Pub Date : 2025-02-18DOI: 10.1016/j.enganabound.2025.106159
Xinxiang Li , Han Liu
The shape parameter and the fictitious radius are important parameters that affect the performance of the polynomial-augmented RBF collocation method (RBFCM) with fictitious centers. It is known that the RBFCM can reduce the accuracy dependency on shape parameter by using extra polynomial constraints. Moreover, we find that calculation inaccuracies exhibit a strong association with the effective condition numbers for various fictitious radii. While there have been some methods for selecting the shape parameter, an approach that allows for the simultaneous selection of and has not yet been widely researched. In this paper, we propose a systematic method to choose parameters for the polynomial-augmented RBFCM with fictitious centers. The method utilizes the effective condition number to find an appropriate fictitious radius and the modified Franke formula to select a good shape parameter . Five examples of second and fourth order PDEs in 2D and 3D are presented to demonstrate the effectiveness of the proposed method.
{"title":"The selection of shape parameter and fictitious radius for RBF collocation method using the modified Franke formula and effective condition number","authors":"Xinxiang Li , Han Liu","doi":"10.1016/j.enganabound.2025.106159","DOIUrl":"10.1016/j.enganabound.2025.106159","url":null,"abstract":"<div><div>The shape parameter <span><math><mi>c</mi></math></span> and the fictitious radius <span><math><mi>R</mi></math></span> are important parameters that affect the performance of the polynomial-augmented RBF collocation method (RBFCM) with fictitious centers. It is known that the RBFCM can reduce the accuracy dependency on shape parameter by using extra polynomial constraints. Moreover, we find that calculation inaccuracies exhibit a strong association with the effective condition numbers for various fictitious radii. While there have been some methods for selecting the shape parameter, an approach that allows for the simultaneous selection of <span><math><mi>c</mi></math></span> and <span><math><mi>R</mi></math></span> has not yet been widely researched. In this paper, we propose a systematic method to choose parameters for the polynomial-augmented RBFCM with fictitious centers. The method utilizes the effective condition number to find an appropriate fictitious radius <span><math><mi>R</mi></math></span> and the modified Franke formula to select a good shape parameter <span><math><mi>c</mi></math></span>. Five examples of second and fourth order PDEs in 2D and 3D are presented to demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"174 ","pages":"Article 106159"},"PeriodicalIF":4.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143427844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-18DOI: 10.1016/j.enganabound.2025.106173
Jin-Woo Kim, Eung Soo Kim
Key features for the versatile industrial applications of smoothed particle hydrodynamics (SPH) are numerical accuracy and stability, computational efficiency, and ease of implementation. To meet these requirements, this study presents a straightforward algorithm to treat large-strain elastoplasticity within Total Lagrangian SPH (TLSPH) framework. In terms of accuracy and stability, the total Lagrangian formulation in SPH completely eliminates tensile instability related to the use of Eulerian kernel functions. This study adopts a multiplicative hyperelastic-based plasticity model, enabling the model to treat from purely elastic to elastoplastic structural deformations. A common strategy of efficient simulations in structural analysis is utilizing predefined local resolution refinement with non-uniform particle spacing. However, within TLSPH framework, numerical accuracy and efficiency of this strategy were not investigated sufficiently. To maintain a proper number of neighboring particles in the presence of non-uniform spacing, an anisotropic kernel and its derivatives are incorporated in SPH approximations. Beyond its inherent stability, TLSPH can offer great convenience for the multi-resolution implementation with minimized computational load, as repeated kernel computations at each time advancement are not required. Several benchmark tests are conducted to validate the proposed TLSPH model with various initial particle distributions, demonstrating good accuracy and robustness while lowering computational load.
