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Journal Articles Journal of Computational and Applied Mathematics Year : 2021

Acceleration of implicit schemes for large linear systems of differential–algebraic equations

Mouhamad Al Sayed Ali
  • Function : Author

Abstract

Implicit schemes for solving large-scale linear di erential-algebraic systems with constant coef- cients necessitate at each integration step the solution of a linear system, typically obtained by a Krylov subspace method such as GMRES. To accelerate the convergence, an approach is proposed that computes good initial guesses for each linear system to be solved in the implicit scheme. This approach requires, at each integration step, a small dimensional subspace where a good initial guess is found using the Petrov-Galerkin process. It is shown that the residual asso- ciated with the computed initial guess depends on the dimension of the subspace, the order of the implicit scheme, and the discretization stepsize. Several numerical illustrations are reported.

Dates and versions

hal-04306757 , version 1 (25-11-2023)

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Cite

Mouhamad Al Sayed Ali, Miloud Sadkane. Acceleration of implicit schemes for large linear systems of differential–algebraic equations. Journal of Computational and Applied Mathematics, 2021, 389, pp.113364. ⟨10.1016/j.cam.2020.113364⟩. ⟨hal-04306757⟩
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