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Mobile Communication Fields in Biological Systems
calculations of the whole-body average SAR in relatively coarse block human models.
The reference levels of incident electric field or power density in various guidelines were
derived mainly from the MoM calculations of the whole-body average SAR.
Nowadays, MoM denotes methods that solve the EM problems with charges, fields,
and current distributions as unknowns in integral equations. The MoM is especially
popular for problems with perfectly conducting objects, such as antennas or scattering
from other metal structures. Modeling of a finitely conducting ground, layered media,
etc., can be introduced via Green’s functions. MoM is mainly implemented using pulse
functions to describe the unknown electric field in each mathematical cell of the model
(the electric field has a constant value everywhere inside the mathematical cell), while
linear basis functions have also been used instead of pulse functions. A variant MoM
based on the tensor integral equation with volumetric discretization was introduced
in the mid 1970s to study the absorption in human models (Gandhi 1980; Hagmann,
Gandhi, and Durney 1979). The scatterer was subdivided into N blocks, in which a constant volume current was expanded with one unknown for each spatial dimension. The
electric field integral equation (EFIE) was evaluated in the centers of the cells. This led
to a system of equations with 3N unknowns and a dense matrix. Furthermore, a surface-discretization MoM using electric and magnetic surface currents for each domain
allows modeling of arbitrary lossy and dielectric domains.
However, the MoM is generally not appropriate for simulating the interactions
between mobile communication devices and the human body. Since the source is generally a regular object, whose geometry is often described by simple equations, the radiation
problem can be efficiently analyzed by MoM. This approach requires only the discretization of the domain where the current flows, without analyzing the space surrounding
the source, because of the use of the suitable Green’s function. On the other hand, lossy
dielectric materials cannot be modeled. The EM characterization of a physically and
geometrically complex object can be very difficult or impossible and time consuming,
when approached with the MoM. Furthermore, as the cost of the solution of the MoM
with volume discretization is roughly proportional to N 3 , the problem size grows so
fast that the method does not allow a reasonably fine discretization of the human body.
This also limits its application at frequencies higher than several hundred MHz because
smaller size blocks are required for higher frequencies, that is, shorter wavelength.
Moment method matrix equations were originally solved by direct methods. Later
iterative methods, such as the conjugate gradient method were also used. Recently there
have been some breakthroughs in iterative methods coupled with good preconditioners
and the faster approximation of the matrix–vector products used during the solution
process. This speedup might again improve the competitiveness of the MoM approach.
The use of MoM for dosimetric studies is reported in Chuang (1994) and Karimullah,
Chen, and Nyquist (1980), while MoM is used in Groot et al. (1997) and Pan, Bahrwas,
and Wolff (1997) for antenna performance studies.
5.2.3.2.2 Finite-Difference Time Domain
The Finite-Difference Time-Domain (FDTD) algorithm, first proposed by Yee (1966), is
the direct discretization of the time-dependent Maxwell’s equations by expressing the
spatial and time derivatives in a central finite-difference form implemented in a mesh
Mobile Communication Fields in Biological Systems
calculations of the whole-body average SAR in relatively coarse block human models.
The reference levels of incident electric field or power density in various guidelines were
derived mainly from the MoM calculations of the whole-body average SAR.
Nowadays, MoM denotes methods that solve the EM problems with charges, fields,
and current distributions as unknowns in integral equations. The MoM is especially
popular for problems with perfectly conducting objects, such as antennas or scattering
from other metal structures. Modeling of a finitely conducting ground, layered media,
etc., can be introduced via Green’s functions. MoM is mainly implemented using pulse
functions to describe the unknown electric field in each mathematical cell of the model
(the electric field has a constant value everywhere inside the mathematical cell), while
linear basis functions have also been used instead of pulse functions. A variant MoM
based on the tensor integral equation with volumetric discretization was introduced
in the mid 1970s to study the absorption in human models (Gandhi 1980; Hagmann,
Gandhi, and Durney 1979). The scatterer was subdivided into N blocks, in which a constant volume current was expanded with one unknown for each spatial dimension. The
electric field integral equation (EFIE) was evaluated in the centers of the cells. This led
to a system of equations with 3N unknowns and a dense matrix. Furthermore, a surface-discretization MoM using electric and magnetic surface currents for each domain
allows modeling of arbitrary lossy and dielectric domains.
However, the MoM is generally not appropriate for simulating the interactions
between mobile communication devices and the human body. Since the source is generally a regular object, whose geometry is often described by simple equations, the radiation
problem can be efficiently analyzed by MoM. This approach requires only the discretization of the domain where the current flows, without analyzing the space surrounding
the source, because of the use of the suitable Green’s function. On the other hand, lossy
dielectric materials cannot be modeled. The EM characterization of a physically and
geometrically complex object can be very difficult or impossible and time consuming,
when approached with the MoM. Furthermore, as the cost of the solution of the MoM
with volume discretization is roughly proportional to N 3 , the problem size grows so
fast that the method does not allow a reasonably fine discretization of the human body.
This also limits its application at frequencies higher than several hundred MHz because
smaller size blocks are required for higher frequencies, that is, shorter wavelength.
Moment method matrix equations were originally solved by direct methods. Later
iterative methods, such as the conjugate gradient method were also used. Recently there
have been some breakthroughs in iterative methods coupled with good preconditioners
and the faster approximation of the matrix–vector products used during the solution
process. This speedup might again improve the competitiveness of the MoM approach.
The use of MoM for dosimetric studies is reported in Chuang (1994) and Karimullah,
Chen, and Nyquist (1980), while MoM is used in Groot et al. (1997) and Pan, Bahrwas,
and Wolff (1997) for antenna performance studies.
5.2.3.2.2 Finite-Difference Time Domain
The Finite-Difference Time-Domain (FDTD) algorithm, first proposed by Yee (1966), is
the direct discretization of the time-dependent Maxwell’s equations by expressing the
spatial and time derivatives in a central finite-difference form implemented in a mesh