{"title":"Total Lagrangian smoothed particle hydrodynamics for large-strain elastoplasticity with particle resolution refinement using an anisotropic Lagrangian kernel","authors":"Jin-Woo Kim, Eung Soo Kim","doi":"10.1016/j.enganabound.2025.106173","DOIUrl":"10.1016/j.enganabound.2025.106173","url":null,"abstract":"<div><div>Key features for the versatile industrial applications of smoothed particle hydrodynamics (SPH) are numerical accuracy and stability, computational efficiency, and ease of implementation. To meet these requirements, this study presents a straightforward algorithm to treat large-strain elastoplasticity within Total Lagrangian SPH (TLSPH) framework. In terms of accuracy and stability, the total Lagrangian formulation in SPH completely eliminates tensile instability related to the use of Eulerian kernel functions. This study adopts a multiplicative hyperelastic-based plasticity model, enabling the model to treat from purely elastic to elastoplastic structural deformations. A common strategy of efficient simulations in structural analysis is utilizing predefined local resolution refinement with non-uniform particle spacing. However, within TLSPH framework, numerical accuracy and efficiency of this strategy were not investigated sufficiently. To maintain a proper number of neighboring particles in the presence of non-uniform spacing, an anisotropic kernel and its derivatives are incorporated in SPH approximations. Beyond its inherent stability, TLSPH can offer great convenience for the multi-resolution implementation with minimized computational load, as repeated kernel computations at each time advancement are not required. Several benchmark tests are conducted to validate the proposed TLSPH model with various initial particle distributions, demonstrating good accuracy and robustness while lowering computational load.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"173 ","pages":"Article 106173"},"PeriodicalIF":4.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops the Zonal Free Element Method (ZFREM) to solve transient nonlinear heat conduction problems. As a novel meshless method, ZFREM utilizes the shape functions of isoparametric elements, which contribute to its enhanced stability compared to other meshless methods. Moreover, through domain partitioning, this method effectively handles complex geometric configurations. Another distinguishing feature is that element is formed by the collocation node (CN) and nodes around it (field nodes), which makes it easy to use high-order elements and obtain more accurate solutions. The paper also establishes a specific unified format for solving nonlinear heat conduction problems using this method. Finally, the authors used the proposed method to analyze three-dimensional unsteady heat conduction problems involving nonlinear thermal conductivity. The results obtained using the proposed method are in agreement with reference results, validating its effectiveness.
{"title":"Zonal free element method for solving nonlinear transient heat conduction problems","authors":"Kai Yang, Jia-Bo Han, Wen-Wei Jiang, Zhi-Yuan Zhou, Chen-Hao Tan, Si-Qi Zhang, Yun-Tao Zhou, Hua-Yu Liu, Xiao-Wei Gao","doi":"10.1016/j.enganabound.2025.106170","DOIUrl":"10.1016/j.enganabound.2025.106170","url":null,"abstract":"<div><div>This paper develops the Zonal Free Element Method (ZFREM) to solve transient nonlinear heat conduction problems. As a novel meshless method, ZFREM utilizes the shape functions of isoparametric elements, which contribute to its enhanced stability compared to other meshless methods. Moreover, through domain partitioning, this method effectively handles complex geometric configurations. Another distinguishing feature is that element is formed by the collocation node (CN) and nodes around it (field nodes), which makes it easy to use high-order elements and obtain more accurate solutions. The paper also establishes a specific unified format for solving nonlinear heat conduction problems using this method. Finally, the authors used the proposed method to analyze three-dimensional unsteady heat conduction problems involving nonlinear thermal conductivity. The results obtained using the proposed method are in agreement with reference results, validating its effectiveness.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"173 ","pages":"Article 106170"},"PeriodicalIF":4.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-15DOI: 10.1016/j.enganabound.2025.106160
Weiwei Li, Chenchen Yang
This study introduces a rapid methodology based on recursive skeletonization factorization (RSF), for the determination of origin intensity factors (OIFs) at Neumann boundaries within the framework of the singular boundary method (SBM). The conventional formula for OIFs, which is derived using the subtracting and adding-back technique (SABT), is reformulated into a matrix-vector product representation. The components of the matrix consist of the fundamental solutions of the double-layer potential that adhere to the governing equations. Consequently, the RSF facilitates the implicit construction of a hierarchically generalized LU decomposition of the matrix, producing decomposition factors that allow for efficient multiplication with any vector. This innovative approach significantly reduces the computational cost associated with the calculation of OIFs, thereby meeting the demands of simulating large-scale problems. Numerical results demonstrate that this method is both accurate and stable, and it is applicable to a variety of problems characterized by irregular geometries.
