This paper describes substantial improvements in analysis capabilities in a large scale commercial finite element program made possible by the implementation of solver technology. The ANSYS program is a commercial finite element analysis program, which has been in use for thirty years. The original code, developed around a direct frontal solver has been expanded over the years to include full f...

In order to apply constraint programming to a particular domain, the problem must first be modelled as a constraint satisfaction problem. There are typically many alternative models of a given problem, and formulating an effective model requires a great deal of expertise. To reduce this bottleneck, the Essence language allows the specification of a problem abstractly, i.e. without making modell...

We report on an extensive experiment to compare an iterative solver preconditioned by several versions of incomplete LU factorization with a sparse direct solver using LU factorization with partial pivoting. Our test suite is 24 nonsymmetric matrices drawn from benchmark sets in the literature. On a few matrices, the best iterative method is more than 5 times as fast and more than 10 times as m...

Convergence results are provided for inexact inverse subspace iteration applied to the problem of finding the invariant subspace associated with a small number of eigenvalues of a large sparse matrix. These results are illustrated by the use of block-GMRES as the iterative solver. The costs of the inexact solves are measured by the number of inner iterations needed by the iterative solver at ea...

Iterative Layering is an existing pre-synthesis technique that can be used for constructing a near-optimal representation of the input circuit. Originally, the Iterative Layering algorithm uses SAT instances extensively. However, in the original implementation, they are solved either by exhaustive enumeration of all possible assignments of input variables, or by using BDDs. Both approaches perf...

The solution of large sparse linear systems is often the most time-consuming part of many science and engineering applications. Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few examples of the application areas in which large sparse linear systems need to be solved effectively. In this paper we introduce a new parallel hybrid sparse l...

We report on an extensive experiment to compare an iterative solver preconditioned by several versions of incomplete LU factorization with a sparse direct solver using LU factorization with partial pivoting. Our test suite is 24 nonsymmetric matrices drawn from benchmark sets in the literature. On a few matrices, the best iterative method is more than 5 times as fast and more than 10 times as m...

In the present work for a quasi-one-dimensional isentropic compressible flow model, an empirical equation of Mach number is constructed as function stagnation pressure ratio analytical that algebraic procedures cannot invert. The Excel 2019 Solver tool was applied to calibrate coefficients and exponents during its construction range from 1 10 5. A specific heat 1.1 1.67 generalized reduced grad...

The anisotropic and active properties of the perfectly matched layer (PML) absorbers significantly deteriorate the finite-element method (FEM) system condition and as a result, convergence of the iterative solver is substantially affected. To address this issue, we examine the generalized minimal residual (GMRES) solver for solving finite-element systems terminated with PML. A strong approximat...