In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated wi...In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium.Numerical examples are presented to examine the influence from material boundaries on dislocations.展开更多
The fault branching phenomenon,which may heavily influence the patterns of rupture propagation in fault systems,is one of the geometric complexities of fault systems that is widely observed in nature.In this study,we ...The fault branching phenomenon,which may heavily influence the patterns of rupture propagation in fault systems,is one of the geometric complexities of fault systems that is widely observed in nature.In this study,we investigate the effect of the branching angle on the rupture inclination and the interaction between branch planes in two-fork branching fault systems by numerical simulation and theoretical analysis based on Mohr’s circle.A friction law dependent on normal stress is used,and special attention is paid to studying how ruptures on the upper and lower branch planes affect the stress and rupture on each other separately.The results show that the two branch planes affect each other in different patterns and that the intensity of the effect changes with the branching angle.The rupture of the lower branch plane has a negative effect on the rupture of the upper branch plane in the case of a small branching angle but has almost no negative effect in the case of a large branching angle.The rupture of the upper branch plane,however,suppresses the rupture of the lower branch plane regardless of whether the branching angle is large or small.展开更多
We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of free...We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy.Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem,we propose a novel Galerkin boundary element method,with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon.Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.展开更多
Hydroelasticity of marine structures with and without forward speed is studied directly using time dependent Boundary Integral Equation Method with Neumann-Kelvin linearisation where the potential is considered as the...Hydroelasticity of marine structures with and without forward speed is studied directly using time dependent Boundary Integral Equation Method with Neumann-Kelvin linearisation where the potential is considered as the impulsive velocity potential.The exciting and radiation hydrodynamic parameters are predicted in time with transient wave Green function whilst the structural analysis is solved with Euler-Bernoulli beam method at which modeshapes are defined analytically.The modal analysis is used to approximate the hydroelastic behaviour of the floating systems through fully coupling of the structural and hydrodynamic analyses.As it is expected,it is found with numerical experience that the effects of the rigid body modes are greater than elastic modes in the case of stiff structures.The predicted numerical results of the present in-house computational tool ITU-WAVE are compared with experimental results for validation purposes and show the acceptable agreements.展开更多
A straightforward method is presented for computing three-dimensional Stokes flow,due to forces on a surface,with high accuracy at points near the surface.The flowquantities arewritten as boundary integrals using the ...A straightforward method is presented for computing three-dimensional Stokes flow,due to forces on a surface,with high accuracy at points near the surface.The flowquantities arewritten as boundary integrals using the free-spaceGreen’s function.To evaluate the integrals near the boundary,the singular kernels are regularized and a simple quadrature is applied in coordinate charts.High order accuracy is obtained by adding special corrections for the regularization and discretization errors,derived here using local asymptotic analysis.Numerical tests demonstrate the uniform convergence rates of the method.展开更多
基金This work is partially supported by Hong Kong Research Grants Council General Research Fund 604208 and the Nano Science and Technology Program at HKUST.
文摘In this paper,we develop an efficient numericalmethod based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium.Numerical examples are presented to examine the influence from material boundaries on dislocations.
基金This study is supported in part by the National Natural Science Foundation of China(grant no.41674050)and by the High-Performance Computing Platform of Peking University.
文摘The fault branching phenomenon,which may heavily influence the patterns of rupture propagation in fault systems,is one of the geometric complexities of fault systems that is widely observed in nature.In this study,we investigate the effect of the branching angle on the rupture inclination and the interaction between branch planes in two-fork branching fault systems by numerical simulation and theoretical analysis based on Mohr’s circle.A friction law dependent on normal stress is used,and special attention is paid to studying how ruptures on the upper and lower branch planes affect the stress and rupture on each other separately.The results show that the two branch planes affect each other in different patterns and that the intensity of the effect changes with the branching angle.The rupture of the lower branch plane has a negative effect on the rupture of the upper branch plane in the case of a small branching angle but has almost no negative effect in the case of a large branching angle.The rupture of the upper branch plane,however,suppresses the rupture of the lower branch plane regardless of whether the branching angle is large or small.
文摘We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy.Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem,we propose a novel Galerkin boundary element method,with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon.Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.
文摘Hydroelasticity of marine structures with and without forward speed is studied directly using time dependent Boundary Integral Equation Method with Neumann-Kelvin linearisation where the potential is considered as the impulsive velocity potential.The exciting and radiation hydrodynamic parameters are predicted in time with transient wave Green function whilst the structural analysis is solved with Euler-Bernoulli beam method at which modeshapes are defined analytically.The modal analysis is used to approximate the hydroelastic behaviour of the floating systems through fully coupling of the structural and hydrodynamic analyses.As it is expected,it is found with numerical experience that the effects of the rigid body modes are greater than elastic modes in the case of stiff structures.The predicted numerical results of the present in-house computational tool ITU-WAVE are compared with experimental results for validation purposes and show the acceptable agreements.
文摘A straightforward method is presented for computing three-dimensional Stokes flow,due to forces on a surface,with high accuracy at points near the surface.The flowquantities arewritten as boundary integrals using the free-spaceGreen’s function.To evaluate the integrals near the boundary,the singular kernels are regularized and a simple quadrature is applied in coordinate charts.High order accuracy is obtained by adding special corrections for the regularization and discretization errors,derived here using local asymptotic analysis.Numerical tests demonstrate the uniform convergence rates of the method.