{"title":"A fast approach evaluating origin intensity factors on Neumann boundary in the singular boundary method","authors":"Weiwei Li, Chenchen Yang","doi":"10.1016/j.enganabound.2025.106160","DOIUrl":"10.1016/j.enganabound.2025.106160","url":null,"abstract":"<div><div>This study introduces a rapid methodology based on recursive skeletonization factorization (RSF), for the determination of origin intensity factors (OIFs) at Neumann boundaries within the framework of the singular boundary method (SBM). The conventional formula for OIFs, which is derived using the subtracting and adding-back technique (SABT), is reformulated into a matrix-vector product representation. The components of the matrix consist of the fundamental solutions of the double-layer potential that adhere to the governing equations. Consequently, the RSF facilitates the implicit construction of a hierarchically generalized LU decomposition of the matrix, producing decomposition factors that allow for efficient multiplication with any vector. This innovative approach significantly reduces the computational cost associated with the calculation of OIFs, thereby meeting the demands of simulating large-scale problems. Numerical results demonstrate that this method is both accurate and stable, and it is applicable to a variety of problems characterized by irregular geometries.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"173 ","pages":"Article 106160"},"PeriodicalIF":4.2,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-15DOI: 10.1016/j.enganabound.2025.106156
Jia-Jie Wang , Fu-Ren Ming , Chang Liu , Qing-Sen Zhang , Hao Chen
The oblique entry process of a vehicle not only generates strong axial forces, but also generates significant normal force due to the asymmetry of air and cavity flows, which poses a great threat to the local and overall strength of the vehicle. This paper employs a multiphase -smoothed particle hydrodynamics (-SPH) method to analyze the flow field evolution and pressure distribution on the vehicle during water entry. Firstly, the accuracy and convergency of numerical model are verified through an oblique water entry case. Furthermore, the normal force formation mechanism is investigated by capturing the pressure evolution on the vehicle. Finally, the influences of half-cone angle and water-entry angle on the normal force during water entry are discussed. The findings indicate that the formation of normal force can be attributed to the hydrodynamic pressure and the aerodynamic pressure difference, which will provide valuable insights for the designs of force reduction and structural safety.
{"title":"Formation mechanism of normal force of a vehicle during the oblique water entry based on multi-phase smoothed particle hydrodynamics","authors":"Jia-Jie Wang , Fu-Ren Ming , Chang Liu , Qing-Sen Zhang , Hao Chen","doi":"10.1016/j.enganabound.2025.106156","DOIUrl":"10.1016/j.enganabound.2025.106156","url":null,"abstract":"<div><div>The oblique entry process of a vehicle not only generates strong axial forces, but also generates significant normal force due to the asymmetry of air and cavity flows, which poses a great threat to the local and overall strength of the vehicle. This paper employs a multiphase <span><math><mi>δ</mi></math></span>-smoothed particle hydrodynamics (<span><math><mi>δ</mi></math></span>-SPH) method to analyze the flow field evolution and pressure distribution on the vehicle during water entry. Firstly, the accuracy and convergency of numerical model are verified through an oblique water entry case. Furthermore, the normal force formation mechanism is investigated by capturing the pressure evolution on the vehicle. Finally, the influences of half-cone angle and water-entry angle on the normal force during water entry are discussed. The findings indicate that the formation of normal force can be attributed to the hydrodynamic pressure and the aerodynamic pressure difference, which will provide valuable insights for the designs of force reduction and structural safety.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"173 ","pages":"Article 106156"},"PeriodicalIF":4.2,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-15DOI: 10.1016/j.enganabound.2025.106172
Youjun Ning , Daofu Zhang , Xinlian Liu
Discontinuous deformation analysis (DDA), a representative discontinuum-based numerical method, has been successfully developed to simulate the important problem of fracturing failures in rock mechanics through a sub-block approach. In the present work, a refinement algorithm of the Voronoi sub-block elements for DDA simulations of rock fracturing is proposed to simultaneously improve the simulation accuracy and control the computation scale through local refinement of the elements. The algorithm includes major procedures of triangular finite element division, random point distribution, Delaunay triangle generation, and Voronoi sub-block element generation. Static and dynamic simulation examples of disc, rectangular and Hopkinson specimens are simulated and quantitatively or qualitatively verified by theoretical, experimental or other numerical simulation results. Blasting-induced rock fracturing failures are simulated as an application example of the Voronoi sub-block DDA with element refinement, in which the effects of blasting shock wave and blasting gas pressure on the rock breakage ability and patterns are specially investigated to reveal the rock blasting characteristics and mechanism. All the simulation examples well indicate the capability and effectiveness to simulate rock fracturing failures by the sub-block DDA with the proposed Voronoi sub-block element refinement algorithm.
