Papers by Keyword: GMRES

Abstract: With the growing of the system size, rapid, accurate method used for calculating power flow is an important task for the real-time analysis of power system. This paper puts forward a new fast method used for calculating power flow based on ODE(ordinary differential equation).The power flow problems are transformed into solving the differential equations, which avoids calculating Jacobian matrix, and doesn’t need any preprocessing. In order to accelerate the computing speed, the diagonal elements of Jacobian matrix is approximately calculated using the node voltage amplitude and the node admittance matrix. Numerical examples show that the method is simple. Compared with Newton's method, GMRES, MA ,this method has a distinct advantage in computing speed.

Abstract: During the modern product design, CAD softwares are widely used for geometric modeling and finite element method is used for structural performance analysis. Plenty of designers’ working time is spending in the pre-processing work of finite element analysis. Boundary Element Method(BEM) has been studied in recent years to analyze 3D elastostatics instead of Finite Element Method(FEM) because of the decrease of unknowns and easier mesh generation process. But the calculation amount of BEM is large, especially for the coefficient integrals and system equations solution. In this paper, we present a Boundary Element parallel computation technique for 3D elastostatics using Computing Unified Device Architecture (CUDA) that runs on GPU. Furthermore, we propose GMRES-DC (GMRES with Dual Compensation) algorithm based on the classic GMRES algorithm to gain a higher solving efficiency. The examples show that the GPU parallel implementation in this paper can accelerate BEM computation greatly, and the GMRES-DC algorithm can solve the BEM system equations efficiently.

Abstract: The fast multipole boundary element method (FM-BEM) has been successfully applied to 2D and 3D large scale elastostatic problems and efficiently reduce the computing operations and memory requirements. In this paper, the FM-BEM based on Taylor series expansions is applied to 2D Potential Problems, the FM-BEM for 2D Potential Problems is presented and relative mathematical foundation is developed.