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Paper II.5

Solving Non-Linear Elliptic Difference Equations by Explicit Preconditioning Semi-Direct Methods

E.A. Lipitakis and A.S. Piperakis

Department of Informatics, Athens University of Economics and Business, Athens, Greece

doi:10.4203/ccp.33.2.5

E.A. Lipitakis, A.S. Piperakis, "Solving Non-Linear Elliptic Difference Equations by Explicit Preconditioning Semi-Direct Methods", in B.H.V. Topping, (Editor), "Developments in Computational Techniques for Structural Engineering", Civil-Comp Press, Edinburgh, UK, pp 45-52, 1995. doi:10.4203/ccp.33.2.5

Abstract

Explicit preconditioned semi-direct schemata are introduced for solving non- linear elliptic partial differential equations in two-space variables. The proposed methods are based on the concept of the Approximate Inverse Matrix techniques for calculating explicitly approximate inverses of large sparse symmetric matrices of regular structure without inverting the corresponding decomposition factors. These explicit methods are used in inner-outer iterative procedures in conjuction with Picard and Newton methods leading to improved composite iterative schemes for solving non-linear elliptic boundary-value problems. Applications of the new techniques on non-linear elliptic PDE's are discussed and numerical results are given.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 33 DEVELOPMENTS IN COMPUTATIONAL TECHNIQUES FOR STRUCTURAL ENGINEERING Edited by: B.H.V. Topping Paper II.5 Solving Non-Linear Elliptic Difference Equations by Explicit Preconditioning Semi-Direct Methods E.A. Lipitakis and A.S. Piperakis Department of Informatics, Athens University of Economics and Business, Athens, Greece doi:10.4203/ccp.33.2.5 purchase the full-text of this paper Full Bibliographic Reference for this paper E.A. Lipitakis, A.S. Piperakis, "Solving Non-Linear Elliptic Difference Equations by Explicit Preconditioning Semi-Direct Methods", in B.H.V. Topping, (Editor), "Developments in Computational Techniques for Structural Engineering", Civil-Comp Press, Edinburgh, UK, pp 45-52, 1995. doi:10.4203/ccp.33.2.5 Abstract Explicit preconditioned semi-direct schemata are introduced for solving non- linear elliptic partial differential equations in two-space variables. The proposed methods are based on the concept of the Approximate Inverse Matrix techniques for calculating explicitly approximate inverses of large sparse symmetric matrices of regular structure without inverting the corresponding decomposition factors. These explicit methods are used in inner-outer iterative procedures in conjuction with Picard and Newton methods leading to improved composite iterative schemes for solving non-linear elliptic boundary-value problems. Applications of the new techniques on non-linear elliptic PDE's are discussed and numerical results are given. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £78 +P&P)
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