Time-Domain Higher-Order Boundary Element Method for Simulating High Forward-Speed Ship Motions in Waves

The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical model is based on the time-domain potential flow theory and higher-order boundary element method,where an analytical expression is completely expanded to determine the base-unsteady coupling flow imposed on the moving condition of the ship.The ship in the numerical model may possess different advancing speeds,i.e.stationary,low speed,and high speed.The role of the water depth,wave height,wave period,and incident wave angle is analyzed by means of the accurate numerical model.It is found that the resonant motions of the high forward-speed ship are triggered by comparison with the stationary one.More specifically,a higher forward speed generates a V-shaped wave region with a larger elevation,which induces stronger resonant motions corresponding to larger wave periods.The shoaling effect is adverse to the motion of the low-speed ship,but is beneficial to the resonant motion of the high-speed ship.When waves obliquely propagate toward the ship,the V-shaped wave region would be broken due to the coupling effect between roll and pitch motions.It is also demonstrated that the maximum heave motion occurs in beam seas for stationary cases but occurs in head waves for high speeds.However,the variation of the pitch motion with period is hardly affected by wave incident angles.

Optimal Boundary Control Method for Domain Decomposition Algorithm

To study the domain decomposition algorithms for the equations of elliptic type, the method of optimal boundary control was used to advance a new procedure for domain decomposition algorithms and regularization method to deal with the ill posedness of the control problem. The determination of the value of the solution of the partial differential equation on the interface——the key of the domain decomposition algorithms——was transformed into a boundary control problem and the ill posedness of the control problem was overcome by regularization. The convergence of the regularizing control solution was proven and the equations which characterize the optimal control were given therefore the value of the unknown solution on the interface of the domain would be obtained by solving a series of coupling equations. Using the boundary control method the domain decomposion algorithm can be carried out.

Solution Domain Boundary Analysis Method and Its Application in Parameter Spaces of Nonlinear Gear System

Mastering the influence laws of parameters on the solution structure of nonlinear systems is the basis of carrying out vibration isolation and control.Many researches on solution structure and bifurcation phenomenon in parameter spaces are carried out broadly in many fields,and the research on nonlinear gear systems has attracted the attention of many scholars.But there is little study on the solution domain boundary of nonlinear gear systems.For a periodic non-autonomous nonlinear dynamic system with several control parameters,a solution domain boundary analysis method of nonlinear systems in parameter spaces is proposed,which combines the cell mapping method based on Poincaré point mapping in phase spaces with the domain decomposition technique of parameter spaces.The cell mapping is known as a global analysis method to analyze the global behavior of a nonlinear dynamic system with finite dimensions,and the basic idea of domain decomposition techniques is to divide and rule.The method is applied to analyze the solution domain boundaries in parameter spaces of a nonlinear gear system.The distribution of different period domains,chaos domain and the domain boundaries between different period domains and chaotic domain are obtained in control parameter spaces constituted by meshing damping ratio with excitation frequency,fluctuation coefficient of meshing stiffness and average exciting force respectively by calculation.The calculation results show that as the meshing damping increases,the responses of the system change towards a single motion,while the variations of the excitation frequency,meshing stiffness and exciting force make the solution domain presenting diversity.The proposed research contribution provides evidence for vibration control and parameter design of the gear system,and confirms the validity of the solution domain boundary analysis method.

3D viscous-spring artificial boundary in time domain

After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary （VSAB） in the time domain is developed in this paper. First, the 3D VSAB equations in the normal and tangential directions are derived based on the elastic wave motion theory. Secondly, a numerical simulation technique of wave motion equations along with the VSAB condition in the time domain is studied. Finally, numerical examples of some classical elastic wave motion problems are presented and the results are compared with the associated theoretical solutions, demonstrating that high precision and adequate stability can be achieved by using the proposed 3D VSAB. The proposed 3D VSAB can be conveniently incorporated in the general finite element program, which is commonly used to study dynamic soil-structure interaction problems.

