In this paper,we use trigonometric polynomial reconstruction,instead of algebraic polynomial reconstruction,as building blocks for the weighted essentially non-oscillatory(WENO)finite difference schemes to solve hyper...In this paper,we use trigonometric polynomial reconstruction,instead of algebraic polynomial reconstruction,as building blocks for the weighted essentially non-oscillatory(WENO)finite difference schemes to solve hyperbolic conservation laws and highly oscillatory problems.The goal is to obtain robust and high order accurate solutions in smooth regions,and sharp and non-oscillatory shock transitions.Numerical results are provided to illustrate the behavior of the proposed schemes.展开更多
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse p...We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question.Numerical examples illustrate the effectiveness of the method.展开更多
This paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave numbe...This paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave number.Rigorous matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic sense.Simulated examples are given to illustrate the conclusion.展开更多
基金supported by NSFC grants 10671091,10811120283the European project ADIGMA on the development of innovative solution algorithms for aerodynamic simulationsAdditional support was provided by USA NSF DMS-0820348 while J.Qiu was in residence at Department of Mathematical Sciences,Rensselaer Polytechnic Institute.
文摘In this paper,we use trigonometric polynomial reconstruction,instead of algebraic polynomial reconstruction,as building blocks for the weighted essentially non-oscillatory(WENO)finite difference schemes to solve hyperbolic conservation laws and highly oscillatory problems.The goal is to obtain robust and high order accurate solutions in smooth regions,and sharp and non-oscillatory shock transitions.Numerical results are provided to illustrate the behavior of the proposed schemes.
基金supported by National Natural Science Foundation of China(Grant Nos.11201370 and 11371287)Projects of International Cooperation and Exchanges NSFC-RS(Grant No.1141101162)+1 种基金the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2014JQ2-1006)the Fundamental Research Funds for the Central Universities
文摘We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question.Numerical examples illustrate the effectiveness of the method.
文摘This paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave number.Rigorous matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic sense.Simulated examples are given to illustrate the conclusion.
