ISSN:0748-8025    

DOI:10.1002/cnm.1630080902

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0748-8025    

DOI:10.1002/cnm.1630080903

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractIn this paper we present three drivers for the Fortran software packages BOXMG and BOXMGP. They both act as black‐box matrix solvers for symmetric positive‐definite matrices using a multigrid method. There are two drivers, BBMG and BBMGP, that simplify the interface to BOXMG and BOXMGP, respectively. The other driver, DIVMG, provides a user‐friendly driver to both BOXMG and BOXMGP for a special class of problems. The DIVMG driver solves a two‐dimensional second‐order partial differential equation in divergence form on a rectangular domain with any combination of the following boundary conditions: Dirichlet, Neumann, Robin and periodic. The BBMG and BBMGP drivers, like the BOXMG solvers, still require the user to define the system of equations, while on the other hand the DIVMG driver also performs the discretization and only requires the user to define th

ISSN:0748-8025    

DOI:10.1002/cnm.1630080904

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe fast adaptive composite grid method (FAC) is a multi‐level adaptive method for the discretization and solution of partial differential equations. This paper compares the speed of solution of the resulting discrete equations by the FAC algorithm and a preconditioned conjugate gradient scheme. Comparisons and information concerning the solutions are given for several model problem

ISSN:0748-8025    

DOI:10.1002/cnm.1630080905

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractWe consider the problem of solving time‐dependent partial differential equations on an MIMD computer. Conventional methods for the solution of this type of equation when discretized by an implicit method such as backward Euler proceed by solving a sequence of problems iteratively. It is shown that, despite the sequential nature of this process, several processors may be employed to solve at several time steps simultaneously, a technique which we shall refer to astime‐parallelism. Details of a time‐parallel multigrid method based on the parabolic multigrid method due to Hackbusch and of a smoothing technique applicable to the two‐dimensional unsteady incompressible Navier‐Stokes equations are given. The parallel complexity of the method is shown to be qualitatively superior to that of previous parallel algorithms. Efficiencies obtained by an implementation of the method on a parallel Transputer system are

ISSN:0748-8025    

DOI:10.1002/cnm.1630080906

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractMappings are discussed fromm‐dimensional process spaces ton‐dimensional crossbar networks which preserve the nearest‐neighbour relation between processes, i.e. neighboured processes are mapped to processors connected by a common crossbar. Even in the case of multi‐level process structures, a neighbouring relation between processes can be derived such that the neighboured processes can communicate d

ISSN:0748-8025    

DOI:10.1002/cnm.1630080907

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe fast adaptive composite grid method (FAC) is an algorithm that uses uniform grids, both global and local, to solve partial differential equations. This method is known to be highly efficient on scalar or singe‐processor vector computers, due to its effective use of uniform grids and multiple levels of resolution of the solution. On distributed memory multiprocesssors, such methods benefit from their tendency to create multiple isolated refinement regions, which may be effectively treated in parallel. However, they suffer from the way in which the levels of refinement are treated sequentially in each region. Specifically, the finer levels must wait to be processed until the coarse‐level approximations have been computed and passed to them; conversely, the coarser levels must wait until the finer level approximations have been computed and used to correct their equations.The asynchronous fast adaptive composite method (AFAC) eliminates this bottleneck of parallelism. Through a simple mechanism used to reduce interlevel dependence, individual refinements levels can be processed by AFAC in parallel. The result is that the convergence rate of AFAC is the square root of that for FAC. Therefore, since both AFAc and FAC have roughly the same number of floating‐point operations, AFAC requires twice the serial computational time as FAC, but AFAC, may be much more efficiently parallelized.This paper presents a comparison of FAC and AFAC under a variety of conditions, including vectorization and parallelization. Results are presented for distributed memory multiprocessor architectures (SUPRENUM, Intel iPSC/2 and iPSC/860). The most crucial factor for the evaluation of both algorithms is the different computation/communication cost ratios of these architectures. It is shown that, under many circumstances, AFAC is superior to FAC in a parallel enviro

ISSN:0748-8025    

DOI:10.1002/cnm.1630080908

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractAn efficient multigrid scheme for elliptic equations with jump discontinuous coefficients is presented. It is based on a cell‐centred grid and finite‐volume method, with the diffusion coefficients at the jump interface being determined by a flux conservation condition. The diffusion coefficients on coarse grids are calculated by a simple restriction of the coefficients from the fine grid. An efficient interpolation operator, which is constructed by the so‐called effective area law, is developed. Computational results for a two‐dimensional scalar elliptic equation and for two‐phase porous media flow show that the new scheme achieves multigrid efficiency typical of the constant‐coeff

ISSN:0748-8025    

DOI:10.1002/cnm.1630080909

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA multigrid method for the solution of the linear multi‐dimensional advection–diffusion equation with variable coefficients is presented. The method efficiently combines odd–even relaxations with semi‐coarsening. Theoretical and computational convergence rates are given for a large range of advection–diffusion coefficients to demonstrate the efficiency of the method. The construction of the coarse‐grid operator is also discussed in detail since it may have a strong influence on the convergence of the multigrid process when the direction of convect

ISSN:0748-8025    

DOI:10.1002/cnm.1630080910

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe fast adaptive composite grid method (FAC) is a discretization and solution method design to achieve efficient local resolution by constructing the discretization based on various regular grids and using these grids as a basis for fast solution. FAC is designed so as to share all of the attributes of the composite grid and multigrid methods. As is the case for most mesh refinement schemes, it is advantageous to optimally choose the grids so as to save both storage and computational costs. The FAC method has previously been shown to be an effective tool in obtaining numerical solutions of many types of steady problems. In addition time‐dependent problems with stationary fronts or singularities have also been resolved efficiently with FAC. An adaptive scheme has been developed and implemented that, based on given error tolerances, calculates the optimal time discretization and locates the spatial regions where more resolution is needed. Patches are set up to be used by the various FAC algorithms. The spatial refinement scheme is able to track areas of resolution which move across the domain, allowing for small composite grids at each time ste

ISSN:0748-8025    

DOI:10.1002/cnm.1630080911

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY