A study on spline quasi-interpolation based quadrature rules for the isogeometric Galerkin BEM
Falini, Antonella ; Kanduč, Tadej, 1985-
Dve nedavno razviti kvadraturni shemi v [Calabrò, F., Falini, A., Sampoli, M. L., Sestini, A.: Efficient quadrature rules based on spline quasi-interpolation for application to IgA-BEMs. J. Comput. ...Appl. Math. 338, 153-167 (2018)] uporabimo za izračun regularnih in singularnih integralov, v kontekstu robnih integralskih enačb, ki se pojavijo v formulaciji Galerkinove metode robnih elementov. V prvi shemi regularni del integranda, ki je sestavljen iz produkta med B-zlepkom in pomožno funkcijo, aproksimiramo s primernim kvazi-interpolacijskim zlepkom. V drugi shemi pomožno funkcijo aproksimiramo preko kvazi-interpolacijskega operatorja in nato produkt med dvema dobljenima zlepkoma predstavimo kot linearno kombinacijo novih B-zlepkov. Shemi testiramo in primerjamo z drugimi metodami, ki se v literaturi uporabljajo za izračun različnih integralov iz Galerkinove formulacije. Numerični testi za drugo shemo razkrijejo, da pri h-zgoščanju mreže in zmernih predpostavkah dobimo optimalni red konvergence, četudi uporabimo majhno število kvadraturnih vozlov. Kvadraturni shemi uporabimo tudi v numeričnih zgledih pri reševanju 2D Laplaceove enačbe z Dirichletovimi robnimi pogoji.
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