Search results for "Solver"
showing 10 items of 157 documents
Path relinking and GRG for artificial neural networks
2006
Artificial neural networks (ANN) have been widely used for both classification and prediction. This paper is focused on the prediction problem in which an unknown function is approximated. ANNs can be viewed as models of real systems, built by tuning parameters known as weights. In training the net, the problem is to find the weights that optimize its performance (i.e., to minimize the error over the training set). Although the most popular method for training these networks is back propagation, other optimization methods such as tabu search or scatter search have been successfully applied to solve this problem. In this paper we propose a path relinking implementation to solve the neural ne…
Optimal placement of 3D sensors considering range and field of view
2017
This paper describes a novel approach to the problem of optimal placement of 3D sensors in a specified volume of interest. The coverage area of the sensors is modelled as a cone having limited field of view and range. The volume of interest is divided into many, smaller cubes each having a set of associated Boolean and continuous variables. The proposed method could be easily extended to handle the case where certain sub-volumes must be covered by several sensors (redundancy), for example ex-zones, regions where humans are not allowed to enter or regions where machine movement may obstruct the view of a single sensor. The optimisation problem is formulated as a Mixed-Integer Linear Program …
On the use of a meshless solver for PDEs governing electromagnetic transients
2009
In this paper some key elements of the Smoothed Particle Hydrodynamics methodology suitably reformulated for analyzing electromagnetic transients are investigated. The attention is focused on the interpolating smoothing kernel function which strongly influences the computational results. Some issues are provided by adopting the polynomial reproducing conditions. Validation tests involving Gaussian and cubic B-spline smoothing kernel functions in one and two dimensions are reported.
Solving the pentahedron problem
2015
Nowadays, all geometric modelers provide some tools for specifying geometric constraints. The 3D pentahedron problem is an example of a 3D Geometric Constraint Solving Problem (GCSP), composed of six vertices, nine edges, five faces (two triangles and three quadrilaterals), and defined by the lengths of its edges and the planarity of its quadrilateral faces. This problem seems to be the simplest non-trivial problem, as the methods used to solve the Stewart platform or octahedron problem fail to solve it. The naive algebraic formulation of the pentahedron yields an under-constrained system of twelve equations in eighteen unknowns. Even if the use of placement rules transforms the pentahedron…
A NEW SOLVER FOR NON-ISOTHERMAL FLOWS IN NATURAL AND MIXED CONVECTION
2022
Most thermal fluid flow of real-life practical problems fall in the category of low Mach-number or incompressible flow (e.g., industrial flows inside ducts, or around stationary/moving objects, flows in biological/biomedical problems, or atmospheric flows). Several numerical techniques have been proposed for simulation of thermal flows, Finite Difference (FDM), Finite Element (FEM), Finite Volume (FVM) and Lattice Boltzmann (LBM) methods. Unlike the FVMs and FEMs, the classical FDMs show some difficulties in handling irregular geometries. Conventional formulation of FEMs (e.g., Galerkin FEMs) suffers from the lack of local mass balance, recovered by modified formulations (Narasimhan & W…
Integration of an LP Solver into Interval Constraint Propagation
2011
This paper describes the integration of an LP solver into iSAT, a Satisfiability Modulo Theories solver that can solve Boolean combinations of linear and nonlinear constraints. iSAT is a tight integration of the well-known DPLL algorithm and interval constraint propagation allowing it to reason about linear and nonlinear constraints. As interval arithmetic is known to be less efficient on solving linear programs, we will demonstrate how the integration of an LP solver can improve the overall solving performance of iSAT.
Capturing Shock Reflections: An Improved Flux Formula
1996
Godunov type schemes, based on exact or approximate solutions to the Riemann problem, have proven to be an excellent tool to compute approximate solutions to hyperbolic systems of conservation laws. However, there are many instances in which a particular scheme produces inappropriate results. In this paper we consider several situations in which Roe's scheme gives incorrect results (or blows up all together) and we propose an alternative flux formula that produces numerical approximations in which the pathological behavior is either eliminated or reduced to computationally acceptable levels.
A fast dual boundary element method for 3D anisotropic crack problems
2009
In the present paper a fast solver for dual boundary element analysis of 3D anisotropic crack problems is formulated, implemented and tested. The fast solver is based on the use of hierarchical matrices for the representation of the collocation matrix. The admissible low rank blocks are computed by adaptive cross approximation (ACA). The performance of ACA against the accuracy of the adopted computational scheme for the evaluation of the anisotropic kernels is investigated, focusing on the balance between the kernel representation accuracy and the accuracy required for ACA. The system solution is computed by a preconditioned GMRES and the preconditioner is built exploiting the hierarchical …
A semi-Lagrangian AMR scheme for 2D transport problems in conservation form
2013
In this paper, we construct a semi-Lagrangian (SL) Adaptive-Mesh-Refinement (AMR) solver for 1D and 2D transport problems in conservation form. First, we describe the a-la-Harten AMR framework: the adaptation process selects a hierarchical set of grids with different resolutions depending on the features of the integrand function, using as criteria the point value prediction via interpolation from coarser meshes, and the appearance of large gradients. We integrate in time by reconstructing at the feet of the characteristics through the Point-Value Weighted Essentially Non-Oscillatory (PV-WENO) interpolator. We propose, then, an extension to the 2D setting by making the time integration dime…
A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems
2010
In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The precond…