How Generous is the ELLPACK Sparse Matrix Storage Scheme for Finite Element Computations

Date

2012-11-03

Author

Akinci, Gokay
YILMAZ, ASIM EGEMEN
Kuzuoğlu, Mustafa

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

134
views

0
downloads

Sparse matrices are occasionally encountered during solutions of various problems by means of numerical methods, such as the finite element method. ELLPACK sparse matrix storage scheme, one of the most widely used methods due to its implementation ease, is investigated in this study. The scheme uses excessive memory due to its definition. For the conventional finite element method, where the node elements are used, the excessive memory caused by redundant entries in the ELLPACK sparse matrix storage scheme becomes negligible for large scale problems. On the other hand, our analyses show that the redundancy is still considerable for the occasions where facet or edge elements have to be used.

Subject Keywords

Finite Element Method, Sparse Matrix, Edge Elements, Computational Electromagnetcis, ELLPACK

URI

https://hdl.handle.net/11511/55797

Conference Name

9th International Conference on Electronics Computer and Computation (ICECCO 2012)

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Excessive Memory Usage of the ELLPACK Sparse Matrix Storage Scheme throughout the Finite Element Computations Akinci, Gokay; YILMAZ, ASIM EGEMEN; Kuzuoğlu, Mustafa (2014-12-01) Sparse matrices are occasionally encountered during solution of various problems by means of numerical methods, particularly the finite element method ELLPACK sparse matrix storage scheme, one of the most widely used methods due to its implementation ease, is investigated in this study. The scheme uses excessive memory due to its definition. For the conventional finite element method, where the node elements are used, the excessive memory caused by redundant entries in the ELLPACK sparse matrix storage sche...
MUTUAL COUPLING EFFECTS OF FINITE RECTANGULAR PHASED-ARRAYS YAVUZ, H; BUYUKDURA, OM (1994-04-14) A rigorous integral equation formulation for the analysis of a phased array of flangemounted waveguide apertures is given for a finite number of elements and nonuniform spacings. The resulting set of ihtegrd equations is reduced to a matrix equation called the coupling matrix which relates the coefficients of all the modes in all the waveguides to one another. The solution then yields the dominant mode reflection coefficient, coefficients of scattered modes and hence the field in each waveguide. The blockTo...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems Bozkaya, Canan (2005-03-18) The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Least-squares finite element solution of Euler equations with adaptive mesh refinement Akargün, Hayri Yiğit; Sert, Cüneyt; Department of Mechanical Engineering (2012) Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the me...
On the solution of nonlinear algebraic equations following periodic forced response analysis of nonlinear structures using different nonlinear solvers Kizilay, H. Sefa; Ciğeroğlu, Ender (2021-01-01) In periodic forced response analysis of nonlinear structures, most of the time analytical solutions cannot be obtained due to the complex behavior of the nonlinearity and/or due to the number of nonlinear equations to be solved. Therefore, numerical methods are widely used. For periodic forced response analysis of nonlinear systems, generally Harmonic Balance Method (HBM) or Describing Function Method (DFM), which transform the nonlinear differential equations into a set of nonlinear algebraic equations, ar...

Citation Formats

G. Akinci, A. E. YILMAZ, and M. Kuzuoğlu, “How Generous is the ELLPACK Sparse Matrix Storage Scheme for Finite Element Computations,” presented at the 9th International Conference on Electronics Computer and Computation (ICECCO 2012), Ankara, TURKEY, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55797.