以正规化无网格法求解含多孔洞拉普拉斯方程式.ppt

Regularized meshless method for solving Laplace equation with multiple holesSpeaker:Kuo-Lun WuCoworker:Jeng-Hong Kao、Kue-Hong Chen and Jeng-Tzong Chen以正規化無網格法求解含多孔洞拉普拉斯方程式以正規化無網格法求解含多孔洞拉普拉斯方程式工學院工學院 2005/04/01OutlinesnMotivationnStatement of problemnMethod of fundamental solutionsnRegularized meshless methodnFormulation for multiple holesnNumerical examplesnConclusions2OutlinesnMotivationnStatement of problemnMethod of fundamental solutionsnRegularized meshless methodnFormulation for multiple holesnNumerical examplesnConclusions3MotivationNumerical Methods Mesh MethodsFinite Difference MethodMeshless Methods Finite Element MethodBoundary Element Method(MFS)(RMM)4OutlinesnMotivationnStatement of problemnMethod of fundamental solutionsnRegularized meshless methodnFormulation for multiple holesnNumerical examplesnConclusions5Statement of problemnLaplace equation with multiple holes:potential flow around cylinderselectrostatic field of wirestorsion bar with holes MZ6OutlinesnMotivationnStatement of problemnMethod of fundamental solutionsnRegularized meshless methodnFormulation for multiple holesnNumerical examplesnConclusions7Method of fundamental solutions(MFS)nMethod of fundamental solutions(MFS):Source point Collocation point Physical boundary-Off-set boundaryd=off-set distancedDouble-layerpotential approach Single-layerPotential approach Dirichlet problemNeumann problemDirichlet problemNeumann problemDistributed type8nThe artificial boundary(off-set boundary)distance is debatable.nThe diagonal coefficients of influence matrices are singular when the source point coincides the collocation point.9OutlinesnMotivationnStatement of problemnMethod of fundamental solutionsnRegularized meshless methodnFormulation for multiple holesnNumerical examplesnConclusions10nRegularized meshless method(RMM)Source point Collocation point Physical boundaryRegularized meshless method(RMM)Double-layerpotential approach Dirichlet problemNeumann problemwhereI=Inward normal vectorO=Outward normal vector11In a similar way,1213OutlinesnMotivationnStatement of problemnMethod of fundamental solutionsnRegularized meshless methodnFormulation with multiple holesnNumerical examplesnConclusions14Formulation with multiple holes Source point Collocation point Physical boundaryinner holes=m-1outer hole=m th15inner holes=m-1outer hole=m th Source point Collocation point Physical boundaryP=116inner holes=m-1outer hole=m th Source point Collocation point Physical boundary17inner holes=m-1outer hole=m th Source point Collocation point Physical boundary18inner holes=m-1outer hole=m th Source point Collocation point Physical boundaryP=m19inner holes=m-1outer hole=m th Source point Collocation point Physical boundaryP=m20nThe linear algebraic systemsssxx21OutlinesnMotivationnStatement of problemnMethod of fundamental solutionsnRegularized meshless methodnFormulation for multiple holesnNumerical examplesnConclusions22Numerical examplesyxyxCase 1 Dirichlet B.C.Case 2 Mixed-type B.C.23Contour of potential(case 1)Exact solutionRMM(360 points)BEM(360 elements)24Contour of potential(case 2)Exact solutionRMM(400 points)BEM(800 elements)25Error convergence(case 2)26OutlinesnMotivationnStatement of problemnMethod of fundamental solutionsnRegularized meshless methodnFormulation for multiple holesnNumerical examplesnConclusions27ConclusionsnOnly boundary nodes on the real boundary are required.nSingularity of kernels is desingularized.nThe present results for multiply-hole cases were well compared with exact solutions and BEM.28The endThanks for your attention.Your comment is much appreciated.29