An Efficient Approach for Solving Mesh Optimization Problems Using Newton's Method. (21st October 2014)

• Record Type: Journal Article
• Authors: Kim, Jibum
• Other Names: Ma Tiedong Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2014(2014)
• Publication Date: 2014-10-21
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2014/273732
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We present an efficient approach for solving various mesh optimization problems. Our approach is based on Newton's method, which uses both first-order (gradient) and second-order (Hessian) derivatives of the nonlinear objective function. The volume and surface mesh optimization algorithms are developed such that mesh validity and surface constraints are satisfied. We also propose several Hessian modification methods when the Hessian matrix is not positive definite. We demonstrate our approach by comparing our method with nonlinear conjugate gradient and steepest descent methods in terms of both efficiency and mesh quality.