{"title":"Discontinuous deformation analysis (DDA) simulations of rock fracturing failures by Voronoi sub-block elements with refinement","authors":"Youjun Ning , Daofu Zhang , Xinlian Liu","doi":"10.1016/j.enganabound.2025.106172","DOIUrl":"10.1016/j.enganabound.2025.106172","url":null,"abstract":"<div><div>Discontinuous deformation analysis (DDA), a representative discontinuum-based numerical method, has been successfully developed to simulate the important problem of fracturing failures in rock mechanics through a sub-block approach. In the present work, a refinement algorithm of the Voronoi sub-block elements for DDA simulations of rock fracturing is proposed to simultaneously improve the simulation accuracy and control the computation scale through local refinement of the elements. The algorithm includes major procedures of triangular finite element division, random point distribution, Delaunay triangle generation, and Voronoi sub-block element generation. Static and dynamic simulation examples of disc, rectangular and Hopkinson specimens are simulated and quantitatively or qualitatively verified by theoretical, experimental or other numerical simulation results. Blasting-induced rock fracturing failures are simulated as an application example of the Voronoi sub-block DDA with element refinement, in which the effects of blasting shock wave and blasting gas pressure on the rock breakage ability and patterns are specially investigated to reveal the rock blasting characteristics and mechanism. All the simulation examples well indicate the capability and effectiveness to simulate rock fracturing failures by the sub-block DDA with the proposed Voronoi sub-block element refinement algorithm.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"173 ","pages":"Article 106172"},"PeriodicalIF":4.2,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of enhancing the electromagnetic (EM) scattering for almost transparent nanotubes via shape modification of their cross section, is studied in this work. An isogeometric analysis approach, in a boundary element method setting, is employed to evaluate the local electric field, which is expressed in terms of the exact same basis functions utilized in the geometric representation of the cylinder boundary. In this way, the overall scattering power becomes computable via proper integration of the far field magnitude around the nanotube and shape optimization can be directly performed with the aim of maximizing the scattering enhancement compared to an equiareal circular nanotube. The optimization framework uses: (i) a hybrid approach combining global optimizers with gradient-based local algorithms for accurately determining the shape at the final stages, (ii) a series of parametric models generating valid non-self-intersecting nanotube shapes, and (iii) an isogeometric-enabled boundary element method solver approximating the value of the electric field with high accuracy. The optimized nanotube shapes give much higher total scattering response than their circular counterparts. In a wide range of operating conditions (such as nanotube’s electric conductivity or cross section area), the optimized shapes assumed a distinct spiky shape which was further studied with respect to the direction of excitation. Apart from boosting scattering for quasi-transparent nanotubes, the developed methodology can be adapted to solve the inverse problem, namely, determining the nanotube shape from its scattering signal, as well as extended to address similar problems with finite arrays of nanotubes comprising EM metasurfaces.
{"title":"Shaping quasi-transparent nanotubes into Maximally strong EM scatterers","authors":"Nurkeldi Iznat , Madeniyet Bespayev , Yerassyl Turarov , Constantinos Valagiannopoulos , Konstantinos Kostas","doi":"10.1016/j.enganabound.2025.106153","DOIUrl":"10.1016/j.enganabound.2025.106153","url":null,"abstract":"<div><div>The problem of enhancing the electromagnetic (EM) scattering for almost transparent nanotubes via shape modification of their cross section, is studied in this work. An isogeometric analysis approach, in a boundary element method setting, is employed to evaluate the local electric field, which is expressed in terms of the exact same basis functions utilized in the geometric representation of the cylinder boundary. In this way, the overall scattering power becomes computable via proper integration of the far field magnitude around the nanotube and shape optimization can be directly performed with the aim of maximizing the scattering enhancement compared to an equiareal circular nanotube. The optimization framework uses: (i) a hybrid approach combining global optimizers with gradient-based local algorithms for accurately determining the shape at the final stages, (ii) a series of parametric models generating valid non-self-intersecting nanotube shapes, and (iii) an isogeometric-enabled boundary element method solver approximating the value of the electric field with high accuracy. The optimized nanotube shapes give much higher total scattering response than their circular counterparts. In a wide range of operating conditions (such as nanotube’s electric conductivity or cross section area), the optimized shapes assumed a distinct spiky shape which was further studied with respect to the direction of excitation. Apart from boosting scattering for quasi-transparent nanotubes, the developed methodology can be adapted to solve the inverse problem, namely, determining the nanotube shape from its scattering signal, as well as extended to address similar problems with finite arrays of nanotubes comprising EM metasurfaces.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"173 ","pages":"Article 106153"},"PeriodicalIF":4.2,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-14DOI: 10.1016/j.enganabound.2025.106155
