In this survey paper we report on recent developments of the hp-version of the boundary element method （BEM）. As model problems we consider weakly singular and hypersingular integral equations of the first kind on a...In this survey paper we report on recent developments of the hp-version of the boundary element method （BEM）. As model problems we consider weakly singular and hypersingular integral equations of the first kind on a planar, open surface. We show that the Galerkin solutions （computed with the hp-version on geometric meshes） converge exponentially fast towards the exact solutions of the integral equations. An hp-adaptive algorithm is given and the implementation of the hp-version BEM is discussed together with the choice of efficient preconditioners for the ill-conditioned boundary element stiffness matrices. We also comment on the use of the hp-version BEM for solving Signorini contact problems in linear elasticity where the contact conditions are enforced only on the discrete set of Gauss-Lobatto points. Numerical results are presented which underline the theoretical results.展开更多
The Klein-Cordon equation arises in many scientific areas of quantum mechanics and quantum field theory. In this paper a novel method based on spectral method and Jacobian free Newton method composed by generalized mi...The Klein-Cordon equation arises in many scientific areas of quantum mechanics and quantum field theory. In this paper a novel method based on spectral method and Jacobian free Newton method composed by generalized minimum residual （JFNGMRes） method with adaptive preconditioner will be introduced to solve nonlinear Klein-Gordon equation. In this work the nonlinear Klein-Gordon equation has been converted to a nonlinear system of algebraic equations using collocation method based on Bessel functions without any linearization, discretization and getting help of any other methods. Finally, by using JFNGMRes, solution of the nonlinear algebraic system will be achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the Klein-Gordon equation and compare our results with other methods.展开更多
Hypoxic preconditioning refers to the exposure of organisms, systems, organs, tissues or cells to moderate hypoxia/ischemia that results in increased resistance to a subsequent episode of severe hypoxia/ischemia. In t...Hypoxic preconditioning refers to the exposure of organisms, systems, organs, tissues or cells to moderate hypoxia/ischemia that results in increased resistance to a subsequent episode of severe hypoxia/ischemia. In this article, we review recent research based on a mouse model of repeated exposure to autohypoxia. Pre-exposure markedly increases the tolerance to or protection against hypoxic insult, and preserves the cellular structure of the brain. Furthermore, the hippocampal activity amplitude and frequency of electroencephalogram, latency of cortical somatosensory-evoked potential and spinal somatosensory-evoked potential progressively decrease, while spatial learning and memory improve. In the brain, detrimental neurochemicals such as free radicals are down-regulated, while beneficial ones such as adenosine are up-regulated. Also, antihypoxia factor（s） and gene（s） are activated. We propose that the tolerance and protective effects depend on energy conservation and plasticity triggered by exposure to hypoxia via oxygen-sensing transduction pathways and hypoxia-inducible factor-initiated cascades. A potential path for further research is the development of devices and pharma-ceuticals acting on antihypoxia factor（s） and gene（s） for the prevention and treatment of hypoxia and related syndromes.展开更多
In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimemsions. The new coarsening algorithm does not require ...In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimemsions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.展开更多
文摘In this survey paper we report on recent developments of the hp-version of the boundary element method （BEM）. As model problems we consider weakly singular and hypersingular integral equations of the first kind on a planar, open surface. We show that the Galerkin solutions （computed with the hp-version on geometric meshes） converge exponentially fast towards the exact solutions of the integral equations. An hp-adaptive algorithm is given and the implementation of the hp-version BEM is discussed together with the choice of efficient preconditioners for the ill-conditioned boundary element stiffness matrices. We also comment on the use of the hp-version BEM for solving Signorini contact problems in linear elasticity where the contact conditions are enforced only on the discrete set of Gauss-Lobatto points. Numerical results are presented which underline the theoretical results.
文摘The Klein-Cordon equation arises in many scientific areas of quantum mechanics and quantum field theory. In this paper a novel method based on spectral method and Jacobian free Newton method composed by generalized minimum residual （JFNGMRes） method with adaptive preconditioner will be introduced to solve nonlinear Klein-Gordon equation. In this work the nonlinear Klein-Gordon equation has been converted to a nonlinear system of algebraic equations using collocation method based on Bessel functions without any linearization, discretization and getting help of any other methods. Finally, by using JFNGMRes, solution of the nonlinear algebraic system will be achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the Klein-Gordon equation and compare our results with other methods.
基金supported by grants from the National Natural Science Foundation of China (3967087, 81060212, and 81160244)the Beijing Natural Science Foundation (7962009)+2 种基金the China Postdoctoral Science Foundation (20080430851)the Science Foundation of Shandong Province, China (ZR2010HM029)the Inner Mongolia Science Foundation (2010BS1104)
文摘Hypoxic preconditioning refers to the exposure of organisms, systems, organs, tissues or cells to moderate hypoxia/ischemia that results in increased resistance to a subsequent episode of severe hypoxia/ischemia. In this article, we review recent research based on a mouse model of repeated exposure to autohypoxia. Pre-exposure markedly increases the tolerance to or protection against hypoxic insult, and preserves the cellular structure of the brain. Furthermore, the hippocampal activity amplitude and frequency of electroencephalogram, latency of cortical somatosensory-evoked potential and spinal somatosensory-evoked potential progressively decrease, while spatial learning and memory improve. In the brain, detrimental neurochemicals such as free radicals are down-regulated, while beneficial ones such as adenosine are up-regulated. Also, antihypoxia factor（s） and gene（s） are activated. We propose that the tolerance and protective effects depend on energy conservation and plasticity triggered by exposure to hypoxia via oxygen-sensing transduction pathways and hypoxia-inducible factor-initiated cascades. A potential path for further research is the development of devices and pharma-ceuticals acting on antihypoxia factor（s） and gene（s） for the prevention and treatment of hypoxia and related syndromes.
基金supported in part by NSF Grant DMS-0811272in part by NIH Grant P50GM76516 and R01GM75309supported by NSF Grant DMS-0915153
文摘In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimemsions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.
