Recent development of structure-preserving geometric particle-in-cell (PIC) algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to ca...Recent development of structure-preserving geometric particle-in-cell (PIC) algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential (or integro-differential) equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.展开更多
Gray cross correlation matching technique is adopted to extract candidate matches with gray cross correlation coefficients less than some certain range of maximal correlation coefficient called multi-peak candidate ma...Gray cross correlation matching technique is adopted to extract candidate matches with gray cross correlation coefficients less than some certain range of maximal correlation coefficient called multi-peak candidate matches. Multi-peak candidates are extracted corresponding to three closest feature points at first. The corresponding multi-peak candidate matches are used to construct the model polygon. Correspondence is determined based on the local geometric relations between the three feature points and the multi-peak candidates. The disparity test and the global consistency checkout are applied to eliminate the remaining ambiguous matches that are not removed by the local geometric relational test. Experimental results show that the proposed algorithm is feasible and accurate.展开更多
We propose a novel spatial phase-shifting interferometry that exploits a genetic algorithm to compensate for geometric errors. Spatial phase-shifting interferometry is more suitable for measuring objects with properti...We propose a novel spatial phase-shifting interferometry that exploits a genetic algorithm to compensate for geometric errors. Spatial phase-shifting interferometry is more suitable for measuring objects with properties that change rapidly in time than the temporal phase-shifting interferometry. However, it is more susceptible to the geometric errors since the positions at which interferograms are collected are different. In this letter, we propose a spatial phase-shifting interferometry with separate paths for object and reference waves. Also, the object wave estimate is parameterized in terms of geometric errors, and the error is compensated by using a genetic algorithm.展开更多
Ribs and fans are interesting geometric entities that are derived from a given Bézier curve or surface based on the recent theory of rib and fan decomposition. In this paper, we present some of new geometric prop...Ribs and fans are interesting geometric entities that are derived from a given Bézier curve or surface based on the recent theory of rib and fan decomposition. In this paper, we present some of new geometric properties of ribs and fans for a Bézier curve including composite fans, rib-invariant deformation, and fan-continuity in subdivision. We also give some examples for the presented properties.展开更多
A geometric intrinsic pre-processing algorithm(GPA for short)for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023).Different from traditional preconditi...A geometric intrinsic pre-processing algorithm(GPA for short)for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023).Different from traditional preconditioning,the authors apply the intrinsic geometric invariance,the Grid matrix G and the discrete PDE mass matrix B,stiff matrix A satisfies commutative operator BG=GB and AG=GA,where G satisfies G^(m)=I,m<<dim(G).A large scale system solvers can be replaced to a more smaller block-solver as a pretreatment in real or complex domain.In this paper,the authors expand their research to 2-D and 3-D mathematical physical equations over more wide polyhedron grids such as triangle,square,tetrahedron,cube,and so on.They give the general form of pre-processing matrix,theory and numerical test of GPA.The conclusion that“the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron”is obtained through research,and it is further found that“commutative of grid mesh matrix and mass matrix is an important basis for the feasibility and reliability of GPA algorithm”.展开更多
The theory and methods of digital geometry processing has been research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce so...The theory and methods of digital geometry processing has been research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient, Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.展开更多
基金supported by National Natural Science Foundation of China (NSFC-11775219, 11775222, 11505186, 11575185 and 11575186)the National Key Research and Development Program (2016YFA0400600, 2016YFA0400601 and 2016YFA0400602)+3 种基金the ITER-China Program (2015GB111003, 2014GB124005)Chinese Scholar Council (201506340103)China Postdoctoral Science Foundation (2017LH002)the GeoA lgorithmic Plasma Simulator (GAPS) Project
文摘Recent development of structure-preserving geometric particle-in-cell (PIC) algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential (or integro-differential) equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.
基金the Leading Academic Discipline Project of Shanghai Educational Committee of China(J50104)the Shanghai Leading Academic Disciplines of China(T0102)
文摘Gray cross correlation matching technique is adopted to extract candidate matches with gray cross correlation coefficients less than some certain range of maximal correlation coefficient called multi-peak candidate matches. Multi-peak candidates are extracted corresponding to three closest feature points at first. The corresponding multi-peak candidate matches are used to construct the model polygon. Correspondence is determined based on the local geometric relations between the three feature points and the multi-peak candidates. The disparity test and the global consistency checkout are applied to eliminate the remaining ambiguous matches that are not removed by the local geometric relational test. Experimental results show that the proposed algorithm is feasible and accurate.
基金supported by the National Research Foundation and the Ministry of Education, Science and Engineering of Korea through the National Creative Re-search Initiative Program (R16-2007-030-01001-0)
文摘We propose a novel spatial phase-shifting interferometry that exploits a genetic algorithm to compensate for geometric errors. Spatial phase-shifting interferometry is more suitable for measuring objects with properties that change rapidly in time than the temporal phase-shifting interferometry. However, it is more susceptible to the geometric errors since the positions at which interferograms are collected are different. In this letter, we propose a spatial phase-shifting interferometry with separate paths for object and reference waves. Also, the object wave estimate is parameterized in terms of geometric errors, and the error is compensated by using a genetic algorithm.
文摘Ribs and fans are interesting geometric entities that are derived from a given Bézier curve or surface based on the recent theory of rib and fan decomposition. In this paper, we present some of new geometric properties of ribs and fans for a Bézier curve including composite fans, rib-invariant deformation, and fan-continuity in subdivision. We also give some examples for the presented properties.
基金supported by the Basic Research Plan on High Performance Computing of Institute of Software(No.ISCAS-PYFX-202302)the National Key R&D Program of China(No.2020YFB1709502)the Advanced Space Propulsion Laboratory of BICE and Beijing Engineering Research Center of Efficient and Green Aerospace Propulsion Technology(No.Lab ASP-2019-03)。
文摘A geometric intrinsic pre-processing algorithm(GPA for short)for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023).Different from traditional preconditioning,the authors apply the intrinsic geometric invariance,the Grid matrix G and the discrete PDE mass matrix B,stiff matrix A satisfies commutative operator BG=GB and AG=GA,where G satisfies G^(m)=I,m<<dim(G).A large scale system solvers can be replaced to a more smaller block-solver as a pretreatment in real or complex domain.In this paper,the authors expand their research to 2-D and 3-D mathematical physical equations over more wide polyhedron grids such as triangle,square,tetrahedron,cube,and so on.They give the general form of pre-processing matrix,theory and numerical test of GPA.The conclusion that“the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron”is obtained through research,and it is further found that“commutative of grid mesh matrix and mass matrix is an important basis for the feasibility and reliability of GPA algorithm”.
基金The research work of this paper is supported by the National Natural Science Foundation of China under Grant No. 60021201 the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China under Grant No. 705027 and the National Grand Fundamental Research 973 Program of China under Grant No. 2002CB312101.
文摘The theory and methods of digital geometry processing has been research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient, Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.