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Uporaba DRM za inverzne probleme in reševanje s Tikhonovim algoritmom
Ogrizek, Dean ; Trlep, Mladen
Članek predstavlja uporabo metode Dual Reciprocity (DRM) za določitev rešitve inverznih problemov, opisanih s Poissonovo diferencialno enačbo. DRM uvaja tehniko, kjer se integral po notranjosti ...problema prevede na integral po robu,pri tem pa upošteva tudi nehomogenost materiala. Zato se DRM navaja kot idealna metoda za reševanje inverznih problemov. Pri uporabi reševanju inverznih problemov dobimo linearni sistem enačb, ki je na splošno predoločen in slabo pogojen. Za reševanje takšnega sistema smo uporabili Tikhonovo numerično shemo (algoritem) in ga primerjali z analitično dobljenimi rezultati. Problem reševanja slabo pogojenih sistemov s Tikhonovim algoritmom je določitev regularizacijskega parametra A.. Mi smo določili regularizacijski parameter po postopku L-krivulje. Na koncu smo metodo testirali na različnih primerih in jih primerjali z analitično rešitvijo.
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