The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of ...The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of symmetric tridiagonal matrix. The multisection method for solving the generalized eigenproblem applied significantly in many science and engineering domains has not been studied. The parallel region preserving multisection method (PRM for short) for solving generalized eigenproblems of large sparse and real symmetric matrix is presented in this paper. This method not only retains the advantages of the conventional determinant search method (DS for short), but also overcomes its disadvantages such as leaking roots and disconvergence. We have tested the method on the YH 1 vector computer, and compared it with the parallel region preserving determinant search method the parallel region preserving bisection method (PRB for short). The numerical results show that PRM has a higher speed up, for instance, it attains the speed up of 7.7 when the scale of the problem is 2 114 and the eigenpair found is 3, and PRM is superior to PRB when the scale of the problem is large.展开更多
The authors propose a numerical algorithm for the two-dimensional Navier-Stokes equations written in stream function-vorticity formulation. The total time derivative term is treated with a first order characteristics ...The authors propose a numerical algorithm for the two-dimensional Navier-Stokes equations written in stream function-vorticity formulation. The total time derivative term is treated with a first order characteristics method. The space approximation is based on a piecewise continuous finite element method. The proposed algorithm is used to simulate the mechanical aeration process in lakes. Such process is used to combat the degradation of the water quality due to the eutrophication phenomena. For this application high computing facilities and capacities are required. In order to optimize the computing time and make possible the simulation of real applications, the authors propose a parallel implementation of the numerical algorithm. The parallelization technique is performed using the Message Passing Interface. The efficiency of the proposed numerical algorithm is illustrated by some numerical results.展开更多
文摘The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of symmetric tridiagonal matrix. The multisection method for solving the generalized eigenproblem applied significantly in many science and engineering domains has not been studied. The parallel region preserving multisection method (PRM for short) for solving generalized eigenproblems of large sparse and real symmetric matrix is presented in this paper. This method not only retains the advantages of the conventional determinant search method (DS for short), but also overcomes its disadvantages such as leaking roots and disconvergence. We have tested the method on the YH 1 vector computer, and compared it with the parallel region preserving determinant search method the parallel region preserving bisection method (PRB for short). The numerical results show that PRM has a higher speed up, for instance, it attains the speed up of 7.7 when the scale of the problem is 2 114 and the eigenpair found is 3, and PRM is superior to PRB when the scale of the problem is large.
文摘The authors propose a numerical algorithm for the two-dimensional Navier-Stokes equations written in stream function-vorticity formulation. The total time derivative term is treated with a first order characteristics method. The space approximation is based on a piecewise continuous finite element method. The proposed algorithm is used to simulate the mechanical aeration process in lakes. Such process is used to combat the degradation of the water quality due to the eutrophication phenomena. For this application high computing facilities and capacities are required. In order to optimize the computing time and make possible the simulation of real applications, the authors propose a parallel implementation of the numerical algorithm. The parallelization technique is performed using the Message Passing Interface. The efficiency of the proposed numerical algorithm is illustrated by some numerical results.
