Acceleration and Parallelization of a Linear Equation Solver for Crack Growth Simulation Based on the Phase Field Model

We aim to accelerate the linear equation solver for crack growth simulation based on the phase field model. As a first step, we analyze the properties of the coefficient matrices and prove that they are symmetric positive definite. This justifies the use of the conjugate gradient method with the efficient incomplete Cholesky preconditioner. We then parallelize this preconditioner using so-called block multi-color ordering and evaluate its performance on multicore processors. The experimental results show that our solver scales well and achieves an acceleration of several times over the original solver based on the diagonally scaled CG method.

PARAMETER VARIATION FOR LINEAR EQUATION SOLVER USING GENETIC ALGORITHM

Genetic Algorithm has been successfully applied for solving systems of Linear Equations; however the effects of varying the various Genetic Algorithms parameters on the GA systems of Linear Equations solver have not been investigated. Varying the GA parameters produces new and exciting information on the behaviour of the GA Linear Equation solver. In this paper, a general introduction on the Genetic Algorithm, its application on finding solutions to the Systems of Linear equation as well as the effects of varying the Population size and Number of Generation is presented. The genetic algorithm simultaneous linear equation solver program was run several times using different sets of simultaneous linear equation while varying the population sizes as well as the number of generations in order to observe their effects on the solution generation. It was observed that small population size does not produce perfect solutions as fast as when large population size is used and small or large number of generations did not really have much impact on the attainment of perfect solution as much as population size.

Next Generation Exascale Capable Mutliphase Solver With Trilinos

A framework is developed to integrate the existing MFiX (Multiphase Flow with Interphase eXchanges) flow solver with state-of-the-art linear equation solver packages in Trilinos. The integrated solver is tested on various flow problems. The performance of the solver is evaluated on fluidized bed problems and observed that the integrated flow solver performs better compared to the native solver.