At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise con...At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise control technologies play a critical role.This study introduces a computational framework for simulating Helmholtz equationgoverned acoustic scattering using a boundary element method(BEM)integrated with Loop subdivision surfaces.By adopting the Loop subdivision scheme—a widely used computer-aided design(CAD)technique-the framework unifies geometric representation and physical field discretization,ensuring seamless compatibility with industrial CAD workflows.The core innovation lies in the novel integration of conditional generative adversarial networks(CGANs)into the subdivision surface BEM to assist and accelerate the numerical computation process.In this study,for the two cases examined,the results show that the CGAN-enhanced approach achieves substantial gains in computational efficiency without compromising accuracy.A hierarchical acceleration strategy is further proposed:the fast multipole method(FMM)first reduces baseline computational complexity,while CGAN-driven secondary acceleration and data augmentation enable real-time parameter exploration.Benchmark validations and practical engineering applications demonstrate the method’s robustness and scalability for large-scale structural-acoustic analysis.展开更多
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-Mill...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.展开更多
We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods...We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.展开更多
A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh. A closed-form analytic formula for thin plate energy of the Catmull-Clark ...A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh. A closed-form analytic formula for thin plate energy of the Catmull-Clark subdivision surface of arbitrary topology is derived through translating the Catmull-Clark subdivision surface into bi-cubic B-spline surface pieces. Using this method, both the membrane energy and the thin plate energy can be evaluated without requiring recursive subdivision. Therefore, it is more efficient and more accurate than the existing methods for calculating the energy of the Catmull-Clark subdivision surface with arbitrary topology. The example of surface fairing demonstrates that this method is efficient and successful for evaluating the energy of subdivision surfaces.展开更多
Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for ...Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline（NURBS） for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system（DCS） and measurement coordinate system（MCS） for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization（QPSO） is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.展开更多
Aiming at the discontinuous traction on contact elements of roller bearing,new concepts of sub- and micro-element are put forward. In the sub-element and micro-element,traction influence coefficient has been modified,...Aiming at the discontinuous traction on contact elements of roller bearing,new concepts of sub- and micro-element are put forward. In the sub-element and micro-element,traction influence coefficient has been modified, which is calculated by the former boundary elementmethod (BEM) with roller bearing load. Hence, three-dimensional distribution of load on rollerbearing is calculated accurately. In practice, it has been proved that this method has highercalculation accuracy. An effective numerical method is offered for analyzing load characteristics ofroller bearing to improve service longevity of roller bearing and operation efficiency of rollingmill.展开更多
On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the...On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the central Pacific Ocean. The formulas of this method are deduced and the interface of program module is designed. The method is carried out in the software ＂Auto mapping system of submarine topography and geomorphology MBChart＂. This method and program will possibly become a potential tool to calculate the resources of seamounts and determine the target diggings for China＇ s next Five-year Plan.展开更多
A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-...A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-th vertex of I(G_1) to each vertex in the i-th copy of G_3.In this paper, we determine the normalized Laplacian spectrum of G_1~S?(G_2~V∪ G_3~E) in terms of the corresponding normalized Laplacian spectra of three connected regular graphs G_1, G_2 and G_3. As applications, we construct some non-regular normalized Laplacian cospectral graphs. In addition, we also give the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of the spanning trees of G_1~S?(G_2~V∪ G_3~E) on three regular graphs.展开更多
In this paper we introduce a new reverse Loop subdivision method. In contrast to current wavelets based Loop subdivision scheme, our method applies the same rules to both regular and extraordinary vertices and reconst...In this paper we introduce a new reverse Loop subdivision method. In contrast to current wavelets based Loop subdivision scheme, our method applies the same rules to both regular and extraordinary vertices and reconstructs the sharp features easily. Furthermore, our method runs faster because it does not need analysis and synthesis procedural. Our main goal is the design of a reverse subdivision method that can reconstruct the coarser mesh from a finer subdivision surface with sharp features for multiresolution representation, The proposed method only needs a little memory storage and brings little error, and it is easy to implement.展开更多
Arbitrary topological curve network has no restriction in topology structure,so it has more powerful representing ability in defining complex surfaces.A complex surface modeling system is presented based on arbitrary ...Arbitrary topological curve network has no restriction in topology structure,so it has more powerful representing ability in defining complex surfaces.A complex surface modeling system is presented based on arbitrary topological curve network and the improved combined subdivision method,its functions including creating and editing curve network,and generating and modifying curve network＇s interpolated surface.This modeling system can be used to the process of products＇concept design,and its applications is also significant to the development of subdivision method.展开更多
In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer m>1) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to ...In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer m>1) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to binary and ternary schemes. The proposed algorithm has been derived from uniform B-spline basis function using the Cox-de Boor recursion formula. In order to determine the convergence and smoothness of the proposed schemes, the Laurent polynomial method has been used.展开更多
By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of t...By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.展开更多
The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built b...The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis.Moreover,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals.Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.展开更多
In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds.? The usefu...In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds.? The usefulness of the scheme is illustrated by considering different examples along with its comparison with the established subdivision schemes. Moreover, B-splines of degree 4and well known 3-point schemes [1, 2, 3, 4, 6, 11, 12, 14, 15] are special cases of our proposed scheme.展开更多
基金the support from the 2025 Henan Provincial Science and Technology Research Project,the Zhumadian 2023 Major Science and Technology Special Projectthe Postgraduate Education Reform and Quality Improvement Project of Henan Province.
