A high performance level-block approximate LU factorization preconditioner algorithm

Bollhöfer, Matthias; Schenk, Olaf; Verbosio, Fabio

doi:10.1016/j.apnum.2020.12.023

Cited by 5 publications

(1 citation statement)

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“…195 are evaluated using just one inverse, the inverse of K. These relations can also be used to decrease the computational cost for polynomial excitation. The inverse of K is particularly interesting in the Finite Element Analysis (FMA) context, since the stiffness matrix is sparse, enabling the use of fast, efficient and tailored algorithms for this kind of matrices [48,49]. Therefore, the inverse of more complicate matrices, like F 2,1,1 and C − F 2,1,1 , can be computed by using an inverse that is cheaper to evaluate.…”

Section: Matrix Complexity For Polynomial Particularized Heavisidementioning

confidence: 99%

A systematic approach to obtain the analytical solution for coupled linear second-order ordinary differential equations: Part II

Janczkowski Fogaça,

Lenz Cardoso

2024

J Braz. Soc. Mech. Sci. Eng.

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Coupled systems of second order ODEs are found in many areas, such as vibrations and electric circuits. Thus, accurate and efficient solutions are of great interest. This manuscript extends the concept of generalized integrating factor, recently introduced by the authors for one dimensional problems, to coupled n-dimensional systems of second order ODEs. The general formulation for time-varying coefficients is found and particularized to the constant coefficients. Closed-form integrating factors are obtained for the constant coefficient case under mild assumptions about the damping coefficient matrix. Analytical solutions for different types of continuous and discontinuous excitations are presented for problems with constant coefficients and proportional damping, disregarding the damping level. Examples are provided for each type of excitation studied in this manuscript. Results obtained with the proposed approach are compared to traditional numerical methods. Results show that the proposed procedure is accurate, not suffering with interpolation errors found in traditional numerical methods.

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Section: Matrix Complexity For Polynomial Particularized Heavisidementioning

confidence: 99%