B. Kiss

26661454200

Publications - 5

On the non hierarchical matrix representation of the negative, non integer order sobolev norms

B. Kiss

Publication Name: Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics

Publication Date: 2006-06-29

Volume: 3743 LNCS

Issue: Unknown

Page Range: 663-670

Description:

In this paper a new cyclic matrix representation of the Sobolev norms Ha, a ∈ (-1, 0) are presented. The matrix-vector multiplication by these matrices requires only O(N · log(N)) arithmetic operations, where N is the number of unknowns, The application of the new H-1/2 norm representation as Schur complement preconditioning matrix requires only matrix-vector multiplication. The efficiency of the construction to elliptic problems has been verified by numerical tests. © Springer-Verlag Berlin Heidelberg 2006.

Open Access: Yes

DOI: 10.1007/11666806_76

On the relational database type numerical programming

B. Kiss A. Krebsz

Publication Name: Proceedings of the Third International Conference on Engineering Computational Technology

Publication Date: 2002-12-01

Volume: Unknown

Issue: Unknown

Page Range: 127-128

Description:

The numerical algorithms became quite complex and require dynamic data structures. As such, an advanced front (AF) algorithm which is a well-known and efficient algorithm of the non-structural mesh generation is given. An accelerated version of this algorithm is presented as an example to demonstrate, that a simplified relational database model is an efficient tool for handling dynamic data structures arising from numerical problems. The main advantage of this technique is the simple and uniform data structure and the application of the balanced trees for searching and modification.

Open Access: Yes

DOI: DOI not available

On the Schur component preconditioners

B. Kiss A. Krebsz

Publication Name: Computers and Structures

Publication Date: 1999-01-01

Volume: 73

Issue: 1-5

Page Range: 537-544

Description:

Some representations of the H 1/2 norm are used as Schur complement preconditioners in PCG-based domain decomposition algorithms for elliptic problems. These norm representations are efficient preconditioners. Here we give a new matrix representation of the Ha (0 < a < 1) norms by a special sparse Toeplitz matrix. It contains O(log(N)) non-zero entries at each row, where N is the number of rows. The special properties of this matrix ensure that it can be used as preconditioner. This is proved by estimating spectral equivalence constants and this fact has also been verified by numerical tests.

Open Access: Yes

DOI: 10.1016/S0045-7949(98)00258-2

A block-circulant preconditioner for domain decomposition algorithm for the solution of the elliptic problems by second order finite elements

B. Kiss G. Molnárka

Publication Name: Computing Systems in Engineering

Publication Date: 1995-01-01

Volume: 6

Issue: 4-5

Page Range: 369-376

Description:

A preconditioned conjugate gradient domain decomposition method was given Refs 1 and 2 for the solution of a system of linear equations arising in the finite element method applied to the elliptic Dirichlet, Neumann and mixed boundary value problems. We have proved that the construction can be generalized2 for higher order finite element method. Here we give a construction and theoretical investigation of preconditioners for second order finite elements. A method and the the results of calculation is given. The presented numerical experiments show that this preconditioner works well. © 1995.

Open Access: Yes

DOI: 10.1016/0956-0521(95)00039-9

A circulant preconditioner for domain decomposition algorithm for the solution of the elliptic problems

N. A.A. Rahman B. Kiss G. Molnárka

Publication Name: Periodica Mathematica Hungarica

Publication Date: 1994-08-01

Volume: 29

Issue: 1

Page Range: 67-80

Description:

A preconditioned conjugate gradient (PCG)-based domain decomposition method was given in [11] and [12] for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed algorithm was that the recommended preconditioner was constructed by using symmetric-cyclic matrix. But we could give only the definitions of the entries of this cyclic matrix. Here we give a short description of this algorithm, the method of calculation of matrix entries and the results of calculation. The numerical experiments presented show, that this construction of precondition in the practice works well. © 1994 Akadémiai Kiadó.

Open Access: Yes

DOI: 10.1007/BF01876204