Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement...Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.展开更多
In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state pr...In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.展开更多
The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is ...The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is examined. With regard to its problem of possible producing illegal elements, this paper proposes a modified smoothing scheme with a constrained optimization model for tetrahedral mesh quality improvement. The constrained optimization model is converted to an unconstrained one and then solved by integrating chaos search and BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm efficiently. Quality improvement for tetrahedral mesh is finally achieved by alternately applying the presented smoothing scheme and re-triangulation. Some testing examples are given to demonstrate the effectiveness of the proposed approach.展开更多
For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions w...For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions where the physical variables vary violently(for example,near the shock waves or in the boundary layers)and larger elements are expected for the regions where the solution is smooth.h-adaptive mesh has been widely used for complex flows.However,there are two difficulties when employing h-adaptivity for high-order discontinuous Galerkin(DG)methods.First,locally curved elements are required to precisely match the solid boundary,which significantly increases the difficulty to conduct the"refining"and"coarsening"operations since the curved information has to be maintained.Second,h-adaptivity could break the partition balancing,which would significantly affect the efficiency of parallel computing.In this paper,a robust and automatic h-adaptive method is developed for high-order DG methods on locally curved tetrahedral mesh,for which the curved geometries are maintained during the h-adaptivity.Furthermore,the reallocating and rebalancing of the computational loads on parallel clusters are conducted to maintain the parallel efficiency.Numerical results indicate that the introduced h-adaptive method is able to generate more reasonable mesh according to the structure of flow-fields.展开更多
This work introduces a scalable and efficient topological structure for tetrahedral and hexahedral meshes. The design of the data structure aims at maximal flexibility and high performance. It provides a high scalabil...This work introduces a scalable and efficient topological structure for tetrahedral and hexahedral meshes. The design of the data structure aims at maximal flexibility and high performance. It provides a high scalability by using hierarchical representa-tions of topological elements. The proposed data structure is array-based, and it is a compact representation of the half-edge data structure for volume elements and half-face data structure for volumetric meshes. This guarantees constant access time to the neighbors of the topological elements. In addition, an open-source implementation named Open Volumetric Mesh （OVM） of the pro-posed data structure is written in C＋＋ using generic programming concepts.展开更多
A novel VOF-type volume-tracking method for two-dimensional free-surface flows based on the unstructured triangular mesh is presented. Owing to the inherent merit of the unstructured triangular mesh in fitting curved ...A novel VOF-type volume-tracking method for two-dimensional free-surface flows based on the unstructured triangular mesh is presented. Owing to the inherent merit of the unstructured triangular mesh in fitting curved boundaries, this method can handle the free-surface problems with complex geometries accurately and directly, without introducing any complicated boundary treatment or artificial diffusion. The method solves the volume transport equation geometrically through the Modified Lagrangian-Eulerian Re-map （MLER） method, which is applied to advective fluid volumes. Moreover, the PLIC method is adopted to give a second-order reconstructed interface approximation. To validate this method, two advection tests were performed for the establishment of the accuracy and convergence rate of the solutions. Numerical results for these complex tests provide convincing evidence for the excellent solution quality and fidelity of the method.展开更多
Curvatures are important geometric attributes of surfaces. There are many applications that require as a first step the accurate estimation of curvatures at arbitrary vertices on a triangulated surface. Chen and Schmi...Curvatures are important geometric attributes of surfaces. There are many applications that require as a first step the accurate estimation of curvatures at arbitrary vertices on a triangulated surface. Chen and Schmitt (1992) and Taubin (1995) presented two simple methods to estimate principal curvatures. They used circular arcs to approximate the normal curvature. We find this may cause large error in some cases. In this paper, we describe a more accurate method to estimate the normal curvature, and present a novel algorithm to estimate principal curvatures by simplifying the Chen and Schmitt’s method. Some comparison results are also shown in this paper.展开更多
