An improved boundary element-free method (IBEFM) for two-dimensional potential problems

The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （BEFM）, combining the boundary integral equation （BIE） method with the IMLS method, the improved boundary element-free method （IBEFM） for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker ~ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.

Forward and inverse problem for cardiac magnetic field and electric potential using two boundary element methods

This paper discusses the forward and inverse problem for cardiac magnetic fields and electric potentials. A torso-heart model established by boundary element method （BEM） is used for studying the distributions of cardiac magnetic fields and electric potentials. Because node-to-node and triangle-to-triangle BEM can lead to discrepant field distributions, their properties and influences are compared. Then based on constructed torso-heart model and supposed current source functional model-current dipole array, the magnetic and electric imaging by optimal constrained linear inverse method are applied at the same time. Through figure and reconstructing parameter comparison, though the magnetic current dipole array imaging possesses better reconstructing effect, however node-to-node BEM and triangleto-triangle BEM make little difference to magnetic and electric imaging.

ANALYTICAL TREATMENT OF BOUNDARY INTEGRALS IN DIRECT BOUNDARY ELEMENT ANALYSIS OF PLAN POTENTIAL AND ELASTICITY PROBLEMS

An analytical scheme, which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method (DBEM) of two-dimensional potential and elastic problems, is established. With some numerical results, it is shown that the better precision and high computational efficiency, especially in the band of the domain near boundary, can be derived by the present scheme.

REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS

A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The factor leading to the singularity was transformed out of the integral representations with integration by parts, so non-singular regularized formulas were presented for the two forms of integrals. Furthermore, quadratic elements are used in addition to linear ones. The quadratic element very close to the internal point can be divided into two linear ones, so that the algorithm is still valid. Numerical examples demonstrate the effectiveness and accuracy of this algorithm. Especially for problems with curved boundaries, the combination of quadratic elements and linear elements can give more accurate results.

A BOUNDARY ELEMENT METHOD FOR STEADY SHIP WAVE-MAKING POTENTIAL PROBLEMS

A boundary element method for three-dimensional steady ship wave-making potential problems is established with the Rankine source function as its fundamental solution. In the treatment of the linearized free surface condition, one-sided, upstream finite difference operator (FDO) is used to suppress the upstream waves, and the equation of the disturbance velocity is established so that the first order FDO can be used in place of the second order FDO. Compared with the method with the second order FDO, the current method gives better precision and stability. Numerical examples are presented for verification.

Performance of Compact Radial Basis Functions in the Direct Interpolation Boundary Element Method for Solving Potential Problems

This study evaluates the effectiveness of a new technique that transforms doma in integrals into boundary integrals that is applicable to the boundary element method.Si mulations were conducted in which two-dimensional surfaces were approximated by inter polation using radial basis functions with full and compact supports.Examples involving Poisson’s equation are presented using the boundary element method and the proposed te chnique with compact radial basis functions.The advantages and the disadvantages are e xamined through simulations.The effects of internal poles,the boundary mesh refinemen t and the value for the support of the radial basis functions on performance are assessed.

ALE FINITE ELEMENT ANALYSIS OF NONLINEAR SLOSHING PROBLEMS BASED ON F LUID VELOCITY POTENTIAL

Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh independently of f luid motion, and the container fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free su rface without producing undesirable distortion of the computational mesh. The fi nite element method and finite difference method are used spacewise and timewise , respectively. A numerical example involving either forced horizontal oscillati on or forced pitching oscillation of the fluid filled container is presented to illustrate the effectiveness and the robustness of the method. In additi on, this work can be extended for the fluid structure interaction problems.

Modes of Occurrence and Cleaning Potential of Trace Elements in Coals from the Northern Ordos Basin and Shanxi Province, China

