设F是李超代数A_(i)(i∈I)和自由李超代数G的自由和,N是F的理想满足N∩A_(i)=1,(i∈I).设U(F)是F的泛包络代数,N_(U)是N生成的U(F)的理想.研究了李超代数F的一个元素v,满足D_(k)(v)≡0 mod N_(U),(k∈I∪J),其中D_(k):U(F)→U(F)(k∈I...设F是李超代数A_(i)(i∈I)和自由李超代数G的自由和,N是F的理想满足N∩A_(i)=1,(i∈I).设U(F)是F的泛包络代数,N_(U)是N生成的U(F)的理想.研究了李超代数F的一个元素v,满足D_(k)(v)≡0 mod N_(U),(k∈I∪J),其中D_(k):U(F)→U(F)(k∈I∪J)是U(F)的Fox导子,得到了李超代数的Fox导子的一些性质.展开更多
An improved Reduced-Order Model(ROM)is proposed based on a flow-solution preprocessing operation and a fast sampling strategy to efficiently and accurately predict ionized hypersonic flows.This ROM is generated in low...An improved Reduced-Order Model(ROM)is proposed based on a flow-solution preprocessing operation and a fast sampling strategy to efficiently and accurately predict ionized hypersonic flows.This ROM is generated in low-dimensional space by performing the Proper Orthogonal Decomposition(POD)on snapshots and is coupled with the Radial Basis Function(RBF)to achieve fast prediction speed.However,due to the disparate scales in the ionized flow field,the conventional ROM usually generates spurious negative errors.Here,this issue is addressed by performing flow-solution preprocessing in logarithmic space to improve the conventional ROM.Then,extra orthogonal polynomials are introduced in the RBF interpolation to achieve additional improvement of the prediction accuracy.In addition,to construct high-efficiency snapshots,a trajectory-constrained adaptive sampling strategy based on convex hull optimization is developed.To evaluate the performance of the proposed fast prediction method,two hypersonic vehicles with classic configurations,i.e.a wave-rider and a reentry capsule,are used to validate the proposed method.Both two cases show that the proposed fast prediction method has high accuracy near the vehicle surface and the free-stream region where the flow field is smooth.Compared with the conventional ROM prediction,the prediction results are significantly improved by the proposed method around the discontinuities,e.g.the shock wave and the ionized layer.As a result,the proposed fast prediction method reduces the error of the conventional ROM by at least 45%,with a speedup of approximately 2.0×105compared to the Computational Fluid Dynamic(CFD)simulations.These test cases demonstrate that the method developed here is efficient and accurate for predicting ionized hypersonic flows.展开更多
In this paper we extend the theory of Grbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module eq...In this paper we extend the theory of Grbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural filtration. We present and verify algorithms for construct-ing these Grbner bases counterparts. To this aim we introduce the concept of "generalized term order" on Nm ×Zn and on difference-differential modules. Using Grbner bases on difference-differential mod-ules we present a direct and algorithmic approach to computing the difference-differential dimension polynomials of a difference-differential module and of a system of linear partial difference-differential equations.展开更多
In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the targe...In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.展开更多
文摘设F是李超代数A_(i)(i∈I)和自由李超代数G的自由和,N是F的理想满足N∩A_(i)=1,(i∈I).设U(F)是F的泛包络代数,N_(U)是N生成的U(F)的理想.研究了李超代数F的一个元素v,满足D_(k)(v)≡0 mod N_(U),(k∈I∪J),其中D_(k):U(F)→U(F)(k∈I∪J)是U(F)的Fox导子,得到了李超代数的Fox导子的一些性质.
基金supported by the National Natural Science Foundation of China(Nos.11902271 and 91952203)the Fundamental Research Funds for the Central Universities of China(No.G2019KY05102)111 project on“Aircraft Complex Flows and the Control”of China(No.B17037)。
文摘An improved Reduced-Order Model(ROM)is proposed based on a flow-solution preprocessing operation and a fast sampling strategy to efficiently and accurately predict ionized hypersonic flows.This ROM is generated in low-dimensional space by performing the Proper Orthogonal Decomposition(POD)on snapshots and is coupled with the Radial Basis Function(RBF)to achieve fast prediction speed.However,due to the disparate scales in the ionized flow field,the conventional ROM usually generates spurious negative errors.Here,this issue is addressed by performing flow-solution preprocessing in logarithmic space to improve the conventional ROM.Then,extra orthogonal polynomials are introduced in the RBF interpolation to achieve additional improvement of the prediction accuracy.In addition,to construct high-efficiency snapshots,a trajectory-constrained adaptive sampling strategy based on convex hull optimization is developed.To evaluate the performance of the proposed fast prediction method,two hypersonic vehicles with classic configurations,i.e.a wave-rider and a reentry capsule,are used to validate the proposed method.Both two cases show that the proposed fast prediction method has high accuracy near the vehicle surface and the free-stream region where the flow field is smooth.Compared with the conventional ROM prediction,the prediction results are significantly improved by the proposed method around the discontinuities,e.g.the shock wave and the ionized layer.As a result,the proposed fast prediction method reduces the error of the conventional ROM by at least 45%,with a speedup of approximately 2.0×105compared to the Computational Fluid Dynamic(CFD)simulations.These test cases demonstrate that the method developed here is efficient and accurate for predicting ionized hypersonic flows.
基金supported by the National Natural Science Foundation of China (Grant No. 60473019)the KLMM (Grant No. 0705)
文摘In this paper we extend the theory of Grbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural filtration. We present and verify algorithms for construct-ing these Grbner bases counterparts. To this aim we introduce the concept of "generalized term order" on Nm ×Zn and on difference-differential modules. Using Grbner bases on difference-differential mod-ules we present a direct and algorithmic approach to computing the difference-differential dimension polynomials of a difference-differential module and of a system of linear partial difference-differential equations.
基金AFOSR and NSF for their support of this work under grants FA9550-19-1-0281 and FA9550-17-1-0394 and NSF grant DMS 191218。
文摘In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.
