This paper presents an efficient algorithm for the simulation of progressive fracture in disordered quasi-brittle materials using discrete lattice networks. The main computational bottleneck involved in modelling the fracture simulations using large discrete lattice networks stems from the fact that a new large set of linear equations needs to be solved every time a lattice bond is broken. Usin...

The solution of large, sparse systems of linear equations is an inherent part of many computational methods in science and engineering. For such systems, iterative methods are often more attractive than direct methods because of their small (and constant) memory requirements. Also, the performance of iterative solvers can easily be improved by using distributed systems. A common performance cha...

We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurately approximated by linear combinations of solutions to linear systems for a small set of fixed parameters. Combined with either direct solvers or preconditioned iterative solvers for each linear system with a fixed p...

Solving large sparse systems of linear equations is required for a wide range of numerical applications. This paper addresses the main issues raised during the parallelization of iterative and direct solvers for such systems in distributed memory multiprocessors. If no preconditioning is considered, iterative solvers are simple to parallelize, as the most time-consuming computational structures...

For maximum computational efficiency, the solvers for each of the seven problems are implemented separately. They all have the same basic structure, however, with the computational bottleneck being the calculation of the Newton step (this is discussed in detail below). The code can be used in either “small scale” mode, where the system is constructed explicitly and solved exactly, or in “large ...