A geometric intrinsic pre-processingalgorithm(GPA for short)for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023).Different from traditional preconditi...
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A geometric intrinsic pre-processingalgorithm(GPA for short)for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023).Different from traditional preconditioning,the authors apply the intrinsic geometric invariance,the Grid matrix G and the discrete PDE mass matrix B,stiff matrix A satisfies commutative operator BG=GB and AG=GA,where G satisfies G^(m)=I,m<pretreatment in real or complex *** this paper,the authors expand their research to 2-D and 3-D mathematical physical equations over more wide polyhedron grids such as triangle,square,tetrahedron,cube,and so *** give the general form of pre-processing matrix,theory and numerical test of *** conclusion that“the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron”is obtained through research,and it is further found that“commutative of grid mesh matrix and mass matrix is an important basis for the feasibility and reliability of GPA algorithm”.
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