Class xlifepp::KernelExpansion

class KernelExpansion

Collaboration diagram for xlifepp::KernelExpansion:

Kernel expansion according to singularity exponents:

• \(\displaystyle G(x,y) = \sum_i F_i(x,y) / |x-y|^{{\alpha_0}_i}\)

• \(\displaystyle grad_x G(x,y) = \sum_i GxF_i(x,y).(x-y) / |x-y|^{{\alpha_x}_i}\)

• \(\displaystyle grad_y G(x,y) = \sum_i GyF_i(x,y).(x-y) / |x-y|^{{\alpha_y}_i}\)

• \(\displaystyle grad_{xy} G(x,y) = \sum_i GxyF_i(x,y).(x-y)(x-y)^T / |x-y|^{{\alpha_{xy}}_i} + \sum_i {GxyF_{diag}}_i(x,y) / |x-y|^{{{\alpha_{xy}}_{diag}}_i} *Identity\)

with the convention \(1/|x-y|^{{\alpha_x}_i} = Log(|x-y|)\) when \({\alpha_x}_i = -1\)

Public Members

std::vector<int_t> alpha

singularity exponents

Function F_i

coefficients of F expansion

Function gradxF_i

coefficients of gradx F expansion

Function gradxyF_i

coefficients of gradxy F expansion

Function gradyF_i

coefficients of grady F expansion

number_t nbterms

number of terms in expansion