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Fast Multipole Accelerated boundary integral equation method for Evaluating the Stress Field Associated with Dislocations in a Finite Medium

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Communications in Computational Physics 2012年第6期12卷 226-246页

作者： Degang Zhao Jingfang Huang Yang Xiang Nano Science and Technology Program The Hong Kong University of Science and TechnologyClear Water BayKowloonHong Kong School of Physics HuazhongUniversity of Science and TechnologyWuhan 430074China Department ofMathematics The University of North Carolina at Chapel HillChapel HillNC 27599-3250USA Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayKowloonHong Kong

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 *** examples are presented to examine the influence from material boundaries on dislocations.

关键词： Fast multipole method boundary integral equation method dislocation dynamics stress

Linear and Nonlinear Solutions of Interfacial Waves Due to a Doublet

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Journal of Mathematical Research with Applications 2024年第2期44卷 269-284页

作者： Di LIU Zhen WANG School of Mathematics Jilin University School of Mathematical Sciences Beihang University

Steady two-dimensional potential flows of two-layer fluids with a submerged doublet in the lower layer are considered. Both linear analytical solutions and fully nonlinear solutions based on boundary integral equation methods are obtained. Nonlinearity strongly influences the downstream wave height and leads to a slight phase difference. When the Froude number is small, wave height fast gets its maximum as the Froude number increases. While wave-less solutions may be obtained if the Froude number is very large. Afterward, the interfacial waves due to one point vortex or a vortex pair are compared with those due to a doublet. It is found that the nonlinear wave profiles due to a doublet are quite close to those due to a vertical vortex pair if the distance between the vortex pair is set appropriately.

关键词： interfacial waves doublet boundary integral equation method linear solutions

PERTURBATION SOLUTION TO 3-D NONLINEAR SUPERCAVITATING FLOW PROBLEMS

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Acta Mechanica Sinica 1993年第1期9卷 13-21页

作者：叶取源何友声朱世权 Shanghai Jiao Tong University Shanghai China 200030

A 3-D nonlinear problem of supercavitating flow past an axisymmetric body at a small angle of attack is investigated by means of the perturbation method and Fourier-cosine-expansion method. The first three order perturbation equations are derived in detail and solved numerically using the boundary integral equation method and iterative techniques. Computational results of the hydrodynamic characteristics and cavity shapes of each order are presented for nonaxisymmetric supercavitating flow past cones with various apex-angles at differ- ent cavitation numbers. The numerical results are found in good agreement with experimental data.

关键词： supercavitating flow perturbation method nonlinear solution boundary integral equation method Fourier expansion elliptic integrals

Interaction of Linear Waves with Infinitely Long Horizontal Cylinders Studied by boundary Element method

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China Ocean Engineering 2007年第2期21卷 317-330页

作者：冯波郑永红游亚戈何再明 Guangzhou Institute of Energy Conversion Chinese Academy of Sciences

The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the boundary integral equation method （BIEM）. Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with those by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two- layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coef- ficients and energies are analyzed in detail, and some imeresting physical phenomena are observed.

关键词： two-layer fluids boundary integral equation method hydrodynamic behavior

Nearly Singular integrals in 3D Stokes Flow

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Communications in Computational Physics 2013年第10期14卷 1207-1227页

作者： Svetlana Tlupova J.Thomas Beale Department of Mathematics University of MichiganAnn ArborMI 48109-1043USA Department of Mathematics Duke UniversityDurhamNC 27708-0320USA

A straightforward method is presented for computing three-dimensional Stokes flow,due to forces on a surface,with high accuracy at points near the *** flowquantities arewritten as boundary integrals using the free-spaceGreen’s *** evaluate the integrals near the boundary,the singular kernels are regularized and a simple quadrature is applied in coordinate *** order accuracy is obtained by adding special corrections for the regularization and discretization errors,derived here using local asymptotic *** tests demonstrate the uniform convergence rates of the method.

关键词： Stokes equations boundary integral equation method nearly singular integrals

Nonlinear Capillary-Gravity Waves Produced by a Vertically Oscillating Plate

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China Ocean Engineering 1998年第2期13卷 147-162页

作者： Philip L.-F.LIU Professor Cornell UniversityIthacaNY14853U.S.A.

The nonlinear capillary-gravity wave produced by a vertically oscillating plate, in which the contact-angle model is considered, is studied by use of the boundary integral equation method (BIEM). The present numerical experiment shows that the code is robust and efficient for modeling the generation and propagation of capillary-gravity waves. It is found that the wave heights of stationary periodic nonlinear waves radiated away from the plate are dependent on the parameters involved in the contact-angle model. The effect of the contact-angle hysteresis and the nonlinearity of capillary-gravity waves on the wave profile is discussed in the paper.

关键词： boundary integral equation method nonlinear capillary-gravity wave wavemaker

Application of A Fast Multipole BIEM for Flow Diffraction from A 3D Body

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海洋工程：英文版 2004年第2期18卷 291-298页

作者：滕斌宁德志 State Key Laboratory of Coastal and Offshore Engineering

A Fast Multipole method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.

关键词： fast multipole method boundary integral equation method generalized conjugate residual method current diffraction

Analysis of the role of branching angle in the dynamic rupture process on a 3-D branching fault system

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Earth and Planetary Physics 2020年第5期4卷 523-531页

作者： JingXing Fang Feng Qian HaiMing Zhang School of Earth and Space Sciences Peking UniversityBeijing 100871China

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 *** 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 *** results show that the two branch planes affect each other in different patterns and that the intensity of the effect changes with the branching *** 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 *** 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.

关键词： branching faults Mohr–Coulomb diagram boundary integral equation method earthquake source dynamics rupture selectivity

Dynamic rupture process of the 1999 Chi-Chi,Taiwan,earthquake

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Earthquake Science 2009年第1期22卷 3-12页

作者： Haiming Zhang Xiaofei Chen College of Earth Sciences Graduate University of Chinese Academy of Sciences Beijing 100049 China School of Earth and Space Sciences University of Science and Technology of China Hefei 230026 China

In this study, we preliminarily investigated the dynamic rupture process of the 1999 Chi-Chi, Taiwan, earthquake by using an extended boundary integral equation method, in which the effect of ground surface can be exactly included. Parameters for numerical modeling were carefully assigned based on previous studies. Numerical results indicated that, although many simplifications are assumed, such as the fault plane is planar and all heterogeneities are neglected, distribution of slip is still consistent roughly with the results of kinematic inversion, implying that for earthquakes in which ruptures run up directly to the ground surface, the dynamic processes are controlled by geometry of the fault to a great extent. By taking the common feature inferred by various kinematic inversion studies as a restriction, we found that the critical slip-weakening distance Dc should locate in a narrow region [60 cm, 70 cm], and supershear rupture might occur during this earthquake, if the initial shear stress before the mainshock is close to the local shear strength.

关键词： dynamic rupture 1999 Chi-Chi earthquake ground surface boundary integral equation method