## Scattering vs Total field

This is the question that arises at the first attempt to use RF module. Answer can be found in Jiaming Jin's books:

The Finite Element Method in Electromagnetics, by Jianming Jin

Finite Element Analysis of Antennas and Arrays, by Jian-Ming Jin and Douglas J. Riley

The former is used by COMSOL developers when the software was developed, and there are few instances when the author discusses about pros and cons of both approaches. In the later book, there is a chapter which I prefer about this matter.

Total and scattered fields are defined as follows:

Et=Ei+Esc,

where Et is total, Ei is incident field and Esc is scattered field.

Soon, I will quote some statements that will help us to understand what choice we should make.

General Helmholtz equation is solved for total field. Total field is inserted on the geometry boundary via special boundary condition. PMLs should not be used, or if used total field should be inserted inside the geometry using assemblies and identity pairs in COMSOL. Since field propagation to the scatterer is numerically calculated, the field reaching the scatterer might suffer some computational loss of accuracy, thus meshing has to be taken into care.

If we separate total field into incident and scatterer fields, then incident field already satisfies Helmholtz equation everywhere except in metallic or other domains (scatterers), of course if properly defined. "...incident fields are only impressed on the conducting surface of the scatterer, and/or withing the penetrable volume of the scatterer throughout the computational domain". Here there is no problem with propagation of the incident field since it is mathematically imposed as solution of the Hellmholtz equation in scatterers-free geometry, consequently this method gives more accurate solution (this is believed).

Referring to meshing requirements, meshing is more flexible for scattering field than total, since in the former we are solving only for scattered field, and if it is evanescent, we might know where it is necessary to use finer mesh. In total field COMSOL is calculating propagation of the excitation, so meshing has to be sufficiently dense everywhere. Moreover, describing excitation sometimes might be very challenging for the geometries consisting of more than one interface, making use of scattering harmonic propagation very complicated. In some cases, one can solve empty geometry by harmonic propagation analysis, and later solve geometry with objects in scattering harmonic propagation, where incident field is the solution of the previous step.

The Finite Element Method in Electromagnetics, by Jianming Jin

Finite Element Analysis of Antennas and Arrays, by Jian-Ming Jin and Douglas J. Riley

The former is used by COMSOL developers when the software was developed, and there are few instances when the author discusses about pros and cons of both approaches. In the later book, there is a chapter which I prefer about this matter.

Total and scattered fields are defined as follows:

Et=Ei+Esc,

where Et is total, Ei is incident field and Esc is scattered field.

Soon, I will quote some statements that will help us to understand what choice we should make.

General Helmholtz equation is solved for total field. Total field is inserted on the geometry boundary via special boundary condition. PMLs should not be used, or if used total field should be inserted inside the geometry using assemblies and identity pairs in COMSOL. Since field propagation to the scatterer is numerically calculated, the field reaching the scatterer might suffer some computational loss of accuracy, thus meshing has to be taken into care.

If we separate total field into incident and scatterer fields, then incident field already satisfies Helmholtz equation everywhere except in metallic or other domains (scatterers), of course if properly defined. "...incident fields are only impressed on the conducting surface of the scatterer, and/or withing the penetrable volume of the scatterer throughout the computational domain". Here there is no problem with propagation of the incident field since it is mathematically imposed as solution of the Hellmholtz equation in scatterers-free geometry, consequently this method gives more accurate solution (this is believed).

Referring to meshing requirements, meshing is more flexible for scattering field than total, since in the former we are solving only for scattered field, and if it is evanescent, we might know where it is necessary to use finer mesh. In total field COMSOL is calculating propagation of the excitation, so meshing has to be sufficiently dense everywhere. Moreover, describing excitation sometimes might be very challenging for the geometries consisting of more than one interface, making use of scattering harmonic propagation very complicated. In some cases, one can solve empty geometry by harmonic propagation analysis, and later solve geometry with objects in scattering harmonic propagation, where incident field is the solution of the previous step.