Quansheng Zang , Yanhui Zhong , Wenbin Ye , Jun Liu , Bin Li , Fan Yang , Songtao Li
Within the framework of scaled boundary finite element method (SBFEM) and inspired by isogeometric analysis (IGA), the NURBS-enhanced semi-analytical method, referred to as the scaled boundary isogeometric analysis (SBIGA), is extended for solving nonlinear liquid sloshing analysis in storage structures. This method leverages the advantages of Non-Uniform Rational B-Splines (NURBS), offering a highly efficient and accurate solution. NURBS provides high-order continuity, making it particularly suitable for capturing the smoothness of free liquid surfaces in sloshing phenomena. Compared to traditional Lagrangian elements, the proposed approach efficiently utilizes control points, enabling accurate geometric representation with fewer degrees of freedom. A semi-Lagrangian algorithm establishes a global fixed coordinate system and a local system moving with the structure, enabling flexible mesh updating and efficient computation. Based on potential flow theory, the SBIGA equations for nonlinear liquid sloshing are derived using the weighted residual method, with dual variables introduced. The eigenfunction expansion method solves the equations, and the fourth-order Runge–Kutta method is applied for time integration. This approach combines the strengths of SBFEM and IGA, featuring boundary-only discretization, radial analytical solutions, and precise geometric boundary representation. Meanwhile, the present SBIGA does not require fundamental solutions as in traditional methods, nor does it require handling corner singularities or singular integrals as in boundary element methods. Numerical examples validate the accuracy of the present model, followed by analyses of the sloshing reduction effects of horizontal and vertical baffles in rectangular liquid storage structures. Finally, a U-shaped aqueduct under seismic loading is examined to evaluate the effectiveness of baffles in reducing sloshing responses in complex structures under seismic conditions.
{"title":"A NURBS-enhanced semi-analytical method for nonlinear liquid sloshing analysis in liquid storage structures with various baffles","authors":"Quansheng Zang , Yanhui Zhong , Wenbin Ye , Jun Liu , Bin Li , Fan Yang , Songtao Li","doi":"10.1016/j.enganabound.2025.106155","DOIUrl":"10.1016/j.enganabound.2025.106155","url":null,"abstract":"<div><div>Within the framework of scaled boundary finite element method (SBFEM) and inspired by isogeometric analysis (IGA), the NURBS-enhanced semi-analytical method, referred to as the scaled boundary isogeometric analysis (SBIGA), is extended for solving nonlinear liquid sloshing analysis in storage structures. This method leverages the advantages of Non-Uniform Rational B-Splines (NURBS), offering a highly efficient and accurate solution. NURBS provides high-order continuity, making it particularly suitable for capturing the smoothness of free liquid surfaces in sloshing phenomena. Compared to traditional Lagrangian elements, the proposed approach efficiently utilizes control points, enabling accurate geometric representation with fewer degrees of freedom. A semi-Lagrangian algorithm establishes a global fixed coordinate system and a local system moving with the structure, enabling flexible mesh updating and efficient computation. Based on potential flow theory, the SBIGA equations for nonlinear liquid sloshing are derived using the weighted residual method, with dual variables introduced. The eigenfunction expansion method solves the equations, and the fourth-order Runge–Kutta method is applied for time integration. This approach combines the strengths of SBFEM and IGA, featuring boundary-only discretization, radial analytical solutions, and precise geometric boundary representation. Meanwhile, the present SBIGA does not require fundamental solutions as in traditional methods, nor does it require handling corner singularities or singular integrals as in boundary element methods. Numerical examples validate the accuracy of the present model, followed by analyses of the sloshing reduction effects of horizontal and vertical baffles in rectangular liquid storage structures. Finally, a U-shaped aqueduct under seismic loading is examined to evaluate the effectiveness of baffles in reducing sloshing responses in complex structures under seismic conditions.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"173 ","pages":"Article 106155"},"PeriodicalIF":4.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-14DOI: 10.1016/j.enganabound.2025.106154
Tadej Dobravec , Boštjan Mavrič , Božidar Šarler
This paper studies and assesses different Neumann boundary conditions (BC) implementations in the radial basis function generated finite difference (RBF-FD) method. We analyse four BC implementations by solving a phase-field model for single dendrite growth in supercooled pure melts. In the first BC implementation, the BC are satisfied when constructing interpolation problems in the local support domains near the boundary. In the second one, the BC are satisfied by solving an additional system of linear equations for the field values in the boundary nodes. In the third one, we add a layer of ghost nodes to the boundary nodes; the BC are satisfied by solving an additional system of linear equations for the field values in the ghost nodes. The fourth BC implementation uses the same node distribution as the third one; since we are dealing with the symmetric BC, we set the values in the ghost nodes by direct mirroring. We analyse the influence of the size of a local support domain and the type of node distribution (regular/scattered) on the accuracy. We show that using ghost nodes is recommended to consider Neumann BC in the RBF-FD method accurately when solving phase-field models for dendritic growth.
