KIOPS

KIOPS: a fast adaptive Krylov subspace solver for exponential integrators. This paper presents a new algorithm KIOPS for computing linear combinations of (varphi)-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no information about the spectrum or norm of the Jacobian matrix is known a priori. We first show that such problems can be solved efficiently by computing a single exponential of a modified matrix. Then our approach is to compute an appropriate basis for the Krylov subspace using the incomplete orthogonalization procedure and project the matrix exponential on this subspace. We also present a novel adaptive procedure that significantly reduces the computational complexity of exponential integrators. Our numerical experiments demonstrate that KIOPS outperforms the current state-of-the-art adaptive Krylov algorithm exttt{phipm}.


References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Buvoli, Tommaso; Minion, Michael L.: On the stability of exponential integrators for non-diffusive equations (2022)
  2. Caliari, Marco; Cassini, Fabio; Einkemmer, Lukas; Ostermann, Alexander; Zivcovich, Franco: A (\mu)-mode integrator for solving evolution equations in Kronecker form (2022)
  3. Gaudreault, Stéphane; Charron, Martin; Dallerit, Valentin; Tokman, Mayya: High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid (2022)
  4. Botchev, Mike A.; Knizhnerman, Leonid; Tyrtyshnikov, Eugene E.: Residual and restarting in Krylov subspace evaluation of the (\varphi) function (2021)
  5. Buvoli, Tommaso: Exponential polynomial block methods (2021)
  6. Chen, Hao; Sun, Hai-Wei: A dimensional splitting exponential time differencing scheme for multidimensional fractional Allen-Cahn equations (2021)
  7. Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua: Maximum bound principles for a class of semilinear parabolic equations and exponential time-differencing schemes (2021)
  8. Gaudreault, Stéphane; Rainwater, Greg; Tokman, Mayya: Corrigendum to: “KIOPS: a fast adaptive Krylov subspace solver for exponential integrators” (2021)
  9. Kang, Shinhoo; Bui-Thanh, Tan: A scalable exponential-DG approach for nonlinear conservation laws: with application to Burger and Euler equations (2021)
  10. Meng, Xucheng; Hoang, Thi-Thao-phuong; Wang, Zhu; Ju, Lili: Localized exponential time differencing method for shallow water equations: algorithms and numerical study (2021)
  11. Naranjo-Noda, F. S.; Jimenez, J. C.: Locally linearized Runge-Kutta method of Dormand and Prince for large systems of initial value problems (2021)
  12. Buvoli, Tommaso: A class of exponential integrators based on spectral deferred correction (2020)
  13. Gao, Huadong; Ju, Lili; Duddu, Ravindra; Li, Hongwei: An efficient second-order linear scheme for the phase field model of corrosive dissolution (2020)
  14. Jimenez, J. C.; de la Cruz, H.; De Maio, P. A.: Efficient computation of phi-functions in exponential integrators (2020)
  15. Isherwood, Leah; Grant, Zachary J.; Gottlieb, Sigal: Strong stability preserving integrating factor two-step Runge-Kutta methods (2019)
  16. Gaudreault, Stéphane; Rainwater, Greg; Tokman, Mayya: KIOPS: a fast adaptive Krylov subspace solver for exponential integrators (2018)
  17. Isherwood, Leah; Grant, Zachary J.; Gottlieb, Sigal: Strong stability preserving integrating factor Runge-Kutta methods (2018)