On accurate and time efficient solution of primal-mixed finite element equations in multiscale solid mechanics

• Published in: International journal for numerical methods in biomedical engineering Vol. 27; no. 1; pp. 95 - 112
• Main Authors: Duff, Iain, Mijuca, Dubravka
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.01.2011; Wiley
• Subjects: Accuracy; Computing time; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); geometrically multiscale; indefinite; Mathematical analysis; Mathematical models; Physics; primal-mixed finite element; reliable; Routines; Solid mechanics; Solvers; sparse; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Thermoelasticity; time efficient; Solid mechanics; time efficient; geometrically multiscale; Thermomechanical properties; Large displacement; Factorization; Modeling; Mixed method; indefinite; Finite element method; reliable; Multiscale method; sparse; Sparse matrix; Thermoelasticity; primal-mixed finite element
• ISSN: 2040-7939; 2040-7947; 2040-7947
• DOI: 10.1002/cnm.1296

In order to identify the best technique to solve a class of geometrically multiscale model problems in thermoelasticity, we examine a combination of a primal‐mixed finite element approach and direct sparse solvers and matrix scaling routines. The criteria for optimality are robustness, accuracy and execution time. It will be shown that the present finite element approach, where displacement and stress variables are simultaneously solved from large‐scale indefinite poorly scaled systems of equations using the sparse HSL solver MA57 with the aid of the matrix scaling routines MC64 or MC30 during the factorization process, enables a reliable solution even if hexahedral finite elements in a mesh differ in size up to six orders of magnitude. A number of tests in multiscale elasticity and thermoelasticity are examined to test the accuracy and execution time efficiency of the proposed solution approach on a standard PC computing platform. Copyright © 2009 John Wiley & Sons, Ltd.