On Solution Algorithms for Large Sparse Systems of Normal Equations in Photogrammetry

1981 ◽  
Vol 35 (1) ◽  
pp. 37-51
Author(s):  
Franz Steidler
Keyword(s):  
Bundle Adjustment ◽  
Solution Technique ◽  
Systems Of Equations ◽  
Direct Solution ◽  
Band Matrices ◽  
Normal Equations ◽  
Simple Version ◽  
Solution Algorithms ◽  
Solution Methods ◽  
Sparse Systems

The question of which algorithm is most appropriate for the solution of normal equations with different structures has been investigated. The solution methods are a direct solution for banded and banded-bordered matrices, a special direct solution technique for arbitrary sparse systems of equations and the method of conjugate gradients. The algorithms have first been applied to photogrammetric bundle adjustment with self-calibration, which leads to a banded-bordered matrix of the normal equations, and secondly to calculations of digital height models that are generated by a simple version of the method of finite elements and which lead to band matrices.

scholarly journals PARALLEL APPROACH TO SOLVE OF THE DIRECT SOLUTION OF LARGE SPARSE SYSTEMS OF LINEAR EQUATIONS

2017 ◽  
Vol 13 ◽  
pp. 16
Author(s):  
Michal Bošanský ◽  
Bořek Patzák
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Distributed Memory ◽  
Linear Equations ◽  
Direct Solution ◽  
Parallel Solution ◽  
Finite Element Software ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Symmetric Systems

The paper deals with parallel approach for the numerical solution of large, sparse, non-symmetric systems of linear equations, that can be part of any finite element software. In this contribution, the differences between the sequential and parallel solution are highlighted and the approach to efficiently interface with distributed memory version of SuperLU solver is described.

scholarly journals Iterative Krylov solution methods for geophysical electromagnetic simulations on throughput-oriented processing units

2011 ◽  
Vol 26 (4) ◽  
pp. 378-385 ◽  
Author(s):  
Michael Commer ◽  
Filipe RNC Maia ◽  
Gregory A Newman
Keyword(s):  
Graphics Processing Units ◽  
Three Dimensional ◽  
Subsurface Imaging ◽  
Systems Of Equations ◽  
Sparse Linear Systems ◽  
Electromagnetic Simulations ◽  
Solution Methods ◽  
Memory Resources ◽  
Graphics Processing ◽  
Linear Systems Of Equations

Many geo-scientific applications involve boundary value problems arising in simulating electrostatic and electromagnetic fields for geophysical prospecting and subsurface imaging of electrical resistivity. Modeling complex geological media with three-dimensional finite-difference grids gives rise to large sparse linear systems of equations. For such systems, we have implemented three common iterative Krylov solution methods on graphics processing units and compared their performance with parallel host-based versions. The benchmarks show that the device efficiency improves with increasing grid sizes. Limitations are currently given by the device memory resources.

Simulation of Mating Between Non-Analytic Surfaces Using a Mathematical Programming Formulation

2005 ◽  
Author(s):  
Robert Scott Pierce ◽  
David Rosen
Keyword(s):  
Constrained Optimization ◽  
End Milling ◽  
Tolerance Analysis ◽  
Mechanical Assembly ◽  
Solution Algorithms ◽  
Solution Methods ◽  
Gradient Based ◽  
Unconstrained Problem ◽  
Typical Component ◽  
Randomized Search

In this paper we describe a new method for simulating mechanical assembly between components that are composed of surfaces that do not have perfect geometric form. Mating between these imperfect form surfaces is formulated as a constrained optimization problem of the form “minimize the distance from perfect fit, subject to non-interference between components.” We explore the characteristics of this mating problem and investigate the applicability of several potential solution algorithms. The problem can be solved by converting the constrained optimization formulation into an unconstrained problem using a penalty-function approach. We describe the characteristics of this unconstrained formulation and test the use of two different solution methods: a randomized search technique and a gradient-based method. We test the algorithm by simulating mating between component models that exhibit form errors typically generated in end-milling processes. These typical component variants are used as validation problems throughout our work. Results of two different validation problems are presented. Using these results, we evaluate the applicability of the mating algorithm to the problem of mechanical tolerance analysis for assemblies and mechanisms.

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