BOUNDS ON THE EXTREMAL EIGEN- VALUES OF THE FINITE ELEMENT STIFF NESS AND MASS MATRIXES AND THEIR SPECTRAL CONDITION NUMBER Fried I. J. Sound and Vib. 22 (4), 407-418 (June 22, 1972) 14 refs Refer to Abstract No. 72-1592

1973 ◽  
Vol 5 (9) ◽  
pp. 47-48
Author(s):  
W. J. Anderson
Keyword(s):  
Finite Element ◽  
Condition Number ◽  
Spectral Condition ◽  
Eigen Values

scholarly journals The spectral condition number plot for regularization parameter evaluation

2019 ◽  
Vol 35 (2) ◽  
pp. 629-646 ◽  
Author(s):  
Carel F. W. Peeters ◽  
Mark A. van de Wiel ◽  
Wessel N. van Wieringen
Keyword(s):  
Condition Number ◽  
Regularization Parameter ◽  
Spectral Condition ◽  
Parameter Evaluation

Solving Topology Optimization Problems Using Wavelet Approximations

1998 ◽  
Author(s):  
Giuseppe C. A. DeRose ◽  
Alejandro R. Díaz
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Finite Element Methods ◽  
Condition Number ◽  
Optimization Problems ◽  
Mesh Size ◽  
Elasticity Problem ◽  
New Method ◽  
Galerkin Scheme

Abstract A new method to solve topology optimization problems is discussed. This method is based on the use of a Wavelet-Galerkin scheme to solve the elasticity problem associated with each iteration of the topology optimization sequence. Typically, finite element methods are used for this analysis. However, as the mesh size grows, the computational requirements necessary to solve the finite element equations increase beyond the capacity of current desk top computers. This problem is inherent to finite element methods, as the condition number of finite element matrices increases with mesh size. Wavelet-Galerkin techniques are used to replace standard finite element methods in an attempt to alleviate this problem. Examples demonstrating the performance of the new methodology are presented.

scholarly journals On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes

2020 ◽  
Author(s):  
Stefan Kunis ◽  
Dominik Nagel
Keyword(s):  
Unit Circle ◽  
Lower Bounds ◽  
Condition Number ◽  
Growth Rates ◽  
Separation Distance ◽  
Upper And Lower Bounds ◽  
Spectral Condition ◽  
Sharp Constants ◽  
Vandermonde Matrices

Abstract We prove upper and lower bounds for the spectral condition number of rectangular Vandermonde matrices with nodes on the complex unit circle. The nodes are “off the grid,” pairs of nodes nearly collide, and the studied condition number grows linearly with the inverse separation distance. Such growth rates are known in greater generality if all nodes collide or for groups of colliding nodes. For pairs of nodes, we provide reasonable sharp constants that are independent of the number of nodes as long as non-colliding nodes are well-separated.

Local Discontinuous Galerkin and Classical Finite Element Methods: Differences and Similarities

2003 ◽  
Author(s):  
Paul Castillo
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Finite Element Methods ◽  
Stiffness Matrix ◽  
Local Discontinuous Galerkin Method ◽  
Rates Of Convergence ◽  
Spectral Condition ◽  
Qualitative Comparison ◽  
Approximation Rates ◽  
Local Discontinuous Galerkin

In this work a quantitative and qualitative comparison of the Local Discontinuous Galerkin method and classical finite element methods applied to elliptic problems is performed. High order discretizations are considered. The methods are compared with respect to accuracy of the approximation, rates of convergence, asymptotic behavior of the spectral condition number of the stiffness matrix.

scholarly journals Spectral condition‐number estimation of large sparse matrices

2019 ◽  
Vol 26 (3) ◽  
pp. e2235 ◽  
Author(s):  
Haim Avron ◽  
Alex Druinsky ◽  
Sivan Toledo
Keyword(s):  
Condition Number ◽  
Sparse Matrices ◽  
Spectral Condition ◽  
Large Sparse Matrices
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