displayed for one source only in sub-section 4.2.1. The outcomes of the results from the sub-section 4.2.1 are used in the Sections 4.2.2 where the method is used in order to evaluate the wave propagation in a 2D example problem. The motivation behind computations is similar to what has been done for the RBIE method in Section 4.1. For example, the effect of local subdomain radius, , will be investigated for the LBIE, as it is done in Figure 4.1 and Table 4.1 for RBIE. Secondly, the behaviour of the error with respect to the variable is investigated. kh The variable is commonly referred to in this context; which is exactly the same kh measure as used in Section 2. It refers to how many source nodes per one λ/h wavelength are used. For example, let us assume a spacing of and a h=0.1 wavenumber This would yield a wavelength which means equals k=1. λ=2π, λ/h approximately 63. Thus, approximately 63 nodes will be used for one wavelength. Finally, a 2D numerical example will be presented in Section 4.2.2 which will allow one to investigate the overall L2 norm error. It will be observed that L2 norm error reduces significantly when the dispersion error at the source nodes is minimized. Dispersion error at a source node Dispersion error depends mainly on the choice of the following parameters: (i) the radial basis function (ii) the polynomial basis vector , (iii) the radius, , of the f(R), local subdomain and (iv) the radius of influence, in the RBF interpolation. rinfl, Throughout this section, the second order polyharmonic spline of the form is used.
displayed for one source only in sub-section 4.2.1. The outcomes of the results from the sub-section 4.2.1 are used in the Sections 4.2.2 where the method is used in order to evaluate the wave propagation in a 2D example problem. The motivation behind computations is similar to what has been done for the RBIE method in Section 4.1. For example, the effect of local subdomain radius, , will be investigated for the LBIE, as it is done in Figure 4.1 and Table 4.1 for RBIE. Secondly, the behaviour of the error with respect to the variable kh is investigated. The variable kh is commonly referred to in this context; which is exactly the same measure as λ/h used in Section 2. It refers to how many source nodes per one wavelength are used. For example, let us assume a spacing of h=0.1 and a wavenumber k=1. This would yield a wavelength λ=2π, which means λ/h equals approximately 63. Thus, approximately 63 nodes will be used for one wavelength. Finally, a 2D numerical example will be presented in Section 4.2.2 which will allow one to investigate the overall L2 norm error. It will be observed that L2 norm error reduces significantly when the dispersion error at the source nodes is minimized. Dispersion error at a source node Dispersion error depends mainly on the choice of the following parameters: (i) the radial basis function f(R), (ii) the polynomial basis vector , (iii) the radius, , of the local subdomain and (iv) the radius of influence, rinfl, in the RBF interpolation. Throughout this section, the second order polyharmonic spline of the form is used.