Dynamic interaction numerical models in the time domain based on the high performance scaled boundary finite element method

Consideration of structure-foundation-soil dynamic interaction is a basic requirement in the evaluation of the seismic safety of nuclear power facilities. An efficient and accurate dynamic interaction numerical model in the time domain has become an important topic of current research. In this study, the scaled boundary finite element method （SBFEM） is improved for use as an effective numerical approach with good application prospects. This method has several advantages, including dimensionality reduction, accuracy of the radial analytical solution, and unlike other boundary element methods, it does not require a fundamental solution. This study focuses on establishing a high performance scaled boundary finite element interaction analysis model in the time domain based on the acceleration unit-impulse response matrix, in which several new solution techniques, such as a dimensionless method to solve the interaction force, are applied to improve the numerical stability of the actual soil parameters and reduce the amount of calculation. Finally, the feasibility of the time domain methods are illustrated by the response of the nuclear power structure and the accuracy of the algorithms are dynamically verified by comparison with the refinement of a large-scale viscoelastic soil model.

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.

Domain boundaries in silicene:Density functional theory calculations on electronic properties

By using density functional theory(DFT)-based first-principles calculations, the structural stability and electronic properties for two kinds of silicene domain boundaries, forming along armchair edge and zigzag edge, have been investigated. The results indicate that a linkage of tetragonal and octagonal rings(4|8) appears along the armchair edge, while a linkage of paired pentagonal and octagonal rings(5|5|8) appears along the zigzag edge. Different from graphene, the buckling properties of silicene lead to two mirror symmetrical edges of silicene line-defect. The formation energies indicate that the 5|5|8 domain boundary is more stable than the 4|8 domain boundary. Similar to graphene, the calculated electronic properties show that the 5|5|8 domain boundaries exhibit metallic properties and the 4|8 domain boundaries are half-metal.Both domain boundaries create the perfect one-dimensional(1D) metallic wires. Due to the metallic properties, these two kinds of nanowires can be used to build the silicene-based devices.

Revealing the dominant factor of domain boundary resistance on bulk conductivity in lanthanum lithium titanates

Perovskite-type lithium lanthanum titanates(LLTO)display a high bulk ionic conductivity and are considered a promising electrolyte for building up to advanced solid-state Li-ion batteries.The LLTO crystals contain a high concentration of intrinsically formed 90ο-rotated domain boundaries(DBs)serving as barriers to bulk Li-ion conduction.However,the mechanism of how the DB concentration and DB resistance can compete with each other to determine the bulk conductivity of LLTO is still unknown.Here we report a comprehensive study of LLTO compounds,aimed to unravel the mechanism and hence explore new path(s)for further improving the conductivity of this material.Our results show that both the sintering temperature and chemical composition can affect significantly the domain structures in LLTO.It is found that a decrease in the DB concentration is always accompanied by increased DB resistance due to the increased lattice mismatch at DBs,and vice versa.By unifying the electrochemical impedance spectroscopy and transmission electron microscopy analysis,it is clearly shown that the high DB resistance,instead of DB concentration,acts as the dominant factor governing the bulk conductivity of LLTO.The results thus renew the conventional understanding of the bulk Li-ion conduction in LLTO and shed light on developing novel LLTO electrolyte materials with improved ionic conductivity.

ON FICTITIOUS DOMAIN METHOD FOR THE NUMERICAL SOLUTION TO HEAT CONDUCTION EQUATION WITH DERIVATIVE BOUNDARY CONDITIONS

This paper investigates the stability and convergence of some knowndifference schemes for the numerical solution to heat conduction equation withderivative boundary conditions by the fictitious domain method.The discrete vari-ables at the false mesh points are firstly eliminated from the difference schemes andthe local truncation errors are then analyzed in detail.The stability and convergenceof the schemes are proved by energy method.An improvement is proposed to obtainbetter schemes over the original ones.Several numerical examples and comparisonswith other schemes are presented.