文摘At present,noise reduction has become an urgent challenge across various fields.Whether in the context of household appliances in daily life or in the enhancement of stealth performance in military equipment,noise control technologies play a critical role.This study introduces a computational framework for simulating Helmholtz equationgoverned acoustic scattering using a boundary element method(BEM)integrated with Loop subdivision surfaces.By adopting the Loop subdivision scheme—a widely used computer-aided design(CAD)technique-the framework unifies geometric representation and physical field discretization,ensuring seamless compatibility with industrial CAD workflows.The core innovation lies in the novel integration of conditional generative adversarial networks(CGANs)into the subdivision surface BEM to assist and accelerate the numerical computation process.In this study,for the two cases examined,the results show that the CGAN-enhanced approach achieves substantial gains in computational efficiency without compromising accuracy.A hierarchical acceleration strategy is further proposed:the fast multipole method(FMM)first reduces baseline computational complexity,while CGAN-driven secondary acceleration and data augmentation enable real-time parameter exploration.Benchmark validations and practical engineering applications demonstrate the method’s robustness and scalability for large-scale structural-acoustic analysis.
基金sponsored by the Graduate Student Research and Innovation Fund of Xinyang Normal University under No.2024KYJJ012.
文摘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.
基金supported by the National Natural Science Foundation of China (NSFC)under Grant Nos.12172350,11772322 and 11702238。
文摘We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.
文摘A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh. A closed-form analytic formula for thin plate energy of the Catmull-Clark subdivision surface of arbitrary topology is derived through translating the Catmull-Clark subdivision surface into bi-cubic B-spline surface pieces. Using this method, both the membrane energy and the thin plate energy can be evaluated without requiring recursive subdivision. Therefore, it is more efficient and more accurate than the existing methods for calculating the energy of the Catmull-Clark subdivision surface with arbitrary topology. The example of surface fairing demonstrates that this method is efficient and successful for evaluating the energy of subdivision surfaces.
基金supported by National Natural Science Foundation of China(Grant No. 51075198)Jiangsu Provincial Natural Science Foundation of China(Grant No. BK2010479)+1 种基金Jiangsu Provincial Project of 333 Talents Engineering of ChinaJiangsu Provincial Project of Six Talented Peak of China
文摘Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline（NURBS） for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system（DCS） and measurement coordinate system（MCS） for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization（QPSO） is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.
基金This project is supported by National Natural Science Foundation of China (No.50205004, No. 50075075).
文摘Aiming at the discontinuous traction on contact elements of roller bearing,new concepts of sub- and micro-element are put forward. In the sub-element and micro-element,traction influence coefficient has been modified, which is calculated by the former boundary elementmethod (BEM) with roller bearing load. Hence, three-dimensional distribution of load on rollerbearing is calculated accurately. In practice, it has been proved that this method has highercalculation accuracy. An effective numerical method is offered for analyzing load characteristics ofroller bearing to improve service longevity of roller bearing and operation efficiency of rollingmill.
基金This study was supported by Projects under contract Nos DY105 China's 0cean-03-01-01 and DY105-03-01-07the National Natural Science Foundation of China under contract No.40506017the Youth Foundation of Marine High-tech Project of China under contract No.2002AA616010.
文摘On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the central Pacific Ocean. The formulas of this method are deduced and the interface of program module is designed. The method is carried out in the software ＂Auto mapping system of submarine topography and geomorphology MBChart＂. This method and program will possibly become a potential tool to calculate the resources of seamounts and determine the target diggings for China＇ s next Five-year Plan.
基金Supported by the Young Scholars Science Foundation of Lanzhou Jiaotong University(Grant Nos.20160142017004+3 种基金 2017021)the Education Foundation of Gansu Province(Grant No.2017A-021)the National Natural Science Foundation of China(Grant Nos.11461038 61163010)
文摘A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-th vertex of I(G_1) to each vertex in the i-th copy of G_3.In this paper, we determine the normalized Laplacian spectrum of G_1~S?(G_2~V∪ G_3~E) in terms of the corresponding normalized Laplacian spectra of three connected regular graphs G_1, G_2 and G_3. As applications, we construct some non-regular normalized Laplacian cospectral graphs. In addition, we also give the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of the spanning trees of G_1~S?(G_2~V∪ G_3~E) on three regular graphs.
基金Supported by the High Technology Research and Development Progrmnn~ of China （No. 2003AA411310）, the National Natural Science Foundation of China （No. 60373070） and Microsoft Research Project 2005-1.
文摘In this paper we introduce a new reverse Loop subdivision method. In contrast to current wavelets based Loop subdivision scheme, our method applies the same rules to both regular and extraordinary vertices and reconstructs the sharp features easily. Furthermore, our method runs faster because it does not need analysis and synthesis procedural. Our main goal is the design of a reverse subdivision method that can reconstruct the coarser mesh from a finer subdivision surface with sharp features for multiresolution representation, The proposed method only needs a little memory storage and brings little error, and it is easy to implement.
基金Project supported by the Fundamental Research Foundations for the Central Universities (Grant No.2009B30514)
文摘Arbitrary topological curve network has no restriction in topology structure,so it has more powerful representing ability in defining complex surfaces.A complex surface modeling system is presented based on arbitrary topological curve network and the improved combined subdivision method,its functions including creating and editing curve network,and generating and modifying curve network＇s interpolated surface.This modeling system can be used to the process of products＇concept design,and its applications is also significant to the development of subdivision method.
文摘In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer m>1) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to binary and ternary schemes. The proposed algorithm has been derived from uniform B-spline basis function using the Cox-de Boor recursion formula. In order to determine the convergence and smoothness of the proposed schemes, the Laurent polynomial method has been used.
文摘By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.
文摘The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis.Moreover,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals.Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.
文摘In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds.? The usefulness of the scheme is illustrated by considering different examples along with its comparison with the established subdivision schemes. Moreover, B-splines of degree 4and well known 3-point schemes [1, 2, 3, 4, 6, 11, 12, 14, 15] are special cases of our proposed scheme.
