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Mobile Communication Fields in Biological Systems
extremely low–frequency (ELF) to microwave frequencies. It is powerful in dealing with
a complex penetrable object such as the human head and has dominated over the other
methods for the study of dosimetric problems related to mobile communications as well
as for wireless device antenna design (Bernardi, Cavagnaro, and Pisa 1996; Cavagnaro
and Pisa 1996; Christ and Kuster 2005; Gandhi and Chen 1995; Gandhi, Lazzi, and Furse
1996; Lazzi and Gandhi 1997; Lu et al. 1996; Martens et al. 1995; Martinez-Burdalo et al.
2005; Okoniewski and Stuchly 1996; Watanabe et al. 1996). This is due to the fact that
enhanced computer power has become available at lower cost and intensive research
work in the fields of source modeling, absorbing boundary conditions, and error checking has facilitated the simulation with more confidence in the obtained results. Several
approaches for accurate absorbing boundary conditions at the boundary of the computational domain have been proposed (Berenger 1994; Bernsten and Hornsleth 1994; Mur
1981), offering excellent approximation of open space with a minimum of “white space.”
Negligible differences in the calculated SAR distributions or the radiation patterns are
obtained regardless of the boundary conditions that are used. Furthermore, the use of
a nonuniform grid has been proposed (Okoniewski and Stuchly 1996) to reduce the
memory requirements, while parallelized versions of FDTD codes can be used to reduce
the execution time. Other notable improvements are in the area of uncertainty assessments and graphical user interfaces (Kuster 2002).
5.2.3.2.3 Finite Integration Technique
The Finite Integration Technique (FIT), introduced by Weiland (1977), is based on the
discretization of the integral form of Maxwell’s equations and transforms them into
a set of matrix equations, the Maxwell grid equations (MGEs), on an orthogonal dual
grid pair. It is a method conceptually slightly different from the FDTD technique, which
however leads to the same numerical scheme. The FIT can be thought of as equivalent to
the FDTD for time-domain problems (Weiland 1990).
The use of FIT for mobile communication dosimetric calculations is reported in
numerous studies (Hombach et al. 1996; Meier et al. 1997; Schoenborn, Burkhardt, and
Kuster 1998).
5.2.3.2.4 Finite Element Method
The Finite Element Method (FEM) was introduced by Silvester and Ferrari (1996). Space
is discretized in a finite element mesh with linear or polynomial expansion functions
within each element. The unknowns are associated with the field values in the nodes.
A variational method or a method of weighted residuals is used to obtain a system of
equations with a sparse matrix. In wave propagation problems, the FEM is often used
in the frequency domain. For a long time, its applicability for solving the Helmholtz
equation was quite limited because of problems with spurious modes. Open domains
were another limitation, as no efficient radiation boundary conditions were available.
Therefore, FEM was often paired with a boundary element method in a hybrid scheme.
Although penalty methods can be used to avoid the corruption of results with spurious solutions, the advent of edge-element techniques that prevent the possibility of
spurious modes altogether seem more promising. In the edge-element technique the
unknowns are associated with the field tangential to the edges of the basic element.
Mobile Communication Fields in Biological Systems
extremely low–frequency (ELF) to microwave frequencies. It is powerful in dealing with
a complex penetrable object such as the human head and has dominated over the other
methods for the study of dosimetric problems related to mobile communications as well
as for wireless device antenna design (Bernardi, Cavagnaro, and Pisa 1996; Cavagnaro
and Pisa 1996; Christ and Kuster 2005; Gandhi and Chen 1995; Gandhi, Lazzi, and Furse
1996; Lazzi and Gandhi 1997; Lu et al. 1996; Martens et al. 1995; Martinez-Burdalo et al.
2005; Okoniewski and Stuchly 1996; Watanabe et al. 1996). This is due to the fact that
enhanced computer power has become available at lower cost and intensive research
work in the fields of source modeling, absorbing boundary conditions, and error checking has facilitated the simulation with more confidence in the obtained results. Several
approaches for accurate absorbing boundary conditions at the boundary of the computational domain have been proposed (Berenger 1994; Bernsten and Hornsleth 1994; Mur
1981), offering excellent approximation of open space with a minimum of “white space.”
Negligible differences in the calculated SAR distributions or the radiation patterns are
obtained regardless of the boundary conditions that are used. Furthermore, the use of
a nonuniform grid has been proposed (Okoniewski and Stuchly 1996) to reduce the
memory requirements, while parallelized versions of FDTD codes can be used to reduce
the execution time. Other notable improvements are in the area of uncertainty assessments and graphical user interfaces (Kuster 2002).
5.2.3.2.3 Finite Integration Technique
The Finite Integration Technique (FIT), introduced by Weiland (1977), is based on the
discretization of the integral form of Maxwell’s equations and transforms them into
a set of matrix equations, the Maxwell grid equations (MGEs), on an orthogonal dual
grid pair. It is a method conceptually slightly different from the FDTD technique, which
however leads to the same numerical scheme. The FIT can be thought of as equivalent to
the FDTD for time-domain problems (Weiland 1990).
The use of FIT for mobile communication dosimetric calculations is reported in
numerous studies (Hombach et al. 1996; Meier et al. 1997; Schoenborn, Burkhardt, and
Kuster 1998).
5.2.3.2.4 Finite Element Method
The Finite Element Method (FEM) was introduced by Silvester and Ferrari (1996). Space
is discretized in a finite element mesh with linear or polynomial expansion functions
within each element. The unknowns are associated with the field values in the nodes.
A variational method or a method of weighted residuals is used to obtain a system of
equations with a sparse matrix. In wave propagation problems, the FEM is often used
in the frequency domain. For a long time, its applicability for solving the Helmholtz
equation was quite limited because of problems with spurious modes. Open domains
were another limitation, as no efficient radiation boundary conditions were available.
Therefore, FEM was often paired with a boundary element method in a hybrid scheme.
Although penalty methods can be used to avoid the corruption of results with spurious solutions, the advent of edge-element techniques that prevent the possibility of
spurious modes altogether seem more promising. In the edge-element technique the
unknowns are associated with the field tangential to the edges of the basic element.