On L ∞ Stability and Convergence of Fictitious Domain Method for the Numerical Solution to Parabolic Differential Equation with Derivative Boundary Conditions

This paper investigates some known difference schemes for the numerical solution to parabolic differential equation with derivative boundary conditions by the fictitious domain method.The stability and convergence in L ∞ are proven.

A DOMAIN DECOMPOSITION ALGORITHM WITH FINITE ELEMENT-BOUNDARY ELEMENT COUPLING

A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method （FEM） and the boundary element method （BEM）. The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element （FE-BE） coupling method.

An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.

ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

In this paper analytic boundary value problems for some classical domains in Cn are developed by using the harmonic analysis due to L.K. Hua. First it is discussed for the version of one variable in order to induce the relation between the analytic boundary value problem and the decomposition of function space L2 on the boundary manifold. Then an easy example of several variables, the version of torus in C2, is stated. For the noncommutative classical group L1, the characteristic boundary of a kind of bounded symmetric domain in C4, the boundary behaviors of the Cauchy integral are obtained by using both the harmonic expansion and polar coordinate transformation. At last we obtain the conditions of solvability of Schwarz problem on L1, if so, the solution is given explicitly.

BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN

After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.

A Novel Absorbing Boundary Condition for the Frequency-Dependent Finite-Difference Time-Domain Method

A new absorbing boundary condition (ABC) for frequency dependent finite difference time domain algorithm for the arbitrary dispersive media is presented. The concepts of the digital systems are introduced to the (FD) 2TD method. On the basis of digital filter designing and vector algebra, the absorbing boundary condition under arbitrary angle of incidence are derived. The transient electromagnetic problems in two dimensions and three dimensions are calculated and the validity of the ABC is verified.

A New Analytical Approach for Solving Nonlinear Boundary Value Problems in Finite Domains

Based on the homotopy analysis method (HAM), we propose an analytical approach for solving the following type of nonlinear boundary value problems in finite domain. In framework of HAM a convenient way to adjust and control the convergence region and rate of convergence of the obtained series solutions, by defining the so-called control parameter h , is provided. This paper aims to propose an efficient way of finding the proper values of h.Such values of parameter can be determined at the any order of approximations of HAM series solutions by solving of a nonlinear polynomial equation. Some examples of nonlinear initial value problems in finite domain are used to illustrate the validity of the proposed approach. Numerical results confirm that obtained series solutions agree very well with the exact solutions.

A TIME DOMAIN BOUNDARY ELEMENT METHOD FOR WATER-SOLID IMPACT ANALYSIS

A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding time-space boundary integral equation: is obtained. Then, a set of time domain boundary element equations with recurrence form is immediately formulated through discretization in both time and boundary. After having carried out the numerical calculation two solutions are found in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impact on the surface of a half-space fluid. The results show that the present method is more efficient than the previous ones.

Chromatin domain boundaries: insulators and beyond

The eukaryotic genome is organized into functionally and structurally distinct domains, representing regulatory unitsfor gene expression and chromosome behavior. DNA sequences that mark the border between adjacent domains are theinsulators or boundary elements, which are required in maintenance of the function of different domains. Some insula-tors need others enable to play insulation activity. Chromatin domains are defined by distinct sets of post-translationallymodified histones. Recent studies show that these histone modifications are also involved in establishment of sharpchromatin boundaries in order to prevent the spreading of distinct domains. Additionally, in some loci, the high-orderchromatin structures for long-range looping interactions also have boundary activities, suggesting a correlation betweeninsulators and chromatin loop domains. In this review, we will discuss recent progress in the field of chromatin domainboundaries.

Boundary Element Method with Non-overlapping Domain Decomposition for Diffusion Equation

A boundary element method based on non-overlapping domain decomposition method to solve the time-dependent diffusion equations is presented. The time-dependent fundamental solution is used in the formulation of boundary integrals and the time integration process always restarts from the initial time condition. The process of replacing the interface values, which needs a summation of boundary integrals related to the boundary values at previous time steps can be treated in parallel iterative procedure. Numerical experiments demonstrate that the implementation of the present algorithm is efficient.

Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.