Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers

In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system, and the design of data structures to take advantage of serial, coarse grain parallel and massively parallel computer architectures, are considered in detail. We put forward arguments as to why integration of the system within a sparse simplex solver is important and outline how the system is designed to achieve this integration

Nonlinear hierarchical substructural parallelism and computer architecture

Computer architecture is investigated in conjunction with the algorithmic structures of nonlinear finite-element analysis. To help set the stage for this goal, the development is undertaken by considering the wide-ranging needs associated with the analysis of rolling tires which possess the full range of kinematic, material and boundary condition induced nonlinearity in addition to gross and local cord-matrix material properties

A parallel algorithm for solving the incompressible Navier-Stokes problems

AbstractWe introduce and analyze a parallel algorithm for solving the Navier-Stokes equations based on the splitting of the two main difficulties involved, the presence of nonlinear terms and the zero divergence condition. The numerical results obtained by using the proposed algorithm are quite consistent with those furnished by other known algorithms. Numerical results are discussed, as well as the advantages of this new algorithm