{"title":"A study on different implementations of Neumann boundary conditions in the meshless RBF-FD method for the phase-field modelling of dendrite growth","authors":"Tadej Dobravec , Boštjan Mavrič , Božidar Šarler","doi":"10.1016/j.enganabound.2025.106154","DOIUrl":"10.1016/j.enganabound.2025.106154","url":null,"abstract":"<div><div>This paper studies and assesses different Neumann boundary conditions (BC) implementations in the radial basis function generated finite difference (RBF-FD) method. We analyse four BC implementations by solving a phase-field model for single dendrite growth in supercooled pure melts. In the first BC implementation, the BC are satisfied when constructing interpolation problems in the local support domains near the boundary. In the second one, the BC are satisfied by solving an additional system of linear equations for the field values in the boundary nodes. In the third one, we add a layer of ghost nodes to the boundary nodes; the BC are satisfied by solving an additional system of linear equations for the field values in the ghost nodes. The fourth BC implementation uses the same node distribution as the third one; since we are dealing with the symmetric BC, we set the values in the ghost nodes by direct mirroring. We analyse the influence of the size of a local support domain and the type of node distribution (regular/scattered) on the accuracy. We show that using ghost nodes is recommended to consider Neumann BC in the RBF-FD method accurately when solving phase-field models for dendritic growth.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"173 ","pages":"Article 106154"},"PeriodicalIF":4.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-14DOI: 10.1016/j.enganabound.2025.106152
Maria De Lauretis , Elena Haller , Daniele Romano , Giulio Antonini , Jonas Ekman , Ivana Kovačević-Badstübner , Ulrike Grossner
In computational electromagnetics, numerical methods are generally optimized for triangular or tetrahedral meshes. However, typical objects of general interest in electronics, such as diode packages or antennas, have a Manhattan-type geometry that can be modeled with orthogonal and rectangular meshes. The advantage of orthogonal meshes is that they allow analytic solutions of the integral equations. In this work, we optimize the decoupling of the integrals used in the Surface formulation of the Partial Element Equivalent Circuit (S-PEEC) method for rectangular meshes. We consider a previously proposed decoupling strategy, and we lighten the underlying math by generalizing it. The new method shows improved accuracy and computational time because the number of decoupling integrals is generally reduced. The new S-PEEC method with decoupling integrals is named S-PEEC-DI. The S-PEEC-DI method is tested on a realistic diode package and compared with the volumetric PEEC (V-PEEC) and two well-known commercial solvers.
{"title":"S-PEEC-DI: Surface Partial Element Equivalent Circuit method with decoupling integrals","authors":"Maria De Lauretis , Elena Haller , Daniele Romano , Giulio Antonini , Jonas Ekman , Ivana Kovačević-Badstübner , Ulrike Grossner","doi":"10.1016/j.enganabound.2025.106152","DOIUrl":"10.1016/j.enganabound.2025.106152","url":null,"abstract":"<div><div>In computational electromagnetics, numerical methods are generally optimized for triangular or tetrahedral meshes. However, typical objects of general interest in electronics, such as diode packages or antennas, have a Manhattan-type geometry that can be modeled with orthogonal and rectangular meshes. The advantage of orthogonal meshes is that they allow analytic solutions of the integral equations. In this work, we optimize the decoupling of the integrals used in the Surface formulation of the Partial Element Equivalent Circuit (S-PEEC) method for rectangular meshes. We consider a previously proposed decoupling strategy, and we lighten the underlying math by generalizing it. The new method shows improved accuracy and computational time because the number of decoupling integrals is generally reduced. The new S-PEEC method with decoupling integrals is named S-PEEC-DI. The S-PEEC-DI method is tested on a realistic diode package and compared with the volumetric PEEC (V-PEEC) and two well-known commercial solvers.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"173 ","pages":"Article 106152"},"PeriodicalIF":4.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143402998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号