Description and comparison of several packages for the iterative solution of linear systems of equations.

Computationally intensive distributed and parallel computing is often bottlenecked by a small set of slow workers known as stragglers. In this paper, we utilize the emerging idea of “coded computation” to design a novel error-correctingcode inspired technique for solving linear inverse problems under specific iterative methods in a parallelized implementation affected by stragglers. Example app...

Numerical solutions to partial differential equations form the backbone of mathematical models that simulate the behavior of various electrochemical systems, specifically, batteries and fuel cells. In this paper, we present a set of numerical algorithms applied to efficiently solve this system of equations. These fast algorithms are identified by fully understanding the physics of the problem a...

A method for efficiently planning one-dimensional pop-limited trajectories is presented, along with a direct method for synchronizing trajectories across multiple dimensions. This heuristic is designed for a double integrator utilizing acceleration commands passed through a 4th-order cascaded filter, the model for which is presented along with the system solution for an arbitrary time step and ...

Richards’ equation and the two-phase flow equations are well-known degenerate parabolic models of air/water flow in porous media. Poor iterative solver performance and small time steps during transient simulations are often reported in field-scale simulations. In this work we study Newton-multigrid and nonlinear multigrid methods applied to discrete air/water flow models. The models are discret...

LINSOL is an iterative linear solver package (solving Ax = b) with direct solvers as preconditioners. The program package is adapted to the application of sparse matrices, but can be efficiently applied to full matrices, too. It contains presently eight iterative methods and a polyalgorithm of generalized Conjugate Gradient (CG) methods. The used direct solver is the Gaussian algorithm working ...

Mathematical models for the description, in a quantitative way, of the damages induced on monuments by the action of specific pollutants are often systems of nonlinear, possibly degenerate, parabolic equations. Although some of the asymptotic properties of the solutions are known, one needs a numerical approximation scheme in order to have a quantitative forecast at any time of interest. In thi...

This article describes a new numerical solver for the Navier-Stokes equations. The proposed solver is written in Python which is a newly developed language. The Python packages are built to solve the Navier-Stokes equations with existing libraries. We have created discretized coefficient matrices from systems of the Navier-Stokes equations by the finite difference method. In addition we focus o...

We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex shifted-Laplace preconditioner combined...

If such an analysis or synthesis question shall be answered automatically, both adequate algorithmic models along with the problem solving expertise of a human problem solver must be operationalized on a computer. Often, the construction of an adequate model turns out to be the key challenge when tackling the engineering task. Model construction—also known as model creation, model formation, mo...