Fast solution for large scale linear algebraic equations in finite element analysis

The computational efficiency of numerical solution of linear algebraic equations in finite elements can be improved in two ways. One is to decrease the fill-in numbers, which are new non-zero numbers in the matrix of global stiffness generated during the process of elimination. The other is to reduce the computational operation of multiplying a real number by zero. Based on the fact that the order of elimination can determine how many fill-in numbers should be generated, we present a new method for optimization of numbering nodes. This method is quite different from bandwidth optimization. Fill-in numbers can be decreased in a large scale by the use of this method. The bi-factorization method is adopted to avoid multiplying real numbers by zero. For large scale finite element analysis, the method presented in this paper is more efficient than the traditional LDLT method.