In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's m...In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method.It is shown that block preconditioners form an excellent approach for the solution,however if the grids are not to fine preconditioning with a Saddle point ILU matrix(SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated.In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.展开更多
In this paper we consider the domain decomposition methods with mortar element Lagrange multipliers to two-dimensional elliptic problems.We shall construct a kind of simple preconditioners for the corresponding interf...In this paper we consider the domain decomposition methods with mortar element Lagrange multipliers to two-dimensional elliptic problems.We shall construct a kind of simple preconditioners for the corresponding interface equation.It will be shown that condition number of the preconditioned interface matrix is almost optimal.展开更多
EPB TBMs(Earth pressure balance Tunneling Boring Machines) are extensively used in tunneling constructions because of its high efficiency and low disturbance on structures above ground. It is critically significant to...EPB TBMs(Earth pressure balance Tunneling Boring Machines) are extensively used in tunneling constructions because of its high efficiency and low disturbance on structures above ground. It is critically significant to predict the thrust acting on TBMs under different geological conditions for both the design of power system and the control of tunneling process. The interaction between the cutterhead and the ground is the core of excavation, through which geological conditions determine the thrust re-quirement combined with operating status and structural characteristics. This paper conducted a mechanical decoupling analysis to obtain a basic expression of the cutterhead-ground interactive stress. Then more engineering factors(such as cutterhead topological structure, underground overburden, thrusts on other parts, etc.) were further considered to establish a predicting model for the total thrust acting on a machine during tunneling. Combined with three subway projects under different geological conditions in China, the model was verified and used to analyze how geological, operating and structural parameters influence the acting thrust.展开更多
The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor form...The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches.展开更多
文摘In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method.It is shown that block preconditioners form an excellent approach for the solution,however if the grids are not to fine preconditioning with a Saddle point ILU matrix(SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated.In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.
基金This research is supported by Special Funds for Major State Basic Research Projects of China (G1999032804).
文摘In this paper we consider the domain decomposition methods with mortar element Lagrange multipliers to two-dimensional elliptic problems.We shall construct a kind of simple preconditioners for the corresponding interface equation.It will be shown that condition number of the preconditioned interface matrix is almost optimal.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11127202 & 11302146)
文摘EPB TBMs(Earth pressure balance Tunneling Boring Machines) are extensively used in tunneling constructions because of its high efficiency and low disturbance on structures above ground. It is critically significant to predict the thrust acting on TBMs under different geological conditions for both the design of power system and the control of tunneling process. The interaction between the cutterhead and the ground is the core of excavation, through which geological conditions determine the thrust re-quirement combined with operating status and structural characteristics. This paper conducted a mechanical decoupling analysis to obtain a basic expression of the cutterhead-ground interactive stress. Then more engineering factors(such as cutterhead topological structure, underground overburden, thrusts on other parts, etc.) were further considered to establish a predicting model for the total thrust acting on a machine during tunneling. Combined with three subway projects under different geological conditions in China, the model was verified and used to analyze how geological, operating and structural parameters influence the acting thrust.
基金supported by National Natural Science Foundation of China (Grant No.10961010)Science and Technology Foundation of Guizhou Province (Grant No. LKS[2009]03)
文摘The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches.