We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a...We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on centroidal Voronoi tessellations (CVTs). The accuracy and good quality of the output triangular mesh are achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.展开更多
We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameteri...We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.展开更多
In the process of numerical control machining simulation,the workpiece surface is usually described with the uniform triangular mesh model.To alleviate the contradiction between the simulation speed and accuracy in th...In the process of numerical control machining simulation,the workpiece surface is usually described with the uniform triangular mesh model.To alleviate the contradiction between the simulation speed and accuracy in this model,two improved methods,i.e.,the local refinement triangular mesh modeling method and the adaptive triangular mesh modeling method were presented.The simulation results show that when the final shape of the workpiece is known and its mathematic representation is simple,the local refinement triangular mesh modeling method is preferred;when the final shape of the workpiece is unknown and its mathematic description is complicated,the adaptive triangular mesh modeling method is more suitable.The experimental results show that both methods are more targeted and practical and can meet the requirements of real-time and precision in simulation.展开更多
The characteristic of Quaternary codes is analyzed. The rule of distinguishing triangle direction is given out. An algorithm of neighbor finding by decomposing the Quaternary code from back to front is presented in th...The characteristic of Quaternary codes is analyzed. The rule of distinguishing triangle direction is given out. An algorithm of neighbor finding by decomposing the Quaternary code from back to front is presented in this paper. The contrastive analysis of time complexity between this algorithm and Bartholdi＇s algorithm is approached. The result illustrates that the average consumed time of this algorithm is about 23.66% of Bartholdi＇s algorithm.展开更多
In some scattered point cloud triangular mesh restoration algorithm, small triangular mesh holes problem will often affect the quality of the model. For small holes at the details, this paper propose a method for iden...In some scattered point cloud triangular mesh restoration algorithm, small triangular mesh holes problem will often affect the quality of the model. For small holes at the details, this paper propose a method for identifying and extracting hollow edge,and use a triangle growth way based on boundary edge angle to fill the empty void. First, according the relationship of the point, side and face of the triangle mesh model to identify the hole, then extracting the holes boundary edge and classifying it. Finally, using a triangle growth method based on holes boundary edge angle to fill each small holes separated from the boundary. Compared with other algorithm of filling holes, this method is high efficiency for small holes of smooth surface,and itimprovesthe quality of the triangular mesh model.展开更多
A new method as a post-processing step is presented to improve the shape quality of triangular meshes, which uses a topological clean up procedure and discrete smoothing interpolate (DSI) algorithm together. T...A new method as a post-processing step is presented to improve the shape quality of triangular meshes, which uses a topological clean up procedure and discrete smoothing interpolate (DSI) algorithm together. This method can improve the angle distribution of mesh element. while keeping the resulting meshes conform to the predefined constraints which are inputted as a PSLG.展开更多
The view prediction is an important step in stereo/multiview video coding, wherein, disparity estil mation （DE） is a key and difficult operation. DE algorithms usually require enormous computing power. A fast DE alg...The view prediction is an important step in stereo/multiview video coding, wherein, disparity estil mation （DE） is a key and difficult operation. DE algorithms usually require enormous computing power. A fast DE algorithm based on Delaunay triangulation （DT） is proposed. First, a flexible and content adaptive DT mesh is established on a target frame by an iterative split-merge algorithm. Second, DE on DT nodes are performed in a three-stage algorithm, which gives the majority of nodes a good estimate of the disparity vectors （DV）, by removing unreliable nodes due to occlusion, and forcing the minority of ＇problematic nodes＇ to be searched again, within their umbrella-shaped polygon, to the best. Finally, the target view is predicted by using affine transformation. Experimental results show that the proposed algorithm can give a satisfactory DE with less computational cost.展开更多
