FDTD formulation, which allows only a single value of permittivity and conductivity to be assigned to the Ey edge. XF typically assigns the permittivity and conductivity from the material with the highest meshing priority to the Ey edge, and in many cases this is a reasonable approximation.

One way to increase accuracy in such cases is to calculate an effective permittivity and conductivity for each cell edge, known in XF as dielectric volume averaging. The dielectric volume averaging option causes XF's meshing algorithm to look at the volume around each cell edge as opposed to looking solely at the geometry with the highest meshing priority. By looking at the volume, this algorithm determines the averaged material properties and applies it to that cell edge. This results in a more accurate representation by smoothing the transition between dielectrics at material interfaces.

Users should note that using DVA to treat material interfaces in the FDTD space requires additional memory and computational resources.


  1. A. Christ, J. F. S. Benkler, and N. Kuster, "Analysis of the accuracy of the numerical reflection coefficient of the finite-difference time-domain method at planar material interfaces," IEEE Trans. Electromagnetic Compatibility, vol. 48, p. 264, May 2006.
  2. T. Hirono, Y. Shibata, W. W. Lui, S. Seki, and Y. Yoshikuni, "The second-order condition for the dielectric interface orthogonal to the yee-lattice axis in the fdtd scheme," IEEE Microwave and Guided Wave Letters, vol. 10, p. 359, September 2000.
  3. K.-P. Hwang and A. Cangellaris, "Effective permittivities for second-order accurate fdtd equations at dielectric interfaces," IEEE Microwave and Wireless Comp. Letters, vol. 11, p. 158, April 2001.
  4. B. Yang and C. A. Balanis, "Dielectric interface conditions for general fourth-order finite difference," IEEE Microwave and Wireless Comp. Letters, vol. 17, p. 559, August 2007.
  5. T. T. Zygiridis, T. K. Katsibas, C. S. Antonopoulos, and T. D. Tsiboukis, "Treatment of grid-conforming dielectric interfaces in fdtd methods," IEEE Trans. Magnetics, vol. 45, p. 1396, March 2009.

Enabling and Visualization

DVA can be enabled and disabled for a part, multiple parts, or an assembly through the right-click menu.

Screenshot of right click menu for a part.
Enable/disable through the part's right-click menu.

The Meshing Properties Editor for a part also contains a check box for enabling/disabling DVA.
Screenshot of meshing properties editor.
Enable/disable through a part's Meshing Properties Editor.

For visual verification, the Parts List includes a percent icon when DVA is enabled for a part.
Screenshot of Part's List.
A percent icon is included in the Parts List when DVA is enabled.

When viewing a slice of the mesh, display the averaged material properties per cell edge by checking the View Mesh Information: Material option.
Screenshot of meshing material info.
View material properties per cell edge with the mesh.
The mesh viewing controls also provide a check box for Averaged Materials Visibility. The computation requirements for visualizing averaged material properties may slow XF down when there are large number of averaged cells, so users can uncheck the box if the interface is sluggish when slicing through the mesh.
Screenshot of meshing controls.
Disable Averaged Materials Visibility if XF is sluggish.

Averaged material properties per cell edge are formulated using the weighted average. To conserve memory, the number of allowable weights is limited and like materials are grouped together for consideration in the computation engine. The user controls how many subdivisions will be considered for an averaged material.

The higher the number of subdivisions specified, the greater the resolution of averaged materials generated and the more computational resources required.
Screenshot of meshing properties.
Set the number of subdivisions for computing weighted average.


DVA improves simulation results for microstrip antennas and similar applications in which antennas are mounted on dielectric substrates. This is due to the averaging of the substrate material and air (free space) for cell edges in the antenna plane, which increases the accuracy of the edge field computations. The importance of DVA for these applications also increases with the permittivity of the substrate, i.e., the higher the permittivity of the substrate, the greater the accuracy improvement due to proper material averaging.

It is also important to activate DVA for SAR calculations involving tissue materials. This will ensure accurate SAR averaging results that are in compliance with the latest SAR standard.

These characteristics lead to multiple recommendations: As with most settings, Remcom recommends running a couple simulations with and without DVA to ensure it has the expected and desired effect on the simulation results.


Not all situations are appropriate for DVA: