A fast multipole methodology (FMM) is developed as a numerical approach to reduce the computational cost andmemory requirements in solving large-scale problems. It is applied to the boundary element method (BEM) for t...A fast multipole methodology (FMM) is developed as a numerical approach to reduce the computational cost andmemory requirements in solving large-scale problems. It is applied to the boundary element method (BEM) for three-dimensional potential flow problems. The algorithm based on mixed multipole expansion and numerical integration isimplemented in combination with an iterative solver. Numerical examinations, on Dirichlet and Neumann problems,are carried out to demonstrate the capability and accuracy of the present method. It has been shown that the methodhas evident advantages in saving memory and computing time when used to solve huge-scale problems which may beprohibitive for the traditional BEM implementation.展开更多
In the low-frequency fast multipole algorithm(LF-FMA)[19,20],scalar addition theorem has been used to factorize the scalar Green’s function.Instead of this traditional factorization of the scalar Green’s function by...In the low-frequency fast multipole algorithm(LF-FMA)[19,20],scalar addition theorem has been used to factorize the scalar Green’s function.Instead of this traditional factorization of the scalar Green’s function by using scalar addition theorem,we adopt the vector addition theorem for the factorization of the dyadic Green’s function to realize memory savings.We are to validate this factorization and use it to develop a low-frequency vector fast multipole algorithm(LF-VFMA)for lowfrequency problems.In the calculation of non-near neighbor interactions,the storage of translators in the method is larger than that in the LF-FMA with scalar addition theorem.Fortunately it is independent of the number of unknowns.Meanwhile,the storage of radiation and receiving patterns is linearly dependent on the number of unknowns.Therefore it is worthwhile for large scale problems to reduce the storage of this part.In this method,the storage of radiation and receiving patterns can be reduced by 25 percent compared with the LF-FMA.展开更多
基金This work was sponsored by the National Natural Science Foundation of China for Distinguished Young Scholars under contract No,50025924the Research Foundation for the Doctoral Program of Higher Education of China under contract No.20030141006.
文摘A fast multipole methodology (FMM) is developed as a numerical approach to reduce the computational cost andmemory requirements in solving large-scale problems. It is applied to the boundary element method (BEM) for three-dimensional potential flow problems. The algorithm based on mixed multipole expansion and numerical integration isimplemented in combination with an iterative solver. Numerical examinations, on Dirichlet and Neumann problems,are carried out to demonstrate the capability and accuracy of the present method. It has been shown that the methodhas evident advantages in saving memory and computing time when used to solve huge-scale problems which may beprohibitive for the traditional BEM implementation.
文摘In the low-frequency fast multipole algorithm(LF-FMA)[19,20],scalar addition theorem has been used to factorize the scalar Green’s function.Instead of this traditional factorization of the scalar Green’s function by using scalar addition theorem,we adopt the vector addition theorem for the factorization of the dyadic Green’s function to realize memory savings.We are to validate this factorization and use it to develop a low-frequency vector fast multipole algorithm(LF-VFMA)for lowfrequency problems.In the calculation of non-near neighbor interactions,the storage of translators in the method is larger than that in the LF-FMA with scalar addition theorem.Fortunately it is independent of the number of unknowns.Meanwhile,the storage of radiation and receiving patterns is linearly dependent on the number of unknowns.Therefore it is worthwhile for large scale problems to reduce the storage of this part.In this method,the storage of radiation and receiving patterns can be reduced by 25 percent compared with the LF-FMA.