A stabilizer-free weak Galerkin(SFWG)finite element method was introduced and analyzed in Ye and Zhang(SIAM J.Numer.Anal.58:2572–2588,2020)for the biharmonic equation,which has an ultra simple finite element formulat...A stabilizer-free weak Galerkin(SFWG)finite element method was introduced and analyzed in Ye and Zhang(SIAM J.Numer.Anal.58:2572–2588,2020)for the biharmonic equation,which has an ultra simple finite element formulation.This work is a continuation of our investigation of the SFWG method for the biharmonic equation.The new SFWG method is highly accurate with a convergence rate of four orders higher than the optimal order of convergence in both the energy norm and the L^(2)norm on triangular grids.This new method also keeps the formulation that is symmetric,positive definite,and stabilizer-free.Four-order superconvergence error estimates are proved for the corresponding SFWG finite element solutions in a discrete H^(2)norm.Superconvergence of four orders in the L^(2)norm is also derived for k≥3,where k is the degree of the approximation polynomial.The postprocessing is proved to lift a P_(k)SFWG solution to a P_(k+4)solution elementwise which converges at the optimal order.Numerical examples are tested to verify the theor ies.展开更多
A new algorithm called the weighted least square discrete parameterization (WLSDP) is presented for the parameterization of triangular meshes over a convex planar region. This algorithm is the linear combination of th...A new algorithm called the weighted least square discrete parameterization (WLSDP) is presented for the parameterization of triangular meshes over a convex planar region. This algorithm is the linear combination of the discrete Conformal mapping(DCM) and the discrete Authalic mapping(DAM). It provides the good properties of both DCM and DAM, such as robustness and low distortion. By adjusting the scaling factor q embedded in the WLSDP, satisfactory parameterizations in different special applications can be achieved.展开更多
This paper is an introduction to mesh based generated reluctance network modeling using triangular elements.Many contributions on mesh based generated reluctance networks using rectangular shaped elements have been pu...This paper is an introduction to mesh based generated reluctance network modeling using triangular elements.Many contributions on mesh based generated reluctance networks using rectangular shaped elements have been published,but very few on those generated from a mesh using triangular elements.The use of triangular elements is aimed at extending the application of the approach to any shape of modeled devices.Basic concepts of the approach are presented in the case of electromagnetic devices.The procedure for coding the approach in the case of a flat linear permanent magnet machine is presented.Codes developed under MATLAB environment are also included.展开更多
基金supported by the 973 Program of China 2005CB321702China NSF 10531080.
文摘Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.
基金supported by the NSFC Grant No.11872210 and Grant No.MCMS-I-0120G01Chi-Wang Shu:Research is supported by the AFOSR Grant FA9550-20-1-0055 and the NSF Grant DMS-2010107Jianxian Qiu:Research is supported by the NSFC Grant No.12071392.
文摘In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.
文摘The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is examined. With regard to its problem of possible producing illegal elements, this paper proposes a modified smoothing scheme with a constrained optimization model for tetrahedral mesh quality improvement. The constrained optimization model is converted to an unconstrained one and then solved by integrating chaos search and BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm efficiently. Quality improvement for tetrahedral mesh is finally achieved by alternately applying the presented smoothing scheme and re-triangulation. Some testing examples are given to demonstrate the effectiveness of the proposed approach.
基金supported by the funding of the Key Laboratory of Aerodynamic Noise Control(No.ANCL20190103)the State Key Laboratory of Aerodynamics(No.SKLA20180102)+1 种基金the Aeronautical Science Foundation of China(Nos.2018ZA52002,2019ZA052011)the National Natural Science Foundation of China(Nos.61672281,61732006)。
文摘For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions where the physical variables vary violently(for example,near the shock waves or in the boundary layers)and larger elements are expected for the regions where the solution is smooth.h-adaptive mesh has been widely used for complex flows.However,there are two difficulties when employing h-adaptivity for high-order discontinuous Galerkin(DG)methods.First,locally curved elements are required to precisely match the solid boundary,which significantly increases the difficulty to conduct the"refining"and"coarsening"operations since the curved information has to be maintained.Second,h-adaptivity could break the partition balancing,which would significantly affect the efficiency of parallel computing.In this paper,a robust and automatic h-adaptive method is developed for high-order DG methods on locally curved tetrahedral mesh,for which the curved geometries are maintained during the h-adaptivity.Furthermore,the reallocating and rebalancing of the computational loads on parallel clusters are conducted to maintain the parallel efficiency.Numerical results indicate that the introduced h-adaptive method is able to generate more reasonable mesh according to the structure of flow-fields.
