Class xlifepp::KernelExpansion#

class KernelExpansion#

Collaboration diagram for xlifepp::KernelExpansion:

digraph { graph [bgcolor="#00000000"] node [shape=rectangle style=filled fillcolor="#FFFFFF" font=Helvetica padding=2] edge [color="#1414CE"] "6" [label="std::map< string_t, number_t >" tooltip="std::map< string_t, number_t >"] "10" [label="std::map< string_t, std::pair< ValueType, StrucType > >" tooltip="std::map< string_t, std::pair< ValueType, StrucType > >"] "7" [label="std::map< K, T >" tooltip="std::map< K, T >"] "5" [label="std::vector< T >" tooltip="std::vector< T >"] "9" [label="std::vector< real_t >" tooltip="std::vector< real_t >"] "4" [label="std::vector< xlifepp::Parameter * >" tooltip="std::vector< xlifepp::Parameter * >"] "2" [label="xlifepp::Function" tooltip="xlifepp::Function"] "1" [label="xlifepp::KernelExpansion" tooltip="xlifepp::KernelExpansion" fillcolor="#BFBFBF"] "3" [label="xlifepp::Parameters" tooltip="xlifepp::Parameters"] "8" [label="xlifepp::Point" tooltip="xlifepp::Point"] "6" -> "7" [dir=forward tooltip="template-instance"] "10" -> "7" [dir=forward tooltip="template-instance"] "9" -> "5" [dir=forward tooltip="template-instance"] "4" -> "5" [dir=forward tooltip="template-instance"] "2" -> "3" [dir=forward tooltip="usage"] "2" -> "2" [dir=forward tooltip="usage"] "2" -> "8" [dir=forward tooltip="usage"] "2" -> "10" [dir=forward tooltip="usage"] "1" -> "2" [dir=forward tooltip="usage"] "3" -> "4" [dir=forward tooltip="usage"] "3" -> "6" [dir=forward tooltip="usage"] "8" -> "9" [dir=forward tooltip="public-inheritance"] }

Kernel expansion according to singularity exponents:

  • G(x,y)=iFi(x,y)/|xy|α0i

  • gradxG(x,y)=iGxFi(x,y).(xy)/|xy|αxi

  • gradyG(x,y)=iGyFi(x,y).(xy)/|xy|αyi

  • gradxyG(x,y)=iGxyFi(x,y).(xy)(xy)T/|xy|αxyi+iGxyFdiagi(x,y)/|xy|αxydiagiIdentity

with the convention 1/|xy|αxi=Log(|xy|) when αxi=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