An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds.The present paper has two parts.The first part investigates topology of the isoparametric fa...An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds.The present paper has two parts.The first part investigates topology of the isoparametric families,namely the homotopy,homeomorphism,or diffeomorphism types,parallelizability,as well as the Lusternik-Schnirelmann category.This part extends substantially the results of Wang(J Differ Geom 27:55-66,1988).The second part is concerned with their curvatures;more precisely,we determine when they have non-negative sectional curvatures or positive Ricci curvatures with the induced metric.展开更多
The projection matrix model is used to describe the physical relationship between reconstructed object and projection.Such a model has a strong influence on projection and backprojection,two vital operations in iterat...The projection matrix model is used to describe the physical relationship between reconstructed object and projection.Such a model has a strong influence on projection and backprojection,two vital operations in iterative computed tomographic reconstruction.The distance-driven model（DDM） is a state-of-the-art technology that simulates forward and back projections.This model has a low computational complexity and a relatively high spatial resolution;however,it includes only a few methods in a parallel operation with a matched model scheme.This study introduces a fast and parallelizable algorithm to improve the traditional DDM for computing the parallel projection and backprojection operations.Our proposed model has been implemented on a GPU（graphic processing unit） platform and has achieved satisfactory computational efficiency with no approximation.The runtime for the projection and backprojection operations with our model is approximately 4.5 s and 10.5 s per loop,respectively,with an image size of 256×256×256 and 360 projections with a size of 512×512.We compare several general algorithms that have been proposed for maximizing GPU efficiency by using the unmatched projection/backprojection models in a parallel computation.The imaging resolution is not sacrificed and remains accurate during computed tomographic reconstruction.展开更多
We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition. We p...We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition. We present an accurate convergence analysis of the algorithm without using the big O notation. We also propose a general framework based on implicit rational transformations which allows us to make connections with several existing algorithms and to derive classes of extensions to our basic algorithm with faster convergence rates. Several numerical examples are given which compare some aspects of the existing algorithms and the new algorithms.展开更多
In this work the authors simulate a contaminant transport problem in three dimensions that takes place in the soil of waste disposals. Such problem is modeled by a diffusion-dominated equation. The solution of this eq...In this work the authors simulate a contaminant transport problem in three dimensions that takes place in the soil of waste disposals. Such problem is modeled by a diffusion-dominated equation. The solution of this equation is addressed by using mixed finite element method for the spatial discretization of the equation. The resulting linear algebraic system is handled by an iterative domain decomposition procedure. This procedure is naturally parallelizable, and permits to implement computational codes in distributed memory machines in order to save on CPU time. Numerical results of the serial and parallel codes were compared with experimental results, and their performance measures were evaluated. The results indicate that the parallelizable procedure is an efficient tool for performing simulations of the problem.展开更多
基金partially supported by the NSFC(Nos.11722101,11871282,11931007)BNSF(Z190003)+1 种基金Nankai Zhide FoundationBeijing Institute of Technology Research Fund Program for Young Scholars.
文摘An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds.The present paper has two parts.The first part investigates topology of the isoparametric families,namely the homotopy,homeomorphism,or diffeomorphism types,parallelizability,as well as the Lusternik-Schnirelmann category.This part extends substantially the results of Wang(J Differ Geom 27:55-66,1988).The second part is concerned with their curvatures;more precisely,we determine when they have non-negative sectional curvatures or positive Ricci curvatures with the induced metric.
基金supported by the National High Technology Research and Development Program of China(Grant No.2012AA011603)the National Natural Science Foundation of China(Grant No.61372172)
文摘The projection matrix model is used to describe the physical relationship between reconstructed object and projection.Such a model has a strong influence on projection and backprojection,two vital operations in iterative computed tomographic reconstruction.The distance-driven model（DDM） is a state-of-the-art technology that simulates forward and back projections.This model has a low computational complexity and a relatively high spatial resolution;however,it includes only a few methods in a parallel operation with a matched model scheme.This study introduces a fast and parallelizable algorithm to improve the traditional DDM for computing the parallel projection and backprojection operations.Our proposed model has been implemented on a GPU（graphic processing unit） platform and has achieved satisfactory computational efficiency with no approximation.The runtime for the projection and backprojection operations with our model is approximately 4.5 s and 10.5 s per loop,respectively,with an image size of 256×256×256 and 360 projections with a size of 512×512.We compare several general algorithms that have been proposed for maximizing GPU efficiency by using the unmatched projection/backprojection models in a parallel computation.The imaging resolution is not sacrificed and remains accurate during computed tomographic reconstruction.
文摘We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition. We present an accurate convergence analysis of the algorithm without using the big O notation. We also propose a general framework based on implicit rational transformations which allows us to make connections with several existing algorithms and to derive classes of extensions to our basic algorithm with faster convergence rates. Several numerical examples are given which compare some aspects of the existing algorithms and the new algorithms.
文摘In this work the authors simulate a contaminant transport problem in three dimensions that takes place in the soil of waste disposals. Such problem is modeled by a diffusion-dominated equation. The solution of this equation is addressed by using mixed finite element method for the spatial discretization of the equation. The resulting linear algebraic system is handled by an iterative domain decomposition procedure. This procedure is naturally parallelizable, and permits to implement computational codes in distributed memory machines in order to save on CPU time. Numerical results of the serial and parallel codes were compared with experimental results, and their performance measures were evaluated. The results indicate that the parallelizable procedure is an efficient tool for performing simulations of the problem.