基金Supported by Fundamental Research Funds for the Central Universities(Nos.2013ZM087,2012zz0062,2012zz0063)Doctoral Fund of Ministry of Education of China(No.20130172120010)
文摘This work introduces a scalable and efficient topological structure for tetrahedral and hexahedral meshes. The design of the data structure aims at maximal flexibility and high performance. It provides a high scalability by using hierarchical representa-tions of topological elements. The proposed data structure is array-based, and it is a compact representation of the half-edge data structure for volume elements and half-face data structure for volumetric meshes. This guarantees constant access time to the neighbors of the topological elements. In addition, an open-source implementation named Open Volumetric Mesh （OVM） of the pro-posed data structure is written in C＋＋ using generic programming concepts.
文摘A novel VOF-type volume-tracking method for two-dimensional free-surface flows based on the unstructured triangular mesh is presented. Owing to the inherent merit of the unstructured triangular mesh in fitting curved boundaries, this method can handle the free-surface problems with complex geometries accurately and directly, without introducing any complicated boundary treatment or artificial diffusion. The method solves the volume transport equation geometrically through the Modified Lagrangian-Eulerian Re-map （MLER） method, which is applied to advective fluid volumes. Moreover, the PLIC method is adopted to give a second-order reconstructed interface approximation. To validate this method, two advection tests were performed for the establishment of the accuracy and convergence rate of the solutions. Numerical results for these complex tests provide convincing evidence for the excellent solution quality and fidelity of the method.
基金Project supported by the National Natural Science Foundation of China (No. 10371110) and the National Basic Research Program (973)of China (No. 2004CB318000)
文摘Curvatures are important geometric attributes of surfaces. There are many applications that require as a first step the accurate estimation of curvatures at arbitrary vertices on a triangulated surface. Chen and Schmitt (1992) and Taubin (1995) presented two simple methods to estimate principal curvatures. They used circular arcs to approximate the normal curvature. We find this may cause large error in some cases. In this paper, we describe a more accurate method to estimate the normal curvature, and present a novel algorithm to estimate principal curvatures by simplifying the Chen and Schmitt’s method. Some comparison results are also shown in this paper.
基金supported by the National Natural Science Foundation of China (No. 60773179)the National Basic Research Program (973) of China (No. 2004CB318000)
文摘We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on centroidal Voronoi tessellations (CVTs). The accuracy and good quality of the output triangular mesh are achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.
基金Project supported by the National Natural Science Foundation of China (Nos. 60673006 and 60533060)the Program for New Century Excellent Talents in University (No. NCET-05-0275), Chinathe IDeA Network of Biomedical Research Excellence Grant (No. 5P20RR01647206) from National Institutes of Health (NIH), USA
文摘We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.
基金Project(60772089) supported by the National Natural Science Foundation of ChinaProject(20080440939) supported by the China Postdoctoral Science Foundation
文摘In the process of numerical control machining simulation,the workpiece surface is usually described with the uniform triangular mesh model.To alleviate the contradiction between the simulation speed and accuracy in this model,two improved methods,i.e.,the local refinement triangular mesh modeling method and the adaptive triangular mesh modeling method were presented.The simulation results show that when the final shape of the workpiece is known and its mathematic representation is simple,the local refinement triangular mesh modeling method is preferred;when the final shape of the workpiece is unknown and its mathematic description is complicated,the adaptive triangular mesh modeling method is more suitable.The experimental results show that both methods are more targeted and practical and can meet the requirements of real-time and precision in simulation.
基金Supported by the Natural Science Foundation of China （No. 40771169 No.40471108 No.40701152）.
