In this paper three classes of high order symplectic partitioned Runge-Kutta (PRK) methods, which are based on the W-transformation of Hairer and Wanner, and a particular class of diagonally implicit symplectic PRK me...In this paper three classes of high order symplectic partitioned Runge-Kutta (PRK) methods, which are based on the W-transformation of Hairer and Wanner, and a particular class of diagonally implicit symplectic PRK methods of arbitrarily high order, which are based on the composite algorithm, are constructed. In particular, the symplectically composite PRK methods of arbitrarily high order become explicit when applied to separable Hamiltonian systems.展开更多
At the beginning of 21st century, with the rapid and steady development of China economy, a lot of large scale hydropower projects with large dams from 200 m to 300 m high are being or to be built. China dam construct...At the beginning of 21st century, with the rapid and steady development of China economy, a lot of large scale hydropower projects with large dams from 200 m to 300 m high are being or to be built. China dam constructions are reaching the level of 300 m high arch dam, 250 high CFRD (concrete face rockfill dam) and 200 m high RCC (roller compacted concrete) gravity dam. Due to the safety and the economy, the type selection for high dams has become the key issue during the argumentation for the hydropower projects, and further efforts are still needed in this aspect for high dams. After reviewing the high dam constructions in China and abroad, authors proposed some advices for the selection of dam types, and hope that it can provide some helpful information for the researches and the design of high dams.展开更多
文摘In this paper three classes of high order symplectic partitioned Runge-Kutta (PRK) methods, which are based on the W-transformation of Hairer and Wanner, and a particular class of diagonally implicit symplectic PRK methods of arbitrarily high order, which are based on the composite algorithm, are constructed. In particular, the symplectically composite PRK methods of arbitrarily high order become explicit when applied to separable Hamiltonian systems.
文摘At the beginning of 21st century, with the rapid and steady development of China economy, a lot of large scale hydropower projects with large dams from 200 m to 300 m high are being or to be built. China dam constructions are reaching the level of 300 m high arch dam, 250 high CFRD (concrete face rockfill dam) and 200 m high RCC (roller compacted concrete) gravity dam. Due to the safety and the economy, the type selection for high dams has become the key issue during the argumentation for the hydropower projects, and further efforts are still needed in this aspect for high dams. After reviewing the high dam constructions in China and abroad, authors proposed some advices for the selection of dam types, and hope that it can provide some helpful information for the researches and the design of high dams.
