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
This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived vi...This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.展开更多
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.
文摘This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.