文摘The characteristic of Quaternary codes is analyzed. The rule of distinguishing triangle direction is given out. An algorithm of neighbor finding by decomposing the Quaternary code from back to front is presented in this paper. The contrastive analysis of time complexity between this algorithm and Bartholdi＇s algorithm is approached. The result illustrates that the average consumed time of this algorithm is about 23.66% of Bartholdi＇s algorithm.
文摘In some scattered point cloud triangular mesh restoration algorithm, small triangular mesh holes problem will often affect the quality of the model. For small holes at the details, this paper propose a method for identifying and extracting hollow edge,and use a triangle growth way based on boundary edge angle to fill the empty void. First, according the relationship of the point, side and face of the triangle mesh model to identify the hole, then extracting the holes boundary edge and classifying it. Finally, using a triangle growth method based on holes boundary edge angle to fill each small holes separated from the boundary. Compared with other algorithm of filling holes, this method is high efficiency for small holes of smooth surface,and itimprovesthe quality of the triangular mesh model.
文摘A new method as a post-processing step is presented to improve the shape quality of triangular meshes, which uses a topological clean up procedure and discrete smoothing interpolate (DSI) algorithm together. This method can improve the angle distribution of mesh element. while keeping the resulting meshes conform to the predefined constraints which are inputted as a PSLG.
基金supported by the National Natural Science Foundation of China (60472083 60872141)
文摘The view prediction is an important step in stereo/multiview video coding, wherein, disparity estil mation （DE） is a key and difficult operation. DE algorithms usually require enormous computing power. A fast DE algorithm based on Delaunay triangulation （DT） is proposed. First, a flexible and content adaptive DT mesh is established on a target frame by an iterative split-merge algorithm. Second, DE on DT nodes are performed in a three-stage algorithm, which gives the majority of nodes a good estimate of the disparity vectors （DV）, by removing unreliable nodes due to occlusion, and forcing the minority of ＇problematic nodes＇ to be searched again, within their umbrella-shaped polygon, to the best. Finally, the target view is predicted by using affine transformation. Experimental results show that the proposed algorithm can give a satisfactory DE with less computational cost.
文摘A stabilizer-free weak Galerkin(SFWG)finite element method was introduced and analyzed in Ye and Zhang(SIAM J.Numer.Anal.58:2572–2588,2020)for the biharmonic equation,which has an ultra simple finite element formulation.This work is a continuation of our investigation of the SFWG method for the biharmonic equation.The new SFWG method is highly accurate with a convergence rate of four orders higher than the optimal order of convergence in both the energy norm and the L^(2)norm on triangular grids.This new method also keeps the formulation that is symmetric,positive definite,and stabilizer-free.Four-order superconvergence error estimates are proved for the corresponding SFWG finite element solutions in a discrete H^(2)norm.Superconvergence of four orders in the L^(2)norm is also derived for k≥3,where k is the degree of the approximation polynomial.The postprocessing is proved to lift a P_(k)SFWG solution to a P_(k+4)solution elementwise which converges at the optimal order.Numerical examples are tested to verify the theor ies.
文摘A new algorithm called the weighted least square discrete parameterization (WLSDP) is presented for the parameterization of triangular meshes over a convex planar region. This algorithm is the linear combination of the discrete Conformal mapping(DCM) and the discrete Authalic mapping(DAM). It provides the good properties of both DCM and DAM, such as robustness and low distortion. By adjusting the scaling factor q embedded in the WLSDP, satisfactory parameterizations in different special applications can be achieved.
文摘This paper is an introduction to mesh based generated reluctance network modeling using triangular elements.Many contributions on mesh based generated reluctance networks using rectangular shaped elements have been published,but very few on those generated from a mesh using triangular elements.The use of triangular elements is aimed at extending the application of the approach to any shape of modeled devices.Basic concepts of the approach are presented in the case of electromagnetic devices.The procedure for coding the approach in the case of a flat linear permanent magnet machine is presented.Codes developed under MATLAB environment are also included.
