An Unstructured Algebraic Multigrid Method On Lattice Materials

In this pWer,we propose a new lteratlve correcting type ofunstructured alge－ braic皿ltipid(AMG)mthod which has。re extensl陀 annlicatlon nrosnects and better stability on the background of＊theound existent AMG method for eL liptic PDE．Applying the new AMG method to solve the Inverse ofsu卜bio ＆ matrix weget the corresponding bio出 Gauss－Seldel iteration based on V－Cycle mthodmd preconditioned coqugate gradient(PCG)mthod for the discrete mdels on Lattice materials．Using the operator mtrlx)矾tending tecncnolo欧 wegmerali沈 the AMG metbd to the case ofequatlon groups and欧t a tWe 。f AMG method called AMV nd APCG method aboutthe discrete modes of lattice materials．A great un灿er ofexperlments show th时 when the imper－ tant paramter a E(0．l,l］the iteration number ofcorresponding AMV and APCG method is on the whole Ind印endent of＊the scale ofquestlons and the parameter a for thetatlce materlajs discrete modets with q＝l,3 azld 4,that when a Is very small the iteration un咖er ofAPCG method Is independent of＊the scale ofquestlons anddauges little s a becomes smaller In the case ofq二1．3．TherefOrethehlghefficlenCyandrobustness oftheALIG algorithm havebeen testd．Its superlorltyls shown In thelargesscale scientific compu－ tatlons about lattice materials二Moreoverby m冰ingfurther analysis forthe approximately continuous models associated wlththe discrete models on fat－ tlce materials with q＝lwe haveproved the result that the condition number of PCG method,whose preconditioner B Is chosen as the Inverse of the block dlagonalmatrlx,Is Independent oftheparameter a．Accordingl。,we verify the correctness of＊thetness corresponding numerical results In theory．...