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High-Order Implicit Low-Rank Method with Spectral Deferred Correction for Matrix Differential Equations
Shun Li, Yan Jiang, Yingda Cheng
In this paper, we develop a low-rank method with high-order temporal accuracy using spectral deferred correction (SDC) to compute linear matrix differential equations. In [1], a lo…
Preconditioning Low Rank Generalized Minimal Residual Method (GMRES) for Implicit Discretizations of Matrix Differential Equations
Shixu Meng, Daniel Appelo, Yingda Cheng
This work proposes a new class of preconditioners for the low rank Generalized Minimal Residual Method (GMRES) for multiterm matrix equations arising from implicit timestepping of…
Kraus is King: High-order Completely Positive and Trace Preserving (CPTP) Low Rank Method for the Lindblad Master Equation
Daniel Appelo, Yingda Cheng
We design high order accurate methods that exploit low rank structure in the density matrix while respecting the essential structure of the Lindblad equation. Our methods preserves…
Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations
Daniel Appelö, Yingda Cheng
In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to cap…