Based on the analyses of 43 elements in 16 samples of the raw coal and feed coal collected from the northern Ordos basin and Shanxi Province, the modes of occurrence of these elements were studied using the method of cluster analysis and factor analysis, and the cleaning potential of the hazardous elements relatively enriched in the coals was discussed by analyzing six samples of the cleaned coal from the coal-washing plants and coal cleaning simulation experiments. The results shows that the elements Br and Ba show a strong affinity to the organic matter, Cs, Cd, Pb, Zn and Hg partly to the organic matter, and the other trace elements are mainly associated with the mineral matter. Cs, Mo, P, Pb, Zn and S have positive correlations with the two principal factors, reflecting the complexity of their modes of occurrence. Some elements that were thought to show a faint relationship (Be with S and Sb with carbonates) in other rocks are found to have a strong interrelation in the coals. Clay minerals (mainly kaolinite) dominate in the coals, and Ta, Th, Ti, Sc, REE, Hf, U, Se, W, V, Nb, Mo, Al, P, Cr, Pb and Zn are distributed mostly in kaolinite, while K, Rb, Cs, and Na have much to do with illite. Conventional cleaning can reduce the concentrations of most hazardous elements in various degrees. The hazardous elements S, As, Sb, Se, Mo, Pb, Cd and Hg relatively enriched in some coals from the area studied have a relatively high potential of environmental risks. However, by physical coal cleaning processes, more than 60% of As and Hg were removed, showing a high degree of removal, more than 30% of Sb, as well as S, Pb and Cd partly associated with the inorganic matter were removed. Se and Mo showing a relatively low degree of removal could be further removed by deep crushing of the coal during physical cleaning processes, and the concentrations of S, Pb, Cd and Hg with a partial association with the organic matter could be decreased in such ways as the coal blending. Cluster analysis together with factor analysis is a rapid and effective way to deduce the mode of occurrence of an element from bulk samples, and the removability data of most hazardous elements are basically consistent with their modes of occurrence suggested, which indicates that the statistical analysis could predict the cleaning potential of hazardous elements during the physical coal cleaning.

The Effects of Climate Change on the Planting Boundary and Potential Yield for Different Rice Cropping Systems in Southern China

Based on climate data from 254 meteorological stations, this study estimated the effects of climate change on rice planting boundaries and potential yields in the southern China during 1951-2010. The results indicated a signiifcant northward shift and westward expansion of northern boundaries for rice planting in the southern China. Compared with the period of 1951-1980, the average temperature during rice growing season in the period of 1981-2010 increased by 0.4＆#176;C, and the northern planting boundaries for single rice cropping system （SRCS）, early triple cropping rice system （ETCRS）, medium triple cropping rice system （MTCRS）, and late triple cropping rice system （LTCRS） moved northward by 10, 30, 52 and 66 km, respectively. In addition, compared with the period of 1951-1980, the suitable planting area for SRCS was reduced by 11%during the period of 1981-2010. However, the suitable planting areas for other rice cropping systems increased, with the increasing amplitude of 3, 8, and 10%for ETCRS, MTCRS and LTCRS, respectively. In general, the light and temperature potential productivity of rice decreased by 2.5%. Without considering the change of rice cultivars, the northern planting boundaries for different rice cropping systems showed a northward shift tendency. Climate change resulted in decrease of per unit area yield for SRCS and the annual average yields of ETCRS and LTCRS. Nevertheless, the overall rice production in the entire research area showed a decreasing trend even with the increasing trend of annual average yield for MTCRS.

A moving Kriging interpolation-based boundary node method for two-dimensional potential problems

In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.

Types and resource potential of continental shale oil in China and its boundary with tight oil

Continental shale oil has two types, low-medium maturity and medium-high maturity, and they are different in terms of resource environment, potential, production methods and technologies, and industrial evaluation criteria. In addition, continental shale oil is different from the shale oil and tight oil in the United States. Scientific definition of connotations of these resource types is of great significance for promoting the exploration of continental shale oil from "outside source" into "inside source" and making it a strategic replacement resource in the future. The connotations of low-medium maturity and medium-high maturity continental shale oils are made clear in this study. The former refers to the liquid hydrocarbons and multiple organic matter buried in the continental organic-rich shale strata with a burial depth deeper than 300 m and a Ro value less than 1.0%. The latter refers to the liquid hydrocarbons present in organic-rich shale intervals with a burial depth that in the "liquid window" range of the Tissot model and a Ro value greater than 1.0%. The geological characteristics, resource potential and economic evaluation criteria of different types of continental shale oil are systematically summarized. According to evaluation, the recoverable resources of in-situ conversion technology for shale oil with low-medium maturity in China is about(700-900)×10^8 t, and the economic recoverable resources under medium oil price condition($ 60-65/bbl) is(150-200)×10^8 t. Shale oil with low-medium maturity guarantees the occurrence of the continental shale oil revolution. Pilot target areas should be optimized and core technical equipment should be developed according to the key parameters such as the cumulative production scale of well groups, the production scale, the preservation conditions, and the economics of exploitation. The geological resources of medium-high maturity shale oil are about 100×10^8 t, and the recoverable resources can to be determined after the daily production and cumulative production of a single well reach the economic threshold. Continental shale oil and tight oil are different in lithological combinations, facies distribution, and productivity evaluation criteria. The two can be independently distinguished and coexist according to different resource types. The determination of China’s continental shale oil types, resources potentials, and tight oil boundary systems can provide a reference for the upcoming shale oil exploration and development practices and help the development of China’s continental shale oil.

Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.

The Boundary Element Method for Ordinary State-Based Peridynamics

The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.

Generalized nth-Order Perturbation Method Based on Loop Subdivision Surface Boundary Element Method for Three-Dimensional Broadband Structural Acoustic Uncertainty Analysis

In this paper,a generalized nth-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems.The Burton-Miller method is employed to solve the problem of non-unique solutions that may be encountered in the external acoustic field,and the nth-order discretization formulation of the boundary integral equation is derived.In addition,the computation of loop subdivision surfaces and the subdivision rules are introduced.In order to confirm the effectiveness of the algorithm,the computed results are contrasted and analyzed with the results under Monte Carlo simulations(MCs)through several numerical examples.

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.

NOVEL REGULARIZED BOUNDARY INTEGRAL EQUATIONS FOR POTENTIAL PLANE PROBLEMS

The universal practices have been centralizing on the research of regularization to the direct boundary integal equations （DBIEs）. The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value （CPV） and Hadamard-finite-part （HFP） integrals are established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system.

A Computational Framework for Parachute Inflation Based on Immersed Boundary/Finite Element Approach

A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation.

A Potential Candidate For the Middle-Upper Cambrian Boundary Stratotype——An Introduction to the Paibi Section in Huayuan,Hunan

The Middle-Upper Cambrian boundary is one of the current stratigraphical problems which remain openin the geological world, since there have been no universally acknowledged delimiting standard and stratotype.Acting on the instruction of Profs. Lu Yanhao and An Taixiang the author studied in details the Paibi Section,which is well exposed as a continuous sequence at an easily accessible locality. The Middle-Upper Cambrianboundary strata are composed of biocalcimicrosparite, indicating the sedimentary environment of anunderwater upheaval on the gentle slope along the frontal margin of the Yangtze carbonate platform. For the upper Middle and lower Upper Cambrian agnostid trilobite zones and conodont zones are erected,and a more accurate correlation between the trilobite and conodont sequences is established. Based on these,the Middle-Upper Cambrian boundary is drawn more reasonably and precisely than what was done before. Inshort, the section studied is superior to other known sections of Middle-Upper Cambrian. and it will probablybe an ideal candidate for the Middle-Upper Cambrian boundary stratotype.

Existence and Uniqueness of Solution for Cahn-Hilliard Hyperbolic Phase-Field System with Dirichlet Boundary Condition and Regular Potentials

Our aim in this paper is to study the existence and the uniqueness of the solutions for hyperbolic Cahn-Hilliard phase-field system, with initial conditions, Dirichlet boundary condition and regular potentials.

Analysis of the Fertilizing and Bioremediation Potential of Leaf Litter Compost Amendment in Different Soils through Indexing Method

This research study explored the efficacy of leaf litter compost as a sustainable soil amendment with the objective of promoting soil health and mitigating the accumulation of potentially toxic elements. The investigation encompassed the impact of various organic compost amendments, including leaf compost, cow dung manure, kitchen waste compost, municipal organic waste compost, and vermicompost. The study employed Inductively Coupled Plasma Mass Spectrometry (ICP-MS) to evaluate soil nutrient levels and concentrations of Potentially Toxic Elements (PTEs) such as arsenic, chromium, cadmium, mercury, lead, nickel, and lithium. The fertilization and bioremediation potential of these compost amendments are quantified using an indexing method. Results indicated a substantial increase in overall nutrient levels (carbon, nitrogen, phosphorus, potassium, and sulfur) in soils treated with leaf compost and other organic composts. Fertility indices (FI) are notably higher in compost-amended soils (ranging from 2.667 to 3.938) compared to those amended with chemical fertilizers (ranging from 2.250 to 2.813) across all soil samples. Furthermore, the mean concentrations of PTEs were significantly lower in soils treated with leaf compost and other organic compost amendments compared to those treated with chemical fertilizers amendments. The assessment through the indexing method revealed a high clean index (CI) for leaf compost amendment (ranging from 3.407 to 3.58), whereas the chemical fertilizer amendment exhibits a relatively lower CI (ranging from 2.78 to 3.20). Consequently, leaf compost and other organic composts exhibit the potential to enhance sustainable productivity, promoting soil health and environmental safety by improving nutrient levels and remediating potentially toxic elements in the soil.