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The BEM divides only the boundary of the region under consideration. Thus, it reduces the dimensionality of the problem to be solved and the number of equations in the system. This advantage becomes more significant for 3-D problems, which are often encountered in geophysics. However, the BEM has drawbacks. For example, if the region has a complex distribution of physical properties, it is difficult to combine the boundary integral equations corresponding to each homogeneous medium and solve the resulting system.

In contrast, when the FEM deals with infinite region or 3-D problems, the number of nodes needed increases greatly; thus, a larger amount of computer memory is required. However, the FEM automatically satisfies the internal boundary condition, so it does not treat each body individually. Therefore, the FEM has a decided advantage in solving geophysical problems with complex distributions of physical properties

The combined use of the BEM and the FEM can be applied to better simulate a 3-D infinite region as well as complex distributions of physical properties. This chapter introduces the basic concept of the combined use. Here we use the problem of the 3-D electric field produced by a point source.

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