Study on improvement of computation performance of the conjugate projected gradient method using dual Lagrange multiplier method

Abstract

The conjugate projected gradient (CPG) method is an iterative solver for a linear problem with linear multipoint constraints. In the present study, a formulation of the projection procedure is rewritten for the dual Lagrange method, which is used in a mortar finite element method. A block matrix with respect to a slave surface of the constraint matrix, C^T , becomes a diagonal matrix due to the biorthogonal shape functions, which is used in the dual Lagrange multiplier method. By utilizing this property, the projection may be conducted without solving a linear problem for a coefficient matrix, C^TC .