Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line sourc...Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.展开更多
We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates ...We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.展开更多
The radiated fields from Gaussian Distributed Aperture (GDA) can be approaximately analyzed bythe Complex Ray Method (CRM). In this article, the radiated fields derived in terms of plana wave spectrumintegral are us...The radiated fields from Gaussian Distributed Aperture (GDA) can be approaximately analyzed bythe Complex Ray Method (CRM). In this article, the radiated fields derived in terms of plana wave spectrumintegral are used as standard, and the error source of the replacement by complex ray fields is found. Withdiscussions on the error characteristics of this CIUN approximation, conclusions are drawn which are expected to be helpful in applications of CRM.展开更多
基金supported by National Natural Science Foundation of China (50978183)
文摘Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.
基金The work is supported by Royal Society International Exchanges(grant IE141214)the Projects of International Cooperation and Exchanges NSFC-RS(Grant No.11511130052)+1 种基金the Key Science and Technology Program of Shaanxi Province of China(Grant No.2016GY-080)the Fundamental Research Funds for the Central Universities.
文摘We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.
文摘The radiated fields from Gaussian Distributed Aperture (GDA) can be approaximately analyzed bythe Complex Ray Method (CRM). In this article, the radiated fields derived in terms of plana wave spectrumintegral are used as standard, and the error source of the replacement by complex ray fields is found. Withdiscussions on the error characteristics of this CIUN approximation, conclusions are drawn which are expected to be helpful in applications of CRM.
