Application of the method of fundamental solutions and radial basis functions for inverse heat source problem in case of steady-state

Inverse Heat Conduction Problems

“…Using FEM to solve the inverse problem gives acceptable solution only for the first row of elements. Even for exact values of the given temperature the results are encumbered with et al, 2008), the finite difference method (Luo & Shih, 2005;Soti et al, 2007), the theory of potentials method (Grysa, 1989), the radial basis functions method (Kołodziej et al, 2010), the artificial bee colony method (Hetmaniok et al, 2010), the Alifanov iterative regularization (Alifanov, 1994), the optimal dynamic filtration, (Guzik & Styrylska, 2002), the control volume approach (Taler & Zima, 1999), the meshless methods ( (Sladek et al, 2006) and many other. …”

A Numerical Solution of One Class of Volterra Integral Equations of the First Kind in Terms of the Machine Arithmetic Features

“…Plot Line 1 corresponds to function |ε h i |, plot Line 2 corresponds to function |ε h i | and plot Line 3 corresponds to function |ε h i min | = min{|ε h i | , |ε h i |}. Figure 2 was obtained at functions y h i accurately specified in (9), (10). Here, the maximum values of errors made up In this case, the maximum values of errors made up…”

Heating source localization in a reduced time

“…Configurations studied in both previous references are related to boundary heat flux identification considering a 1D mathematical model. In the works of Kolodziej et al (2010) or Mierzwiczak and Kolodziej (2010;, the method of fundamental solutions was successfully implemented for an IHCP. This meshless method is relatively new and is an attractive alternative to the finite or boundary element methods.…”