A novel direct resolution method for coupled systems in finite element analysis. Issue 5 (30th November 2020)

• Record Type: Journal Article
• Authors: Boutora, Youcef; Takorabet, Noureddine
• Is Part Of: Compel. Volume 39:Issue 5(2020)
• Page Start: 1271
• Page End: 1280
• Publication Date: 2020-11-30
• Subjects: Numerical analysis -- Permanent magnet machine -- Finite element analysis -- Numerical linear algebra -- Finite elements method -- Direct solvers -- Sparse matrices -- Coupled problems; Electrical engineering -- Data Processing -- Periodicals; Electrical engineering -- Mathematics -- Periodicals; Electrical engineering -- Periodicals; Electronics -- Data Processing -- Periodicals; Electronics -- Mathematics -- Periodicals; 621.3
• DOI: 10.1108/COMPEL-01-2020-0032
• Languages: English
• ISSNs: 0332-1649

Abstract

Abstract : Purpose: This paper aims to propose a novel direct method for indefinite algebraic linear systems. It is well adapted for sparse linear systems, such as those of two-dimensional (2-D) finite elements problems, especially for coupled systems. Design/methodology/approach: The proposed method is developed on an example of an indefinite symmetric matrix. The algorithm of the method is given next, and a comparison between the numbers of operations required by the method and the Cholesky method is also given. Finally, an application on a magnetostatic problem for classical methods (Gauss and Cholesky) shows the relative efficiency of the proposed method. Findings: The proposed method can be used advantageously for 2-D finite elements in stepping methods without using a block decomposition of matrices. Research limitations/implications: This method is advantageous for direct linear solving for 2-D problems, but it is not recommended at this time for three-dimensional problems. Originality/value: The proposed method is the first direct solver for algebraic linear systems proposed since more than a half century. It is not limited for symmetric positive systems such as many of direct and iterative methods.