GPU-Based N-1 Static Security Analysis Algorithm With Preconditioned Conjugate Gradient Method
IEEE Access, 2020 N-1 static security analysis (SSA) is an important method for power system stability analysis that requires solving N alternating-current power flows (ACPF) for a system with N elements to obtain strictly accurate results.
Meng Fu +5 more
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Mathematics, 2021 The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite ...
Jaroslav Haslinger +3 more
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On numerical solution of nonlinear parabolic multicomponent diffusion-reaction problems
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 This work continues our previous analysis concerning the numerical solution of the multi-component mass transfer equations. The present test problems are two-dimensional, parabolic, non-linear, diffusion- reaction equations. An implicit finite difference
Juncu Gh., Popa C., Sarbu Gh.
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Recursive-Based PCG Methods for Toeplitz Systems with Nonnegative Generating Functions [PDF]
, 2003 In this paper, we consider the solutions of symmetric positive definite, but ill-conditioned, Toeplitz systems An x = b. Here we propose to solve the system by the recursive-based preconditioned conjugate gradient method.
Jin, XQ, Ng, KP, Sun, HW
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Preconditioning the modified conjugate gradient method
Global Journal of Mathematical Sciences, 2010 In this paper, the convergence analysis of the conventional conjugate Gradient method was reviewed. And the convergence analysis of the modified conjugate Gradient method was analysed with our extension on preconditioning the algorithm. Convergence of the algorithm is a function of the condition number of M-1A.
Omorogbe, D.E.A, Osagiede, A.A
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Condition number estimation of preconditioned matrices. [PDF]
PLoS ONE, 2015 The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results.
Noriyuki Kushida
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Research of the Algebraic Multigrid Method for Electron Optical Simulator
Entropy, 2022 At present, electron optical simulator (EOS) takes a long time to solve linear FEM systems. The algebraic multigrid preconditioned conjugate gradient (AMGPCG) method can improve the efficiency of solving systems.
Zhi Wang +7 more
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Preconditioned Bi-Conjugate Gradient Method for Radiative Transfer in Spherical Media
, 2009 A robust numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG)method is proposed for the solution of radiative transfer equation in spherical geometry.A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient ...
Asensio Ramos +24 more
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Analysis of Iterative Methods for the Steady and Unsteady Stokes Problem: Application to Spectral Element Discretizations [PDF]
, 1993 A new and detailed analysis of the basic Uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady Stokes operator is presented.
Maday, Yvon +3 more
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A new approximate inverse preconditioner based on the Vaidya’s maximum spanning tree for matrix equation AXB = C [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2019 We propose a new preconditioned global conjugate gradient (PGL-CG) method for the solution of matrix equation AXB = C, where A and B are sparse Stieltjes matrices. The preconditioner is based on the support graph preconditioners.
K. Rezaei, F. Rahbarnia, F. Toutounian
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