Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d）...Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d） for all 1 ≤ p, q ≤ ∞. When p ≥ q, we show this bound is optimal by deriving the matching upper bound. In this case, the quantum al- gorithms are not significantly better than the classical deterministic or randomized ones. We conjecture that the bound is also optimal for the case p 〈 q. This conjecture was confirmed in the situation s = 0.展开更多
The paper is concerned with solving periodic boundary problem of semilinear systems,which will be differentiably embedded into an one-parameter family of operators.The solution of the systems is then found by continui...The paper is concerned with solving periodic boundary problem of semilinear systems,which will be differentiably embedded into an one-parameter family of operators.The solution of the systems is then found by continuing the solution curve of operator homotopy.When the Newton-Kantorovich's procedure is applied to the corresponding operator equations,an efficient algorithm is derived.Finally,the theoretical results are in excellent agreement with the numerical examples.展开更多
The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive comp...The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive computational costs.To overcome this limitation,a message passing interface(MPI)parallel DEM-IMB-LBM framework is proposed aimed at enhancing computation efficiency.This framework utilises a static domain decomposition scheme,with the entire computation domain being decomposed into multiple subdomains according to predefined processors.A detailed parallel strategy is employed for both contact detection and hydrodynamic force calculation.In particular,a particle ID re-numbering scheme is proposed to handle particle transitions across sub-domain interfaces.Two benchmarks are conducted to validate the accuracy and overall performance of the proposed framework.Subsequently,the framework is applied to simulate scenarios involving multi-particle sedimentation and submarine landslides.The numerical examples effectively demonstrate the robustness and applicability of the MPI parallel DEM-IMB-LBM framework.展开更多
基金Supported by the Natural Science Foundation of China (10971251)
文摘Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d） for all 1 ≤ p, q ≤ ∞. When p ≥ q, we show this bound is optimal by deriving the matching upper bound. In this case, the quantum al- gorithms are not significantly better than the classical deterministic or randomized ones. We conjecture that the bound is also optimal for the case p 〈 q. This conjecture was confirmed in the situation s = 0.
文摘The paper is concerned with solving periodic boundary problem of semilinear systems,which will be differentiably embedded into an one-parameter family of operators.The solution of the systems is then found by continuing the solution curve of operator homotopy.When the Newton-Kantorovich's procedure is applied to the corresponding operator equations,an efficient algorithm is derived.Finally,the theoretical results are in excellent agreement with the numerical examples.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.12072217 and 42077254)the Natural Science Foundation of Hunan Province,China(Grant No.2022JJ30567).
文摘The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive computational costs.To overcome this limitation,a message passing interface(MPI)parallel DEM-IMB-LBM framework is proposed aimed at enhancing computation efficiency.This framework utilises a static domain decomposition scheme,with the entire computation domain being decomposed into multiple subdomains according to predefined processors.A detailed parallel strategy is employed for both contact detection and hydrodynamic force calculation.In particular,a particle ID re-numbering scheme is proposed to handle particle transitions across sub-domain interfaces.Two benchmarks are conducted to validate the accuracy and overall performance of the proposed framework.Subsequently,the framework is applied to simulate scenarios involving multi-particle sedimentation and submarine landslides.The numerical examples effectively demonstrate the robustness and applicability of the MPI parallel DEM-IMB-LBM framework.
