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Repeated Solution (repeated + solution)
Selected AbstractsImpact of Simulation Model Solver Performance on Ground Water Management ProblemsGROUND WATER, Issue 5 2008David P. Ahlfeld Ground water management models require the repeated solution of a simulation model to identify an optimal solution to the management problem. Limited precision in simulation model calculations can cause optimization algorithms to produce erroneous solutions. Experiments are conducted on a transient field application with a streamflow depletion control management formulation solved with a response matrix approach. The experiment consists of solving the management model with different levels of simulation model solution precision and comparing the differences in optimal solutions obtained. The precision of simulation model solutions is controlled by choice of solver and convergence parameter and is monitored by observing reported budget discrepancy. The difference in management model solutions results from errors in computation of response coefficients. Error in the largest response coefficients is found to have the most significant impact on the optimal solution. Methods for diagnosing the adequacy of precision when simulation models are used in a management model framework are proposed. [source] A continuum mechanics-based framework for boundary and finite element mesh optimization in two dimensions for application in excavation analysisINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2005Attila M. Zsáki Abstract The determination of the optimum excavation sequences in mining and civil engineering using numerical stress analysis procedures requires repeated solution of large models. Often such models contain much more complexity and geometric detail than required to arrive at an accurate stress analysis solution, especially considering our limited knowledge of rock mass properties. This paper develops an automated framework for estimating the effects of excavations at a region of interest, and optimizing the geometry used for stress analysis. It eliminates or simplifies the excavations in a model while maintaining the accuracy of analysis results. The framework can equally be applied to two-dimensional boundary and finite element models. The framework will have the largest impact for non-linear finite element analysis. It can significantly reduce computational times for such analysis by simplifying models. Error estimators are used in the framework to assess accuracy. The advantages of applying the framework are demonstrated on an excavation-sequencing scenario. Copyright © 2005 John Wiley & Sons, Ltd. [source] Efficient implicit finite element analysis of sheet forming processesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003A. H. van den Boogaard Abstract The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time-savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton,Raphson iterations. This also applies to quasi-static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10. Copyright © 2003 John Wiley & Sons, Ltd. [source] Projection and partitioned solution for two-phase flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2005Andrea Comerlati Abstract Multiphase flow through porous media is a highly nonlinear process that can be solved numerically with the aid of finite elements (FE) in space and finite differences (FD) in time. For an accurate solution much refined FE grids are generally required with the major computational effort consisting of the resolution to the nonlinearity frequently obtained with the classical Picard linearization approach. The efficiency of the repeated solution to the linear systems within each individual time step represents the key to improve the performance of a multiphase flow simulator. The present paper discusses the performance of the projection solvers (GMRES with restart, TFQMR, and BiCGSTAB) for two global schemes based on a different nodal ordering of the unknowns (ORD1 and ORD2) and a scheme (SPLIT) based on the straightforward inversion of the lumped mass matrix which allows for the preliminary elimination and substitution of the unknown saturations. It is shown that SPLIT is between two and three time faster than ORD1 and ORD2, irrespective of the solver used. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||