KIOPS swMATH ID: 30345 Software Authors: Gaudreault, Stéphane; Rainwater, Greg; Tokman, Mayya Description: 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}. Homepage: https://www.sciencedirect.com/science/article/pii/S0021999118304042 Keywords: adaptive Krylov subspace methods; incomplete orthogonalization; time integration; exponential integrators; (varphi)-functions; matrix exponential Related Software: phipm; Algorithm 919; Expokit; mftoolbox; Expint; GitHub; chammp; RODAS; Matlab; imexLNL; ImplicitLNLMethods; HE-E1GODF; AUSM; FELTOR; Vador; Chebfun; FFTW; EXPODE; MATLAB ODE suite; ode23s Cited in: 17 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year KIOPS: a fast adaptive Krylov subspace solver for exponential integrators. Zbl 1418.65074Gaudreault, Stéphane; Rainwater, Greg; Tokman, Mayya 2018 all top 5 Cited by 35 Authors 3 Buvoli, Tommaso 3 Gaudreault, Stéphane 3 Ju, Lili 3 Tokman, Mayya 2 Gottlieb, Sigal 2 Grant, Zachary J. 2 Isherwood, Leah 2 Rainwater, Greg 1 Bochev, M. A. 1 Bui-Thanh, Tan 1 Caliari, Marco 1 Cassini, Fabio 1 Charron, Martin 1 Dallerit, Valentin 1 de la Cruz, H. 1 De Maio, P. A. 1 Du, Qiang 1 Duddu, Ravindra 1 Einkemmer, Lukas 1 Gao, Huadong 1 Hoang, Thi-Thao-Phuong 1 Jimenez, Juan Carlos 1 Kang, Shinhoo 1 Knizhnerman, Leonid 1 Li, Hongwei 1 Li, Xiao 1 Meng, Xucheng 1 Minion, Michael L. 1 Naranjo-Noda, F. S. 1 Ostermann, Alexander 1 Qiao, Zhonghua 1 Sun, Haiwei 1 Tyrtyshnikov, Evgeniĭ Evgen’evich 1 Wang, Zhu 1 Zivcovich, Franco all top 5 Cited in 8 Serials 5 Journal of Computational Physics 3 Journal of Computational and Applied Mathematics 3 SIAM Journal on Scientific Computing 2 Journal of Scientific Computing 1 Computer Methods in Applied Mechanics and Engineering 1 SIAM Journal on Numerical Analysis 1 SIAM Review 1 Communications in Computational Physics all top 5 Cited in 7 Fields 17 Numerical analysis (65-XX) 3 Partial differential equations (35-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Fluid mechanics (76-XX) 1 Ordinary differential equations (34-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) Citations by Year